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IRIDIA BibTeX Repository

[1]
Emile H. L. Aarts, Jan H. M. Korst, and Wil Michiels. Simulated Annealing. In Search Methodologies, pages 187–210. Springer, 2005.
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Hussein A. Abbass. The self-adaptive Pareto differential evolution algorithm. In Proceedings of the 2002 Congress on Evolutionary Computation (CEC'02), pages 831–836, Piscataway, NJ, 2002. IEEE Press.
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Hussein A. Abbass, Ruhul Sarker, and Charles Newton. PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In Proceedings of the 2001 Congress on Evolutionary Computation (CEC'01), pages 971–978, Piscataway, NJ, 2001. IEEE Press.
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Keywords: memory-based ACO
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A. Acan. An external partial permutations memory for ant colony optimization. In G. R. Raidl and J. Gottlieb, editors, Proceedings of EvoCOP 2005 – 5th European Conference on Evolutionary Computation in Combinatorial Optimization, volume 3448 of Lecture Notes in Computer Science, pages 1–11. Springer, Heidelberg, Germany, 2005.
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Keywords: memory-based ACO
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Tobias Achterberg. SCIP: Solving constraint integer programs. Mathematical Programming Computation, 1(1):1–41, July 2009.
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http://mpc.zib.de/archive/2009/1/Achterberg2009_Article_SCIPSolvingConstraintIntegerPr.pdf
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Héctor-Gabriel Acosta-Mesa, Fernando Rechy-Ramírez, Efrén Mezura-Montes, Nicandro Cruz-Ramírez, and Rodolfo Hernández Jiménez. Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions. Journal of Biomedical Informatics, 49:73–83, 2014.
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Keywords: irace
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Bernardetta Addis, Marco Locatelli, and Fabio Schoen. Disk Packing in a Square: A New Global Optimization Approach. INFORMS Journal on Computing, 20(4):516–524, 2008.
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Hernán E. Aguirre and Kiyoshi Tanaka. Working principles, behavior, and performance of MOEAs on MNK-landscapes. European Journal of Operational Research, 181(3):1670–1690, 2007.
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Hernán E. Aguirre and Kiyoshi Tanaka. Many-Objective Optimization by Space Partitioning and Adaptive ε-Ranking on MNK-Landscapes. In M. Ehrgott, C. M. Fonseca, X. Gandibleux, J.-K. Hao, and M. Sevaux, editors, Evolutionary Multi-criterion Optimization, EMO 2009, volume 5467 of Lecture Notes in Computer Science, pages 407–422. Springer, Heidelberg, Germany, 2009.
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Hernán E. Aguirre. Advances on Many-objective Evolutionary Optimization. In C. Blum and E. Alba, editors, GECCO (Companion), pages 641–666, New York, NY, 2013. ACM Press.
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Keywords: many-objective evolutionary optimization
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Sandip Aine, Rajeev Kumar, and P. P. Chakrabarti. Adaptive parameter control of evolutionary algorithms to improve quality-time trade-off. Applied Soft Computing, 9(2):527–540, 2009.
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Enrique Alba and Francisco Chicano. ACOhg: dealing with huge graphs. In D. Thierens et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2007, pages 10–17. ACM Press, New York, NY, 2007.
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Aldeida Aleti and Irene Moser. A systematic literature review of adaptive parameter control methods for evolutionary algorithms. ACM Computing Surveys, 49(3, Article 56):35, October 2016.
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Mohamad Alissa, Kevin Sim, and Emma Hart. Algorithm Selection Using Deep Learning without Feature Extraction. In M. López-Ibáñez, A. Auger, and T. Stützle, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2019, pages 198–206, New York, NY, 2019. ACM Press.
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Ali Allahverdi and Harun Aydilek. Algorithms for no-wait flowshops with total completion time subject to makespan. International Journal of Advanced Manufacturing Technology, pages 1–15, 2013.
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Richard Allmendinger and Joshua D. Knowles. Evolutionary Search in Lethal Environments. In International Conference on Evolutionary Computation Theory and Applications (ECTA), pages 63–72. SciTePress, 2011.
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Richard Allmendinger. Tuning evolutionary search for closed-loop optimization. PhD thesis, The University of Manchester, UK, 2012.
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Christian Almeder. A hybrid optimization approach for multi-level capacitated lot-sizing problems. European Journal of Operational Research, 200(2):599–606, 2010.
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Solving multi-level capacitated lot-sizing problems is still a challenging task, in spite of increasing computational power and faster algorithms. In this paper a new approach combining an ant-based algorithm with an exact solver for (mixed-integer) linear programs is presented. A MAX-MIN ant system is developed to determine the principal production decisions, a LP/MIP solver is used to calculate the corresponding production quantities and inventory levels. Two different local search methods and an improvement strategy based on reduced mixed-integer problems are developed and integrated into the ant algorithm. This hybrid approach provides superior results for small and medium-sized problems in comparison to the existing approaches in the literature. For large-scale problems the performance of this method is among the best

Keywords: Ant colony optimization, Manufacturing, Material requirements planning, Mixed-integer programming
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A. Alsheddy and E. Tsang. Guided Pareto local search and its application to the 0/1 multi-objective knapsack problems. In M. Caserta and S. Voß, editors, Proceedings of MIC 2009, the 8th Metaheuristics International Conference, Hamburg, Germany, 2010. University of Hamburg.
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S. Alupoaei and S. Katkoori. Ant Colony System Application to Marcocell Overlap Removal. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 12(10):1118–1122, 2004.
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Sanae Amani, Mahnoosh Alizadeh, and Christos Thrampoulidis. Linear Stochastic Bandits Under Safety Constraints. In H. M. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. B. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems (NIPS 32), pages 9256–9266, 2019.
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C. Amir, A. Badr, and I Farag. A Fuzzy Logic Controller for Ant Algorithms. Computing and Information Systems, 11(2):26–34, 2007.
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Christophe Andrieu, Nando de Freitas, Arnaud Doucet, and Michael I. Jordan. An Introduction to MCMC for Machine Learning. Machine Learning, 50(1-2):5–43, 2003.
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Klaus Andersen, René Victor Valqui Vidal, and Villy Bæk Iversen. Design of a Teleprocessing Communication Network Using Simulated Annealing. In R. V. V. Vidal, editor, Applied Simulated Annealing, pages 201–215. Springer, 1993.
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Eric Angel, Evripidis Bampis, and Laurent Gourvés. Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem. Theoretical Computer Science, 310(1-3):135–146, 2004.
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Keywords: Archiving, Local search, Multicriteria TSP, Approximation algorithms
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D. Anghinolfi, A. Boccalatte, M. Paolucci, and C. Vecchiola. Performance Evaluation of an Adaptive Ant Colony Optimization Applied to Single Machine Scheduling. In X. Li et al., editors, Simulated Evolution and Learning, 7th International Conference, SEAL 2008, volume 5361 of Lecture Notes in Computer Science, pages 411–420. Springer, Heidelberg, Germany, 2008.
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Daniel Angus and Clinton Woodward. Multiple Objective Ant Colony Optimisation. Swarm Intelligence, 3(1):69–85, 2009.
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Daniel Angus. Population-Based Ant Colony Optimisation for Multi-objective Function Optimisation. In M. Randall, H. A. Abbass, and J. Wiles, editors, Progress in Artificial Life (ACAL), volume 4828 of Lecture Notes in Computer Science, pages 232–244. Springer, Heidelberg, Germany, 2007.
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J. Ansel, S. Kamil, K. Veeramachaneni, J. Ragan-Kelley, J. Bosboom, U. M. O'Reilly, and S. Amarasinghe. OpenTuner: An extensible framework for program autotuning. In Proceedings of the 23rd International Conference on Parallel Architectures and Compilation, pages 303–315. ACM New York, NY, USA, 2014.
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Carlos Ansótegui, Yuri Malitsky, Horst Samulowitz, Meinolf Sellmann, and Kevin Tierney. Model-Based Genetic Algorithms for Algorithm Configuration. In Q. Yang and M. Wooldridge, editors, Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI-15), pages 733–739. IJCAI/AAAI Press, Menlo Park, CA, 2015.
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Keywords: GGA++
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Keywords: GGA
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David Applegate, Robert E. Bixby, Vasek Chvátal, and William J. Cook. Finding Tours in the TSP. Technical Report 99885, Forschungsinstitut für Diskrete Mathematik, University of Bonn, Germany, 1999.
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David Applegate, Robert E. Bixby, Vasek Chvátal, and William J. Cook. The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton, NJ, 2006.
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Florian Arnold, Ítalo Santana, Kenneth Sörensen, and Thibaut Vidal. PILS: Exploring high-order neighborhoods bypattern mining and injection. Arxiv preprint arXiv:1912.11462, 2019.
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The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.

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Keywords: IPOP-CMA-ES
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Hossein Baharmand, Tina Comes, and Matthieu Lauras. Bi-objective multi-layer location–allocation model for the immediate aftermath of sudden-onset disasters. Transportation Research Part E: Logistics and Transportation Review, 127:86–110, 2019.
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Locating distribution centers is critical for humanitarians in the immediate aftermath of a sudden-onset disaster. A major challenge lies in balancing the complexity and uncertainty of the problem with time and resource constraints. To address this problem, we propose a location-allocation model that divides the topography of affected areas into multiple layers; considers constrained number and capacity of facilities and fleets; and allows decision-makers to explore trade-offs between response time and logistics costs. To illustrate our theoretical work, we apply the model to a real dataset from the 2015 Nepal earthquake response. For this case, our method results in a considerable reduction of logistics costs.

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Consider the following restricted (symmetric or asymmetric) traveling-salesman problem (TSP): given an initial ordering of the n cities and an integer k > 0, find a minimum-cost feasible tour, where a feasible tour is one in which city i precedes city j whenever j >= i + k in the initial ordering. Balas (1996) has proposed a dynamic-programming algorithm that solves this problem in time linear in n, though exponential in k. Some important real-world problems are amenable to this model or some of its close relatives. The algorithm of Balas (1996) constructs a layered network with a layer of nodes for each position in the tour, such that source-sink paths in this network are in one-to-one correspondence with tours that satisfy the postulated precedence constraints. In this paper we discuss an implementation of the dynamic-programming algorithm for the general case when the integer k is replaced with city-specific integers k(j), j = 1, . . ., n. We discuss applications to, and computational experience with, TSPs with time windows, a model frequently used in vehicle routing as well as in scheduling with setup, release and delivery times. We also introduce a new model, the TSP with target times, applicable to Just-in-Time scheduling problems. Finally for TSPs that have no precedence restrictions, we use the algorithm as a heuristic that finds in linear time a local optimum over an exponential-size neighborhood. For this case, we implement an iterated version of our procedure, based on contracting some arcs of the tour produced by a first application of the algorithm, then reapplying the algorithm to the shrunken graph with the same k.

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Agent-based models (ABM) are examples of complex adaptive systems, which can be characterized as those systems for which no model less complex than the system itself can accurately predict in detail how the system will behave at future times. Consequently, the standard tools of policy analysis, based as they are on devising policies that perform well on some best estimate model of the system, cannot be reliably used for ABM. This paper argues that policy analysis by using ABM requires an alternative approach to decision theory. The general characteristics of such an approach are described, and examples are provided of its application to policy analysis.ABM, agent-based model

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Peer reviews are a unique governance tool that use expertise from one city or country to assess and strengthen the capabilities of another. Peer review tools are gaining momentum in disaster management and remain an important but understudied topic in risk governance. Methodologies to conduct a peer review are still in their infancy. To enhance these, a systematic literature review (SLR) of academic and non-academic literature was conducted on city resilience peer reviews. Thirty-three attributes of resilience are identified, which provides useful insights into how research and practice can inform risk governance, and utilise peer reviews, to drive meaningful change. Moreover, it situates the challenges associated with resilience building tools within risk governance to support the development of interdisciplinary perspectives for integrated city resilience frameworks. Results of this research have been used to develop a peer review methodology and an international standard on conducting peer reviews for disaster risk reduction.

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The goal of multi-objective optimization is to find a set of best compromise solutions for typically conflicting objectives. Due to the complex nature of most real-life problems, only an approximation to such an optimal set can be obtained within reasonable (computing) time. To compare such approximations, and thereby the performance of multi-objective optimizers providing them, unary quality measures are usually applied. Among these, the hypervolume indicator (or S-metric) is of particular relevance due to its favorable properties. Moreover, this indicator has been successfully integrated into stochastic optimizers, such as evolutionary algorithms, where it serves as a guidance criterion for finding good approximations to the Pareto front. Recent results show that computing the hypervolume indicator can be seen as solving a specialized version of Klee's Measure Problem. In general, Klee's Measure Problem can be solved with O(n logn + nd/2logn) comparisons for an input instance of size n in d dimensions; as of this writing, it is unknown whether a lower bound higher than Ω(n logn) can be proven. In this article, we derive a lower bound of Ω(nlogn) for the complexity of computing the hypervolume indicator in any number of dimensions d>1 by reducing the so-called UniformGap problem to it. For the three dimensional case, we also present a matching upper bound of O(nlogn) comparisons that is obtained by extending an algorithm for finding the maxima of a point set.

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Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatic Component-Wise Design of Multi-Objective Evolutionary Algorithms. http://iridia.ulb.ac.be/supp/IridiaSupp2014-010/, 2015.
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[186]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. To DE or Not to DE? Multi-objective Differential Evolution Revisited from a Component-Wise Perspective: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2015-001/, 2015.
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[187]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. To DE or Not to DE? Multi-objective Differential Evolution Revisited from a Component-Wise Perspective. In A. Gaspar-Cunha, C. H. Antunes, and C. A. Coello Coello, editors, Evolutionary Multi-criterion Optimization, EMO 2015 Part I, volume 9018 of Lecture Notes in Computer Science, pages 48–63. Springer, Heidelberg, Germany, 2015.
bib | DOI ]
[188]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Comparing Decomposition-Based and Automatically Component-Wise Designed Multi-Objective Evolutionary Algorithms. In A. Gaspar-Cunha, C. H. Antunes, and C. A. Coello Coello, editors, Evolutionary Multi-criterion Optimization, EMO 2015 Part I, volume 9018 of Lecture Notes in Computer Science, pages 396–410. Springer, Heidelberg, Germany, 2015.
bib | DOI ]
[189]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatic Component-Wise Design of Multi-Objective Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation, 20(3):403–417, 2016.
bib | DOI | pdf | supplementary material ]
[190]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatically designing and understanding evolutionary algorithms for multi- and many-objective optimization, 2016. To be submitted.
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[191]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. A Large-Scale Experimental Evaluation of High-Performing Multi- and Many-Objective Evolutionary Algorithms. http://iridia.ulb.ac.be/supp/IridiaSupp2015-007/, 2017.
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[192]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. A Large-Scale Experimental Evaluation of High-Performing Multi- and Many-Objective Evolutionary Algorithms. Technical Report TR/IRIDIA/2017-005, IRIDIA, Université Libre de Bruxelles, Belgium, February 2017.
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[193]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. A Large-Scale Experimental Evaluation of High-Performing Multi- and Many-Objective Evolutionary Algorithms. Evolutionary Computation, 26(4):621–656, 2018.
bib | DOI | pdf | supplementary material ]
Research on multi-objective evolutionary algorithms (MOEAs) has produced over the past decades a large number of algorithms and a rich literature on performance assessment tools to evaluate and compare them. Yet, newly proposed MOEAs are typically compared against very few, often a decade older MOEAs. One reason for this apparent contradiction is the lack of a common baseline for comparison, with each subsequent study often devising its own experimental scenario, slightly different from other studies. As a result, the state of the art in MOEAs is a disputed topic. This article reports a systematic, comprehensive evaluation of a large number of MOEAs that covers a wide range of experimental scenarios. A novelty of this study is the separation between the higher-level algorithmic components related to multi-objective optimization (MO), which characterize each particular MOEA, and the underlying parameters-such as evolutionary operators, population size, etc.-whose configuration may be tuned for each scenario. Instead of relying on a common or "default" parameter configuration that may be low-performing for particular MOEAs or scenarios and unintentionally biased, we tune the parameters of each MOEA for each scenario using automatic algorithm configuration methods. Our results confirm some of the assumed knowledge in the field, while at the same time they provide new insights on the relative performance of MOEAs for many-objective problems. For example, under certain conditions, indicator-based MOEAs are more competitive for such problems than previously assumed. We also analyze problem-specific features affecting performance, the agreement between performance metrics, and the improvement of tuned configurations over the default configurations used in the literature. Finally, the data produced is made publicly available to motivate further analysis and a baseline for future comparisons.

[194]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. An Empirical Assessment of the Properties of Inverted Generational Distance Indicators on Multi- and Many-objective Optimization. In H. Trautmann, G. Rudolph, K. Klamroth, O. Schütze, M. M. Wiecek, Y. Jin, and C. Grimme, editors, Evolutionary Multi-criterion Optimization, EMO 2017, Lecture Notes in Computer Science, pages 31–45. Springer International Publishing, Cham, Switzerland, 2017.
bib | DOI ]
[195]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. An empirical assessment of the properties of inverted generational distance indicators on multi- and many-objective optimization: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2016-006/, 2016.
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[196]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatically Designing State-of-the-Art Multi- and Many-Objective Evolutionary Algorithms. Evolutionary Computation, 28(2):195–226, 2020.
bib | DOI | pdf | supplementary material ]
[197]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatically Designing State-of-the-Art Multi- and Many-Objective Evolutionary Algorithms: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2016-004/, 2019.
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[198]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Archiver Effects on the Performance of State-of-the-art Multi- and Many-objective Evolutionary Algorithms: Supplementary material. In M. López-Ibáñez, A. Auger, and T. Stützle, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2019. ACM Press, New York, NY, 2019.
bib | DOI | pdf | supplementary material ]
[199]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Archiver Effects on the Performance of State-of-the-art Multi- and Many-objective Evolutionary Algorithms: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2019-004/, 2019.
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[200]
Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatic Configuration of Multi-objective Optimizers and Multi-objective Configuration. In T. Bartz-Beielstein, B. Filipič, P. Korošec, and E.-G. Talbi, editors, High-Performance Simulation-Based Optimization, pages 69–92. Springer International Publishing, Cham, Switzerland, 2020.
bib | DOI ]
Heuristic optimizers are an important tool in academia and industry, and their performance-optimizing configuration requires a significant amount of expertise. As the proper configuration of algorithms is a crucial aspect in the engineering of heuristic algorithms, a significant research effort has been dedicated over the last years towards moving this step to the computer and, thus, make it automatic. These research efforts go way beyond tuning only numerical parameters of already fully defined algorithms, but exploit automatic configuration as a means for automatic algorithm design. In this chapter, we review two main aspects where the research on automatic configuration and multi-objective optimization intersect. The first is the automatic configuration of multi-objective optimizers, where we discuss means and specific approaches. In addition, we detail a case study that shows how these approaches can be used to design new, high-performing multi-objective evolutionary algorithms. The second aspect is the research on multi-objective configuration, that is, the possibility of using multiple performance metrics for the evaluation of algorithm configurations. We highlight some few examples in this direction.

[201]
Leonardo C. T. Bezerra. A component-wise approach to multi-objective evolutionary algorithms: from flexible frameworks to automatic design. PhD thesis, IRIDIA, École polytechnique, Université Libre de Bruxelles, Belgium, 2016.
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[202]
Leonora Bianchi, Mauro Birattari, M. Manfrin, M. Mastrolilli, Luís Paquete, O. Rossi-Doria, and Tommaso Schiavinotto. Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands. Journal of Mathematical Modelling and Algorithms, 5(1):91–110, 2006.
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[203]
Leonora Bianchi, Marco Dorigo, L. M. Gambardella, and Walter J. Gutjahr. A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8(2):239–287, 2009.
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[204]
Leonora Bianchi, L. M. Gambardella, and Marco Dorigo. An Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem. In J. J. Merelo et al., editors, Parallel Problem Solving from Nature, PPSN VII, volume 2439 of Lecture Notes in Computer Science, pages 883–892. Springer, Heidelberg, Germany, 2002.
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[205]
Armin Biere. Yet another Local Search Solver and Lingeling and Friends Entering the SAT Competition 2014. In A. Belov, D. Diepold, M. Heule, and M. Järvisalo, editors, Proceedings of SAT Competition 2014: Solver and Benchmark Descriptions, volume B-2014-2 of Science Series of Publications B, pages 39–40. University of Helsinki, 2014.
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[206]
André Biedenkapp, Marius Lindauer, Katharina Eggensperger, Frank Hutter, Chris Fawcett, and Holger H. Hoos. Efficient Parameter Importance Analysis via Ablation with Surrogates. In S. P. Singh and S. Markovitch, editors, AAAI Conference on Artificial Intelligence. AAAI Press, February 2017.
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[207]
André Biedenkapp, Joshua Marben, Marius Lindauer, and Frank Hutter. Cave: Configuration assessment, visualization and evaluation. In R. Battiti, M. Brunato, I. Kotsireas, and P. M. Pardalos, editors, Learning and Intelligent Optimization, 12th International Conference, LION 12, volume 11353 of Lecture Notes in Computer Science, pages 115–130, Cham, Switzerland, 2018. Springer.
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[208]
George Bilchev and Ian C. Parmee. The Ant Colony Metaphor for Searching Continuous Design Spaces. In T. C. Fogarty, editor, Evolutionary Computing, AISB Workshop, volume 993 of Lecture Notes in Computer Science, pages 25–39. Springer, Heidelberg, Germany, Heidelberg, Germany, 1995.
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[209]
M. Binois, D. Ginsbourger, and O. Roustant. Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations. European Journal of Operational Research, 243(2):386–394, 2015.
bib | DOI ]
Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob'ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob'ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

Keywords: Attainment function, Expected Hypervolume Improvement, Kriging, Multi-objective optimization, Vorob'ev expectation
[210]
Mauro Birattari, Prasanna Balaprakash, and Marco Dorigo. The ACO/F-RACE algorithm for combinatorial optimization under uncertainty. In K. F. Doerner, M. Gendreau, P. Greistorfer, W. J. Gutjahr, R. F. Hartl, and M. Reimann, editors, Metaheuristics – Progress in Complex Systems Optimization, volume 39 of Operations Research/Computer Science Interfaces Series, pages 189–203. Springer, New York, NY, 2006.
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[211]
Mauro Birattari, Prasanna Balaprakash, Thomas Stützle, and Marco Dorigo. Estimation Based Local Search for Stochastic Combinatorial Optimization. INFORMS Journal on Computing, 20(4):644–658, 2008.
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[212]
Mauro Birattari, Marco Chiarandini, Marco Saerens, and Thomas Stützle. Learning Graphical Models for Algorithm Configuration. In T. Berthold, A. M. Gleixner, S. Heinz, and T. Koch, editors, Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimization Problems, Lecture Notes in Computer Science. Springer, Heidelberg, Germany, 2011.
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[213]
Mauro Birattari, Gianni A. Di Caro, and Marco Dorigo. Toward the formal foundation of Ant Programming. In M. Dorigo et al., editors, Ant Algorithms, Third International Workshop, ANTS 2002, volume 2463 of Lecture Notes in Computer Science, pages 188–201. Springer, Heidelberg, Germany, 2002.
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[214]
Steven Bird, Ewan Klein, and Edward Loper. Natural language processing with Python: analyzing text with the natural language toolkit. " O'Reilly Media, Inc.", 2009.
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[215]
Mauro Birattari, Paola Pellegrini, and Marco Dorigo. On the invariance of ant colony optimization. IEEE Transactions on Evolutionary Computation, 11(6):732–742, 2007.
bib | DOI | pdf ]
[216]
Mauro Birattari, Thomas Stützle, Luís Paquete, and Klaus Varrentrapp. A Racing Algorithm for Configuring Metaheuristics. In W. B. Langdon et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2002, pages 11–18. Morgan Kaufmann Publishers, San Francisco, CA, 2002.
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Keywords: F-race
[217]
Mauro Birattari, Zhi Yuan, Prasanna Balaprakash, and Thomas Stützle. F-Race and Iterated F-Race: An Overview. In T. Bartz-Beielstein, M. Chiarandini, L. Paquete, and M. Preuss, editors, Experimental Methods for the Analysis of Optimization Algorithms, pages 311–336. Springer, Berlin, Germany, 2010.
bib ]
Keywords: F-race, iterated F-race, irace, tuning
[218]
Mauro Birattari, Zhi Yuan, Prasanna Balaprakash, and Thomas Stützle. Parameter Adaptation in Ant Colony Optimization. In M. Caserta and S. Voß, editors, Proceedings of MIC 2009, the 8th Metaheuristics International Conference, Hamburg, Germany, 2010. University of Hamburg.
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[219]
Mauro Birattari, M. Zlochin, and Marco Dorigo. Towards a theory of practice in metaheuristics design: A machine learning perspective. Theoretical Informatics and Applications, 40(2):353–369, 2006.
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[220]
Mauro Birattari. Tuning Metaheuristics: A Machine Learning Perspective, volume 197 of Studies in Computational Intelligence. Springer, Berlin, Heidelberg, 2009.
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[221]
Mauro Birattari. The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective. PhD thesis, IRIDIA, École polytechnique, Université Libre de Bruxelles, Belgium, 2004.
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Supervised by Marco Dorigo
[222]
Francesco Biscani, Dario Izzo, and Chit Hong Yam. A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation. In Astrodynamics Tools and Techniques (ICATT 2010), 4th International Conference on, 2010.
bib | http ]
Keywords: PaGMO
[223]
Francesco Biscani, Dario Izzo, and Chit Hong Yam. A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation. Arxiv preprint arXiv:1004.3824, 2010.
bib | http ]
A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle high-dimensional global optimisation problems, and it has been successfully used to find solutions to real-life engineering problems among which the preliminary design of interplanetary spacecraft trajectories - both chemical (including multiple flybys and deep-space maneuvers) and low-thrust (limited, at the moment, to single phase trajectories), the inverse design of nano-structured radiators and the design of non-reactive controllers for planetary rovers. Featuring an arsenal of global and local optimisation algorithms (including genetic algorithms, differential evolution, simulated annealing, particle swarm optimisation, compass search, improved harmony search, and various interfaces to libraries for local optimisation such as SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs an object-oriented architecture providing a clean and easily-extensible optimisation framework. Adoption of multi-threaded programming ensures the efficient exploitation of modern multi-core architectures and allows for a straightforward implementation of the island model paradigm, in which multiple populations of candidate solutions asynchronously exchange information in order to speed-up and improve the optimisation process. In addition to the C++ interface, PaGMO's capabilities are exposed to the high-level language Python, so that it is possible to easily use PaGMO in an interactive session and take advantage of the numerous scientific Python libraries available.

Keywords: PaGMO
[224]
Bernd Bischl, Pascal Kerschke, Lars Kotthoff, Marius Thomas Lindauer, Yuri Malitsky, Alexandre Fréchette, Holger H. Hoos, Frank Hutter, Kevin Leyton-Brown, Kevin Tierney, and Joaquin Vanschoren. ASlib: A Benchmark Library for Algorithm Selection. Artificial Intelligence, 237:41–58, 2016.
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[225]
Bernd Bischl, Michel Lang, Lars Kotthoff, Julia Schiffner, Jakob Richter, Erich Studerus, Giuseppe Casalicchio, and Zachary M. Jones. mlr: Machine Learning in R. Journal of Machine Learning Research, 17(170):1–5, 2016.
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[226]
Bernd Bischl, Olaf Mersmann, Heike Trautmann, and Mike Preuss. Algorithm Selection Based on Exploratory Landscape Analysis and Cost-sensitive Learning. In T. Soule and J. H. Moore, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2012, pages 313–320. ACM Press, New York, NY, 2012.
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Keywords: continuous optimization, landscape analysis, algorithm selection
[227]
Christopher M. Bishop. Pattern recognition and machine learning. Springer, 2006.
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[228]
Erdem Biyik, Jonathan Margoliash, Shahrouz Ryan Alimo, and Dorsa Sadigh. Efficient and Safe Exploration in Deterministic Markov Decision Processes with Unknown Transition Models. In 2019 American Control Conference (ACC), pages 1792–1799. IEEE, 2019.
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[229]
Xavier Blasco, Juan M. Herrero, Javier Sanchis, and Manuel Martínez. A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20):3908–3924, 2008.
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[230]
Craig Blackmore, Oliver Ray, and Kerstin Eder. Automatically Tuning the GCC Compiler to Optimize the Performance of Applications Running on Embedded Systems. Arxiv preprint arXiv:1703.08228, 2017.
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[231]
María J. Blesa and Christian Blum. Ant Colony Optimization for the Maximum Edge-Disjoint Paths Problem. In G. R. Raidl et al., editors, Applications of Evolutionary Computing, Proceedings of EvoWorkshops 2004, volume 3005 of Lecture Notes in Computer Science, pages 160–169. Springer, Heidelberg, Germany, 2004.
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[232]
María J. Blesa and Christian Blum. Finding edge-disjoint paths in networks by means of artificial ant colonies. Journal of Mathematical Modelling and Algorithms, 6(3):361–391, 2007.
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[233]
Aymeric Blot, Holger H. Hoos, Laetitia Jourdan, Marie-Eléonore Kessaci-Marmion, and Heike Trautmann. MO-ParamILS: A Multi-objective Automatic Algorithm Configuration Framework. In P. Festa, M. Sellmann, and J. Vanschoren, editors, Learning and Intelligent Optimization, 10th International Conference, LION 10, volume 10079 of Lecture Notes in Computer Science, pages 32–47. Springer, Cham, Switzerland, 2016.
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[234]
Aymeric Blot, Laetitia Jourdan, and Marie-Eléonore Kessaci-Marmion. Automatic design of multi-objective local search algorithms: case study on a bi-objective permutation flowshop scheduling problem. In P. A. N. Bosman, editor, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, pages 227–234. ACM Press, New York, NY, 2017.
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[235]
Aymeric Blot, Manuel López-Ibáñez, Marie-Eléonore Kessaci-Marmion, and Laetitia Jourdan. New Initialisation Techniques for Multi-Objective Local Search: Application to the Bi-objective Permutation Flowshop. In A. Auger, C. M. Fonseca, N. Lourenço, P. Machado, L. Paquete, and D. Whitley, editors, Parallel Problem Solving from Nature - PPSN XV, volume 11101 of Lecture Notes in Computer Science, pages 323–334. Springer, Cham, 2018.
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[236]
Aymeric Blot, Alexis Pernet, Laetitia Jourdan, Marie-Eléonore Kessaci-Marmion, and Holger H. Hoos. Automatically Configuring Multi-objective Local Search Using Multi-objective Optimisation. In H. Trautmann, G. Rudolph, K. Klamroth, O. Schütze, M. M. Wiecek, Y. Jin, and C. Grimme, editors, Evolutionary Multi-criterion Optimization, EMO 2017, Lecture Notes in Computer Science, pages 61–76. Springer International Publishing, Cham, Switzerland, 2017.
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[237]
Christian Blum. Beam-ACO—Hybridizing Ant Colony Optimization with Beam Search: An Application to Open Shop Scheduling. Computers & Operations Research, 32(6):1565–1591, 2005.
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[238]
Christian Blum. Beam-ACO for simple assembly line balancing. INFORMS Journal on Computing, 20(4):618–627, 2008.
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[239]
Christian Blum, J. Bautista, and J. Pereira. Beam-ACO applied to assembly line balancing. In M. Dorigo et al., editors, Ant Colony Optimization and Swarm Intelligence, 5th International Workshop, ANTS 2006, volume 4150 of Lecture Notes in Computer Science, pages 96–107. Springer, Heidelberg, Germany, 2006.
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[240]
Christian Blum, María J. Blesa, and Manuel López-Ibáñez. Beam Search for the Longest Common Subsequence Problem. Technical Report LSI-08-29, Department LSI, Universitat Politècnica de Catalunya, 2008. Published in Computers & Operations Research [241].
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[241]
Christian Blum, María J. Blesa, and Manuel López-Ibáñez. Beam search for the longest common subsequence problem. Computers & Operations Research, 36(12):3178–3186, 2009.
bib | DOI | pdf ]
The longest common subsequence problem is a classical string problem that concerns finding the common part of a set of strings. It has several important applications, for example, pattern recognition or computational biology. Most research efforts up to now have focused on solving this problem optimally. In comparison, only few works exist dealing with heuristic approaches. In this work we present a deterministic beam search algorithm. The results show that our algorithm outperforms the current state-of-the-art approaches not only in solution quality but often also in computation time.

[242]
Christian Blum, Borja Calvo, and María J. Blesa. FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs. Swarm Intelligence, 9(2-3):205–227, 2015.
bib | DOI ]
Keywords: irace
[243]
Christian Blum, Carlos Cotta, Antonio J. Fernández, and J. E. Gallardo. A probabilistic beam search algorithm for the shortest common supersequence problem. In C. Cotta et al., editors, Proceedings of EvoCOP 2007 – Seventh European Conference on Evolutionary Computation in Combinatorial Optimisation, volume 4446 of Lecture Notes in Computer Science, pages 36–47. Springer, Berlin, 2007.
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[244]
Christian Blum and Marco Dorigo. The hyper-cube framework for ant colony optimization. IEEE Transactions on Systems, Man, and Cybernetics – Part B, 34(2):1161–1172, 2004.
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[245]
Christian Blum and Marco Dorigo. Search Bias in Ant Colony Optimization: On the Role of Competition-Balanced Systems. IEEE Transactions on Evolutionary Computation, 9(2):159–174, 2005.
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[246]
Christian Blum and Manuel López-Ibáñez. Ant Colony Optimization. In The Industrial Electronics Handbook: Intelligent Systems. CRC Press, second edition, 2011.
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[247]
Christian Blum and M. Mastrolilli. Using Branch & Bound Concepts in Construction-Based Metaheuristics: Exploiting the Dual Problem Knowledge. In T. Bartz-Beielstein, M. J. Blesa, C. Blum, B. Naujoks, A. Roli, G. Rudolph, and M. Sampels, editors, Hybrid Metaheuristics, volume 4771 of Lecture Notes in Computer Science, pages 123–139. Springer, Heidelberg, Germany, 2007.
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[248]
C. Blum and D. Merkle, editors. Swarm Intelligence–Introduction and Applications. Natural Computing Series. Springer Verlag, Berlin, Germany, 2008.
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[249]
Christian Blum, Pedro Pinacho, Manuel López-Ibáñez, and José A. Lozano. Construct, Merge, Solve & Adapt: A New General Algorithm for Combinatorial Optimization. Computers & Operations Research, 68:75–88, 2016.
bib | DOI ]
Keywords: irace
[250]
Christian Blum, Jakob Puchinger, Günther R. Raidl, and Andrea Roli. Hybrid Metaheuristics in Combinatorial Optimization: A Survey. Applied Soft Computing, 11(6):4135–4151, 2011.
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[251]
Christian Blum and Günther R. Raidl. Hybrid Metaheuristics—Powerful Tools for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Springer, Berlin, Germany, 2016.
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[252]
Christian Blum and Andrea Roli. Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison. ACM Computing Surveys, 35(3):268–308, 2003.
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[253]
Christian Blum and Andrea Roli. Hybrid metaheuristics: an introduction. In C. Blum, M. J. Blesa, A. Roli, and M. Sampels, editors, Hybrid Metaheuristics: An emergent approach for optimization, volume 114 of Studies in Computational Intelligence, pages 1–30. Springer, Berlin, Germany, 2008.
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[254]
Christian Blum and M. Sampels. An Ant Colony Optimization Algorithm for Shop Scheduling Problems. Journal of Mathematical Modelling and Algorithms, 3(3):285–308, 2004.
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[255]
Christian Blum and M. Yábar Vallès. Multi-level ant colony optimization for DNA sequencing by hybridization. In F. Almeida et al., editors, Hybrid Metaheuristics, volume 4030 of Lecture Notes in Computer Science, pages 94–109. Springer, Heidelberg, Germany, 2006.
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[256]
Christian Blum, M. Yábar Vallès, and María J. Blesa. An ant colony optimization algorithm for DNA sequencing by hybridization. Computers & Operations Research, 35(11):3620–3635, 2008.
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Endre Boros, Peter L. Hammer, and Gabriel Tavares. Local search heuristics for Quadratic Unconstrained Binary Optimization (QUBO). Journal of Heuristics, 13(2):99–132, 2007.
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Urban traffic planning is a fertile area of Smart Cities to improve efficiency, environmental care, and safety, since the traffic jams and congestion are one of the biggest sources of pollution and noise. Traffic lights play an important role in solving these problems since they control the flow of the vehicular network at the city. However, the increasing number of vehicles makes necessary to go from a local control at one single intersection to a holistic approach considering a large urban area, only possible using advanced computational resources and techniques. Here we propose HITUL, a system that supports the decisions of the traffic control managers in a large urban area. HITUL takes the real traffic conditions and compute optimal traffic lights plans using bio-inspired techniques and micro-simulations. We compare our system against plans provided by experts. Our solutions not only enable continuous traffic flows but reduce the pollution. A case study of Málaga city allows us to validate the approach and show its benefits for other cities as well.

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Recently, there has been a large interest in set-based evolutionary algorithms for multi objective optimization. They are based on the definition of indicators that characterize the quality of the current population while being compliant with the concept of Pareto-optimality. It has been shown that the hypervolume indicator, which measures the dominated volume in the objective space, enables the design of efficient search algorithms and, at the same time, opens up opportunities to express user preferences in the search by means of weight functions. The present paper contains the necessary theoretical foundations and corresponding algorithms to (i) select appropriate weight functions, to (ii) transform user preferences into weight functions and to (iii) efficiently evaluate the weighted hypervolume indicator through Monte Carlo sampling. The algorithm W-HypE, which implements the previous concepts, is introduced, and the effectiveness of the search, directed towards the user's preferred solutions, is shown using an extensive set of experiments including the necessary statistical performance assessment.

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Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

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Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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In its current state, evolutionary multiobjective optimization (EMO) is an established field of research and application with more than 150 PhD theses, more than ten dedicated texts and edited books, commercial softwares and numerous freely downloadable codes, a biannual conference series running successfully since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this chapter, we provide a brief introduction to EMO principles, illustrate some EMO algorithms with simulated results, and outline the current research and application potential of EMO. For solving multiobjective optimization problems, EMO procedures attempt to find a set of well-distributed Pareto-optimal points, so that an idea of the extent and shape of the Pareto-optimal front can be obtained. Although this task was the early motivation of EMO research, EMO principles are now being found to be useful in various other problem solving tasks, enabling one to treat problems naturally as they are. One of the major current research thrusts is to combine EMO procedures with other multiple criterion decision making (MCDM) tools so as to develop hybrid and interactive multiobjective optimization algorithms for finding a set of trade-off optimal solutions and then choose a preferred solution for implementation. This chapter provides the background of EMO principles and their potential to launch such collaborative studies with MCDM researchers in the coming years.

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Kalyanmoy Deb. Multi-objective optimization. In Search methodologies, pages 403–449. Springer, 2014.
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Kalyanmoy Deb. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester, UK, 2001.
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Kalyanmoy Deb and S. Agrawal. A Niched-Penalty Approach for Constraint Handling in Genetic Algorithms. In A. Dobnikar, N. C. Steele, D. W. Pearson, and R. F. Albrecht, editors, Artificial Neural Nets and Genetic Algorithms (ICANNGA-99), pages 235–243. Springer Verlag, 1999.
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Keywords: polynomial mutation
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Kalyanmoy Deb and Ram Bhushan Agrawal. Simulated binary crossover for continuous search spaces. Complex Systems, 9(2):115–148, 1995.
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Keywords: SBX
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Kalyanmoy Deb, S. Agarwal, A. Pratap, and T. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In M. Schoenauer et al., editors, Proceedings of PPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature, volume 1917 of Lecture Notes in Computer Science, pages 849–858. Springer, Heidelberg, Germany, 2000.
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Kalyanmoy Deb and Debayan Deb. Analysing mutation schemes for real-parameter genetic algorithms. International Journal of Artificial Intelligence and Soft Computing, 4(1):1–28, 2014.
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Kalyanmoy Deb and Sachin Jain. Multi-Speed Gearbox Design Using Multi-Objective Evolutionary Algorithms. Technical Report 2002001, KanGAL, February 2002.
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Kalyanmoy Deb and Sachin Jain. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints. IEEE Transactions on Evolutionary Computation, 18(4):577–601, 2014.
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Kalyanmoy Deb and Murat Köksalan. Guest Editorial: Special Issue on Preference-based Multiobjective Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation, 14(5):669–670, October 2010.
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Kalyanmoy Deb and Christie Myburgh. Breaking the billion-variable barrier in real-world optimization using a customized evolutionary algorithm. In T. Friedrich, F. Neumann, and A. M. Sutton, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2015, pages 653–660. ACM Press, New York, NY, 2016.
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Kalyanmoy Deb and Ankur Sinha. Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms. In M. Ehrgott, C. M. Fonseca, X. Gandibleux, J.-K. Hao, and M. Sevaux, editors, Evolutionary Multi-criterion Optimization, EMO 2009, volume 5467 of Lecture Notes in Computer Science, pages 110–124. Springer, Heidelberg, Germany, 2009.
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Kalyanmoy Deb, J. Sundar, N. Udaya Bhaskara Rao, and Shamik Chaudhuri. Reference point based multi-objective optimization using evolutionary algorithms. In M. Cattolico et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2006, pages 635–642. ACM Press, New York, NY, 2006.
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Kalyanmoy Deb, Rahul Tewari, Mayur Dixit, and Joydeep Dutta. Finding trade-off solutions close to KKT points using evolutionary multi-objective optimization. In Proceedings of the 2007 Congress on Evolutionary Computation (CEC 2007), pages 2109–2116. IEEE Press, Piscataway, NJ, 2007.
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Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, and Eckart Zitzler. Scalable Test Problems for Evolutionary Multi-Objective Optimization. Technical Report 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zürich, Switzerland, 2001. Do not cite this TR! It is incorrect and it is superseeded by [480].
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Keywords: DTLZ benchmark
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Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, and Eckart Zitzler. Scalable Test Problems for Evolutionary Multiobjective Optimization. In A. Abraham, L. Jain, and R. Goldberg, editors, Evolutionary Multiobjective Optimization, Advanced Information and Knowledge Processing, pages 105–145. Springer, London, UK, January 2005.
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Keywords: DTLZ benchmark
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Kalyanmoy Deb, Ling Zhu, and Sandeep Kulkarni. Handling Multiple Scenarios in Evolutionary Multi-Objective Numerical Optimization. IEEE Transactions on Evolutionary Computation, 22(6):920–933, 2018.
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Solutions to most practical numerical optimization problems must be evaluated for their performance over a number of different loading or operating conditions, which we refer here as scenarios. Therefore, a meaningful and resilient optimal solution must be such that it remains feasible under all scenarios and performs close to an individual optimal solution corresponding to each scenario. Despite its practical importance, multi-scenario consideration has received a lukewarm attention, particularly in the context of multi-objective optimization. The usual practice is to optimize for the worst-case scenario. In this paper, we review existing methodologies in this direction and set our goal to suggest a new and potential population-based method for handling multiple scenarios by defining scenario-wise domination principle and scenario-wise diversity-preserving operators. To evaluate, the proposed method is applied to a number of numerical test problems and engineering design problems with a detail explanation of the obtained results and compared with an existing method. This first systematic evolutionary based multi-scenario, multiobjective, optimization study on numerical problems indicates that multiple scenarios can be handled in an integrated manner using an EMO framework to find a well-balanced compromise set of solutions to multiple scenarios and maintain a tradeoff among multiple objectives. In comparison to an existing serial multiple optimization approach, the proposed approach finds a set of compromised trade-off solutions simultaneously. An achievement of multi-objective trade-off and multi-scenario trade-off is algorithmically challenging, but due to its practical appeal, further research and application must be spent.

Keywords: scenario-based
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Many real-world optimization problems can be modelled as combinatorial optimization problems. Often, these problems are characterized by their large size and the presence of multiple, conflicting objectives. Despite progress in solving multi-objective combinatorial optimization problems exactly, the large size often means that heuristics are required for their solution in acceptable time. Since the middle of the nineties the trend is towards heuristics that “pick and choose” elements from several of the established metaheuristic schemes. Such hybrid approximation techniques may even combine exact and heuristic approaches. In this chapter we give an overview over approximation methods in multi-objective combinatorial optimization. We briefly summarize “classical” metaheuristics and focus on recent approaches, where metaheuristics are hybridized and/or combined with exact methods.

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The attainment function has been proposed as a measure of the statistical performance of stochastic multiobjective optimisers which encompasses both the quality of individual non-dominated solutions in objective space and their spread along the trade-off surface. It has also been related to results from random closed-set theory, and cast as a mean-like, first-order moment measure of the outcomes of multiobjective optimisers. In this work, the use of more informative, second-order moment measures for the evaluation and comparison of multiobjective optimiser performance is explored experimentally, with emphasis on the interpretability of the results.

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This paper presents a recursive, dimension-sweep algorithm for computing the hypervolume indicator of the quality of a set of n non-dominated points in d>2 dimensions. It improves upon the existing HSO (Hypervolume by Slicing Objectives) algorithm by pruning the recursion tree to avoid repeated dominance checks and the recalculation of partial hypervolumes. Additionally, it incorporates a recent result for the three-dimensional special case. The proposed algorithm achieves O(nd-2 logn) time and linear space complexity in the worst-case, but experimental results show that the pruning techniques used may reduce the time complexity exponent even further.

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A core feature of evolutionary algorithms is their mutation operator. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this line of work, we propose a new mutation operator and analyze its performance on the (1+1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1+1)-EA on classes of problems for which results on the other mutation operators are available. We present a “jump” function for which the performance of the (1+1)-EA using any static uniform mutation and any restart strategy can be worse than the performance of the (1+1)-EA using our mutation operator with no restarts. We show that the (1+1)-EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve this problem.

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Satisfiability testing (SAT) is a very active area of research today, with numerous real-world applications. We describe CLASS2.0, a genetic programming system for semi-automatically designing SAT local search heuristics. An empirical comparison shows that that the heuristics generated by our GP system outperform the state of the art human-designed local search algorithms, as well as previously proposed evolutionary approaches, with respect to both runtime as well as search efficiency (number of variable flips to solve a problem).

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The development of successful metaheuristic algorithms such as local search for a difficult problem such as satisfiability testing (SAT) is a challenging task. We investigate an evolutionary approach to automating the discovery of new local search heuristics for SAT. We show that several well-known SAT local search algorithms such as Walksat and Novelty are composite heuristics that are derived from novel combinations of a set of building blocks. Based on this observation, we developed CLASS, a genetic programming system that uses a simple composition operator to automatically discover SAT local search heuristics. New heuristics discovered by CLASS are shown to be competitive with the best Walksat variants, including Novelty+. Evolutionary algorithms have previously been applied to directly evolve a solution for a particular SAT instance. We show that the heuristics discovered by CLASS are also competitive with these previous, direct evolutionary approaches for SAT. We also analyze the local search behavior of the learned heuristics using the depth, mobility, and coverage metrics proposed by Schuurmans and Southey.

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Algorithm selection is typically based on models of algorithm performance,learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which models of the runtime distributions of the available algorithms are iteratively updated and used to guide the allocation of computational resources, while solving a sequence of problem instances. The models are estimated using survival analysis techniques, which allow us to reduce computation time, censoring the runtimes of the slower algorithms. Here, we review the statistical aspects of our online selection method, discussing the bias induced in the runtime distributions (RTD) models by the competition of different algorithms on the same problem instances.

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The customer order scheduling problem (COSP) is defined as to determine the sequence of tasks to satisfy the demand of customers who order several types of products produced on a single machine. A setup is required whenever a product type is launched. The objective of the scheduling problem is to minimize the average customer order flow time. Since the customer order scheduling problem is known to be strongly NP-hard, we solve it using four major metaheuristics and compare the performance of these heuristics, namely, simulated annealing, genetic algorithms, tabu search, and ant colony optimization. These are selected to represent various characteristics of metaheuristics: nature-inspired vs. artificially created, population-based vs. local search, etc. A set of problems is generated to compare the solution quality and computational efforts of these heuristics. Results of the experimentation show that tabu search and ant colony perform better for large problems whereas simulated annealing performs best in small-size problems. Some conclusions are also drawn on the interactions between various problem parameters and the performance of the heuristics.

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Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. Automated Configuration of Mixed Integer Programming Solvers. In A. Lodi, M. Milano, and P. Toth, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 7th International Conference, CPAIOR 2010, volume 6140 of Lecture Notes in Computer Science, pages 186–202. Springer, Heidelberg, Germany, 2010.
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Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. Parallel Algorithm Configuration. In Y. Hamadi and M. Schoenauer, editors, Learning and Intelligent Optimization, 6th International Conference, LION 6, volume 7219 of Lecture Notes in Computer Science, pages 55–70. Springer, Heidelberg, Germany, 2012.
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Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. Bayesian Optimization With Censored Response Data. Arxiv preprint arXiv:1310.1947, 2013.
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Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. Identifying key algorithm parameters and instance features using forward selection. In P. M. Pardalos and G. Nicosia, editors, Learning and Intelligent Optimization, 7th International Conference, LION 7, volume 7997 of Lecture Notes in Computer Science, pages 364–381. Springer, Heidelberg, Germany, 2013.
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Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. An Efficient Approach for Assessing Hyperparameter Importance. In E. P. Xing and T. Jebara, editors, Proceedings of the 31th International Conference on Machine Learning, volume 32, pages 754–762, 2014.
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Frank Hutter, Holger H. Hoos, Kevin Leyton-Brown, and Kevin Murphy. Time-Bounded Sequential Parameter Optimization. In C. Blum and R. Battiti, editors, Learning and Intelligent Optimization, 4th International Conference, LION 4, volume 6073 of Lecture Notes in Computer Science, pages 281–298. Springer, Heidelberg, Germany, 2010.
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Frank Hutter, Holger H. Hoos, Kevin Leyton-Brown, and Thomas Stützle. ParamILS: An Automatic Algorithm Configuration Framework. Journal of Artificial Intelligence Research, 36:267–306, October 2009.
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Frank Hutter, Holger H. Hoos, and Thomas Stützle. Automatic Algorithm Configuration Based on Local Search. In R. C. Holte and A. Howe, editors, Proc. of the Twenty-Second Conference on Artifical Intelligence (AAAI '07), pages 1152–1157. AAAI Press/MIT Press, Menlo Park, CA, 2007.
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Frank Hutter, Marius Thomas Lindauer, Adrian Balint, Sam Bayless, Holger H. Hoos, and Kevin Leyton-Brown. The Configurable SAT Solver Challenge (CSSC). Artificial Intelligence, 243(1–25), 2017.
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Frank Hutter, Manuel López-Ibáñez, Chris Fawcett, Marius Thomas Lindauer, Holger H. Hoos, Kevin Leyton-Brown, and Thomas Stützle. AClib: a Benchmark Library for Algorithm Configuration. In P. M. Pardalos, M. G. C. Resende, C. Vogiatzis, and J. L. Walteros, editors, Learning and Intelligent Optimization, 8th International Conference, LION 8, volume 8426 of Lecture Notes in Computer Science, pages 36–40. Springer, Heidelberg, Germany, 2014.
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Frank Hutter, Lin Xu, Holger H. Hoos, and Kevin Leyton-Brown. Algorithm runtime prediction: Methods & evaluation. Artificial Intelligence, 206:79–111, 2014.
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Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization. Technical Report TR/IRIDIA/2009-015, IRIDIA, Université Libre de Bruxelles, Belgium, May 2009. Published as a book chapter [1229].
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Manuel López-Ibáñez and Thomas Stützle. An Analysis of Algorithmic Components for Multiobjective Ant Colony Optimization: A Case Study on the Biobjective TSP. Technical Report TR/IRIDIA/2009-019, IRIDIA, Université Libre de Bruxelles, Belgium, June 2009. Published in the proceedings of Evolution Artificielle, 2009 [1238].
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Jérémie Dubois-Lacoste, Manuel López-Ibáñez, and Thomas Stützle. Effective Hybrid Stochastic Local Search Algorithms for Biobjective Permutation Flowshop Scheduling. Technical Report TR/IRIDIA/2009-020, IRIDIA, Université Libre de Bruxelles, Belgium, June 2009. Published in the proceedings of Hybrid Metaheuristics 2009 [555].
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Jérémie Dubois-Lacoste, Manuel López-Ibáñez, and Thomas Stützle. Adaptive “Anytime” Two-Phase Local Search. Technical Report TR/IRIDIA/2009-026, IRIDIA, Université Libre de Bruxelles, Belgium, 2010. Published in the proceedings of LION 4 [558].
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Thomas Stützle, Manuel López-Ibáñez, Paola Pellegrini, Michael Maur, Marco A. Montes de Oca, Mauro Birattari, and Marco Dorigo. Parameter Adaptation in Ant Colony Optimization. Technical Report TR/IRIDIA/2010-002, IRIDIA, Université Libre de Bruxelles, Belgium, January 2010. Published as a book chapter [1800].
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Jérémie Dubois-Lacoste, Manuel López-Ibáñez, and Thomas Stützle. A Hybrid TP+PLS Algorithm for Bi-objective Flow-Shop Scheduling Problems. Technical Report TR/IRIDIA/2010-019, IRIDIA, Université Libre de Bruxelles, Belgium, 2010. Published in Computers & Operations Research [561].
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M. S. Hussin and Thomas Stützle. Tabu Search vs. Simulated Annealing for Solving Large Quadratic Assignment Instances. Technical Report TR/IRIDIA/2010-020, IRIDIA, Université Libre de Bruxelles, Belgium, 2010.
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Jérémie Dubois-Lacoste, Manuel López-Ibáñez, and Thomas Stützle. Improving the Anytime Behavior of Two-Phase Local Search. Technical Report TR/IRIDIA/2010-022, IRIDIA, Université Libre de Bruxelles, Belgium, 2010. Published in Annals of Mathematics and Artificial Intelligence [560].
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Manuel López-Ibáñez, Joshua D. Knowles, and Marco Laumanns. On Sequential Online Archiving of Objective Vectors. Technical Report TR/IRIDIA/2011-001, IRIDIA, Université Libre de Bruxelles, Belgium, 2011. This is a revised version of the paper published in EMO 2011 [1221].
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Mauro Birattari, Marco Chiarandini, Marco Saerens, and Thomas Stützle. Learning graphical models for parameter tuning. Technical Report TR/IRIDIA/2011-002, IRIDIA, Université Libre de Bruxelles, Belgium, 2011.
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Manuel López-Ibáñez and Thomas Stützle. The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms. Technical Report TR/IRIDIA/2011-003, IRIDIA, Université Libre de Bruxelles, Belgium, 2011. Published in IEEE Transactions on Evolutionary Computation [1245].
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Tianjun Liao, Daniel Molina, Marco A. Montes de Oca, and Thomas Stützle. A Note on the Effects of Enforcing Bound Constraints on Algorithm Comparisons using the IEEE CEC'05 Benchmark Function Suite. Technical Report TR/IRIDIA/2011-010, IRIDIA, Université Libre de Bruxelles, Belgium, 2011.
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Tianjun Liao, Daniel Molina, Marco A. Montes de Oca, and Thomas Stützle. Computational Results for an Automatically Tuned IPOP-CMA-ES on the CEC'05 Benchmark Set. Technical Report TR/IRIDIA/2011-022, IRIDIA, Université Libre de Bruxelles, Belgium, 2011.
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Manuel López-Ibáñez and Thomas Stützle. Automatically Improving the Anytime Behaviour of Optimisation Algorithms. Technical Report TR/IRIDIA/2012-012, IRIDIA, Université Libre de Bruxelles, Belgium, May 2012. Published in European Journal of Operations Research [1246].
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Andreea Radulescu, Manuel López-Ibáñez, and Thomas Stützle. Automatically Improving the Anytime Behaviour of Multiobjective Evolutionary Algorithms. Technical Report TR/IRIDIA/2012-019, IRIDIA, Université Libre de Bruxelles, Belgium, 2012. Published in the proceedings of EMO 2013 [1590].
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Tianjun Liao, Thomas Stützle, Marco A. Montes de Oca, and Marco Dorigo. A Unified Ant Colony Optimization Algorithm for Continuous Optimization. Technical Report TR/IRIDIA/2013-002, IRIDIA, Université Libre de Bruxelles, Belgium, 2013.
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Franco Mascia, Manuel López-Ibáñez, Jérémie Dubois-Lacoste, and Thomas Stützle. Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools. Technical Report TR/IRIDIA/2013-015, IRIDIA, Université Libre de Bruxelles, Belgium, 2013.
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Manuel López-Ibáñez, Arnaud Liefooghe, and Sébastien Verel. Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives. Technical Report TR/IRIDIA/2014-009, IRIDIA, Université Libre de Bruxelles, Belgium, 2014.
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Vito Trianni and Manuel López-Ibáñez. Advantages of Multi-Objective Optimisation in Evolutionary Robotics: Survey and Case Studies. Technical Report TR/IRIDIA/2014-014, IRIDIA, Université Libre de Bruxelles, Belgium, 2014.
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Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. A Large-Scale Experimental Evaluation of High-Performing Multi- and Many-Objective Evolutionary Algorithms. Technical Report TR/IRIDIA/2017-005, IRIDIA, Université Libre de Bruxelles, Belgium, November 2017.
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Alberto Franzin, Leslie Pérez Cáceres, and Thomas Stützle. Effect of Transformations of Numerical Parameters in Automatic Algorithm Configuration. Technical Report TR/IRIDIA/2017-006, IRIDIA, Université Libre de Bruxelles, Belgium, March 2017.
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Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatic Configuration of Multi-objective Optimizers and Multi-objective Configuration. Technical Report TR/IRIDIA/2017-011, IRIDIA, Université Libre de Bruxelles, Belgium, November 2017. Published as [200].
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Manuel López-Ibáñez, Marie-Eléonore Kessaci, and Thomas Stützle. Automatic Design of Hybrid Metaheuristics from Algorithmic Components. Technical Report TR/IRIDIA/2017-012, IRIDIA, Université Libre de Bruxelles, Belgium, December 2017.
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Leonardo C. T. Bezerra, Manuel López-Ibáñez, and Thomas Stützle. Automatically Designing State-of-the-Art Multi- and Many-Objective Evolutionary Algorithms. Technical Report TR/IRIDIA/2018-001, IRIDIA, Université Libre de Bruxelles, Belgium, January 2018. Published as [196].
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Alberto Franzin and Thomas Stützle. Revisiting Simulated Annealing: a Component-Based Analysis. Technical Report TR/IRIDIA/2018-010, IRIDIA, Université Libre de Bruxelles, Belgium, 2018.
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Claudio Iacopino and Phil Palmer. The Dynamics of Ant Colony Optimization Algorithms Applied to Binary Chains. Swarm Intelligence, 6(4):343–377, 2012.
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Significant gains in the performance of the simulated annealing algorithm in the DASH software package have been realized by using the irace automatic configuration tool to optimize the values of three key simulated annealing parameters. Specifically, the success rate in finding the global minimum in intensity χ2 space is improved by up to an order of magnitude. The general applicability of these revised simulated annealing parameters is demonstrated using the crystal structure determinations of over 100 powder diffraction datasets.

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In this article, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focusing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that, compared to the portfolio's single best solver, on average requires less than half of the resources for solving a given problem. Therefore, there is a huge gain in efficiency compared to classical ensemble methods combined with an increased insight into problem characteristics and algorithm properties by using informative features. The model acts on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications. The model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial population of an evolutionary (optimization) algorithm so that even the feature costs become negligible.

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Keywords: S-metric, hypervolume
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Joshua D. Knowles and David Corne. Bounded Pareto Archiving: Theory and Practice. In X. Gandibleux, M. Sevaux, K. Sörensen, and V. T'Kindt, editors, Metaheuristics for Multiobjective Optimisation, volume 535 of Lecture Notes in Economics and Mathematical Systems, pages 39–64. Springer, Berlin, Germany, 2004.
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Joshua D. Knowles, David Corne, and Kalyanmoy Deb. Introduction: Problem solving, EC and EMO. In J. D. Knowles, D. Corne, K. Deb, and D. R. Chair, editors, Multiobjective Problem Solving from Nature, Natural Computing Series, pages 1–28. Springer, 2008.
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This paper considers heuristics for the well-known resource-constrained project scheduling problem (RCPSP). It provides an update of our survey which was published in 2000. We summarize and categorize a large number of heuristics that have recently been proposed in the literature. Most of these heuristics are then evaluated in a computational study and compared on the basis of our standardized experimental design. Based on the computational results we discuss features of good heuristics. The paper closes with some remarks on our test design and a summary of the recent developments in research on heuristics for the RCPSP.

Keywords: Computational evaluation, Heuristics, Project scheduling, Resource constraints
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Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes to the theoretical analysis of ant colony optimization and studies this type of algorithm on one of the most prominent combinatorial optimization problems, namely the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used for constructing solutions of the TSP. The rigorous runtime analysis for two ant colony optimization algorithms, based on these two construction procedures, shows that they lead to good approximation in expected polynomial time on random instances. Furthermore, we point out in which situations our algorithms get trapped in local optima and show where the use of the right amount of heuristic information is provably beneficial.

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Application of heuristic solution procedures to the practical problem of project scheduling has previously been studied by numerous researchers. However, there is little consensus about their findings, and the practicing manager is currently at a loss as to which scheduling rule to use. Furthermore, since no categorization process was developed, it is assumed that once a rule is selected it must be used throughout the whole project. This research breaks away from this tradition by providing a categorization process based on two powerful project summary measures. The first measure identifies the location of the peak of total resource requirements and the second measure identifies the rate of utilization of each resource type. The performance of the rules are classified according to values of these two measures, and it is shown that a rule introduced by this research performs significantly better on most categories of projects.

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Keywords: racing
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This paper discusses simple local search approaches for approximating the efficient set of multiobjective combinatorial optimization problems. We focus on algorithms defined by a neighborhood structure and a dominance relation that iteratively improve an archive of nondominated solutions. Such methods are referred to as dominance-based multiobjective local search. We first provide a concise overview of existing algorithms, and we propose a model trying to unify them through a fine-grained decomposition. The main problem-independent search components of dominance relation, solution selection, neighborhood exploration and archiving are largely discussed. Then, a number of state-of-the-art and original strategies are experimented on solving a permutation flowshop scheduling problem and a traveling salesman problem, both on a two- and a three-objective formulation. Experimental results and a statistical comparison are reported in the paper, and some directions for future research are highlighted.

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A simple {ACO} algorithm called λ-MMAS for dynamic variants of the single-destination shortest paths problem is studied by rigorous runtime analyses. Building upon previous results for the special case of 1-MMAS, it is studied to what extent an enlarged colony using λ ants per vertex helps in tracking an oscillating optimum. It is shown that easy cases of oscillations can be tracked by a constant number of ants. However, the paper also identifies more involved oscillations that with overwhelming probability cannot be tracked with any polynomial-size colony. Finally, parameters of dynamic shortest-path problems which make the optimum difficult to track are discussed. Experiments illustrate theoretical findings and conjectures.

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Manuel López-Ibáñez. High Performance Ant Colony Optimisation of the Pump Scheduling Problem. In P. Alberigo, G. Erbacci, F. Garofalo, and S. Monfardini, editors, Science and Sumpercomputing in Europe, pages 371–375. CINECA, 2007.
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Manuel López-Ibáñez and Christian Blum. Beam-ACO Based on Stochastic Sampling: A Case Study on the TSP with Time Windows. Technical Report LSI-08-28, Department LSI, Universitat Politècnica de Catalunya, 2008. Extended version published in Computers & Operations Research [1214].
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Manuel López-Ibáñez, Christian Blum, Dhananjay Thiruvady, Andreas T. Ernst, and Bernd Meyer. Beam-ACO based on stochastic sampling for makespan optimization concerning the TSP with time windows. In C. Cotta and P. Cowling, editors, Proceedings of EvoCOP 2009 – 9th European Conference on Evolutionary Computation in Combinatorial Optimization, volume 5482 of Lecture Notes in Computer Science, pages 97–108. Springer, Heidelberg, Germany, 2009.
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[1213]
Manuel López-Ibáñez and Christian Blum. Beam-ACO Based on Stochastic Sampling: A Case Study on the TSP with Time Windows. In T. Stützle, editor, Learning and Intelligent Optimization, Third International Conference, LION 3, volume 5851 of Lecture Notes in Computer Science, pages 59–73. Springer, Heidelberg, Germany, 2009.
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[1214]
Manuel López-Ibáñez and Christian Blum. Beam-ACO for the travelling salesman problem with time windows. Computers & Operations Research, 37(9):1570–1583, 2010.
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The travelling salesman problem with time windows is a difficult optimization problem that arises, for example, in logistics. This paper deals with the minimization of the travel-cost. For solving this problem, this paper proposes a Beam-ACO algorithm, which is a hybrid method combining ant colony optimization with beam search. In general, Beam-ACO algorithms heavily rely on accurate and computationally inexpensive bounding information for differentiating between partial solutions. This work uses stochastic sampling as a useful alternative. An extensive experimental evaluation on seven benchmark sets from the literature shows that the proposed Beam-ACO algorithm is currently a state-of-the-art technique for the travelling salesman problem with time windows when travel-cost optimization is concerned.

Keywords: Ant colony optimization, Travelling salesman problem with time windows, Hybridization
[1215]
Manuel López-Ibáñez, Christian Blum, Jeffrey W. Ohlmann, and Barrett W. Thomas. The Travelling Salesman Problem with Time Windows: Adapting Algorithms from Travel-time to Makespan Optimization. Applied Soft Computing, 13(9):3806–3815, 2013.
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[1216]
Manuel López-Ibáñez, Jérémie Dubois-Lacoste, Leslie Pérez Cáceres, Thomas Stützle, and Mauro Birattari. The irace package: Iterated Racing for Automatic Algorithm Configuration. Operations Research Perspectives, 3:43–58, 2016.
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[1217]
Manuel López-Ibáñez, Jérémie Dubois-Lacoste, Leslie Pérez Cáceres, Thomas Stützle, and Mauro Birattari. The irace Package: Iterated Racing for Automatic Algorithm Configuration. http://iridia.ulb.ac.be/supp/IridiaSupp2016-003/, 2016.
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[1218]
Manuel López-Ibáñez, Jérémie Dubois-Lacoste, Thomas Stützle, and Mauro Birattari. The irace package, Iterated Race for Automatic Algorithm Configuration. Technical Report TR/IRIDIA/2011-004, IRIDIA, Université Libre de Bruxelles, Belgium, 2011. Published in Operations Research Perspectives [1216].
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[1219]
Manuel López-Ibáñez, Marie-Eléonore Kessaci, and Thomas Stützle. Automatic Design of Hybrid Metaheuristics from Algorithmic Components. Submitted, 2017.
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[1220]
Manuel López-Ibáñez and Joshua D. Knowles. Machine Decision Makers as a Laboratory for Interactive EMO. In A. Gaspar-Cunha, C. H. Antunes, and C. A. Coello Coello, editors, Evolutionary Multi-criterion Optimization, EMO 2015 Part II, volume 9019 of Lecture Notes in Computer Science, pages 295–309. Springer, Heidelberg, Germany, 2015.
bib | DOI | pdf ]
A key challenge, perhaps the central challenge, of multi-objective optimization is how to deal with candidate solutions that are ultimately evaluated by the hidden or unknown preferences of a human decision maker (DM) who understands and cares about the optimization problem. Alternative ways of addressing this challenge exist but perhaps the favoured one currently is the interactive approach (proposed in various forms). Here, an evolutionary multi-objective optimization algorithm (EMOA) is controlled by a series of interactions with the DM so that preferences can be elicited and the direction of search controlled. MCDM has a key role to play in designing and evaluating these approaches, particularly in testing them with real DMs, but so far quantitative assessment of interactive EMOAs has been limited. In this paper, we propose a conceptual framework for this problem of quantitative assessment, based on the definition of machine decision makers (machine DMs), made somewhat realistic by the incorporation of various non-idealities. The machine DM proposed here draws from earlier models of DM biases and inconsistencies in the MCDM literature. As a practical illustration of our approach, we use the proposed machine DM to study the performance of an interactive EMOA, and discuss how this framework could help in the evaluation and development of better interactive EMOAs.

[1221]
Manuel López-Ibáñez, Joshua D. Knowles, and Marco Laumanns. On Sequential Online Archiving of Objective Vectors. In R. H. C. Takahashi et al., editors, Evolutionary Multi-criterion Optimization, EMO 2011, volume 6576 of Lecture Notes in Computer Science, pages 46–60. Springer, Heidelberg, Germany, 2011.
bib | DOI ]
In this paper, we examine the problem of maintaining an approximation of the set of nondominated points visited during a multiobjective optimization, a problem commonly known as archiving. Most of the currently available archiving algorithms are reviewed, and what is known about their convergence and approximation properties is summarized. The main scenario considered is the restricted case where the archive must be updated online as points are generated one by one, and at most a fixed number of points are to be stored in the archive at any one time. In this scenario, the better-monotonicity of an archiving algorithm is proposed as a weaker, but more practical, property than negative efficiency preservation. This paper shows that hypervolume-based archivers and a recently proposed multi-level grid archiver have this property. On the other hand, the archiving methods used by SPEA2 and NSGA-II do not, and they may better-deteriorate with time. The better-monotonicity property has meaning on any input sequence of points. We also classify archivers according to limit properties, i.e. convergence and approximation properties of the archiver in the limit of infinite (input) samples from a finite space with strictly positive generation probabilities for all points. This paper establishes a number of research questions, and provides the initial framework and analysis for answering them.

Revised version available at http://iridia.ulb.ac.be/IridiaTrSeries/IridiaTr2011-001.pdf
[1222]
Manuel López-Ibáñez, Tianjun Liao, and Thomas Stützle. On the anytime behavior of IPOP-CMA-ES. In C. A. Coello Coello et al., editors, Parallel Problem Solving from Nature, PPSN XII, volume 7491 of Lecture Notes in Computer Science, pages 357–366. Springer, Heidelberg, Germany, 2012.
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[1223]
Manuel López-Ibáñez, Tianjun Liao, and Thomas Stützle. On the anytime behavior of IPOP-CMA-ES: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2012-010/, 2012.
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Manuel López-Ibáñez, Arnaud Liefooghe, and Sébastien Verel. Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives. In T. Bartz-Beielstein, J. Branke, B. Filipič, and J. Smith, editors, PPSN 2014, volume 8672 of Lecture Notes in Computer Science, pages 621–630. Springer, Heidelberg, Germany, 2014.
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[1225]
Manuel López-Ibáñez, Franco Mascia, Marie-Eléonore Marmion, and Thomas Stützle. Automatic Design of a Hybrid Iterated Local Search for the Multi-Mode Resource-Constrained Multi-Project Scheduling Problem. In G. Kendall, G. V. Berghe, and B. McCollum, editors, Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA 2013), pages 1–6, Gent, Belgium, 2013.
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https://hal.inria.fr/hal-01094681
[1226]
Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. On the Design of ACO for the Biobjective Quadratic Assignment Problem. In M. Dorigo et al., editors, Ant Colony Optimization and Swarm Intelligence, 4th International Workshop, ANTS 2004, volume 3172 of Lecture Notes in Computer Science, pages 214–225. Springer, Heidelberg, Germany, 2004.
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[1227]
Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. Hybrid Population-based Algorithms for the Bi-objective Quadratic Assignment Problem. Technical Report AIDA–04–11, FG Intellektik, FB Informatik, TU Darmstadt, December 2004. Published in Journal of Mathematical Modelling and Algorithms [1228].
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Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. Hybrid Population-based Algorithms for the Bi-objective Quadratic Assignment Problem. Journal of Mathematical Modelling and Algorithms, 5(1):111–137, 2006.
bib | DOI | pdf ]
We present variants of an ant colony optimization (MO-ACO) algorithm and of an evolutionary algorithm (SPEA2) for tackling multi-objective combinatorial optimization problems, hybridized with an iterative improvement algorithm and the robust tabu search algorithm. The performance of the resulting hybrid stochastic local search (SLS) algorithms is experimentally investigated for the bi-objective quadratic assignment problem (bQAP) and compared against repeated applications of the underlying local search algorithms for several scalarizations. The experiments consider structured and unstructured bQAP instances with various degrees of correlation between the flow matrices. We do a systematic experimental analysis of the algorithms using outperformance relations and the attainment functions methodology to asses differences in the performance of the algorithms. The experimental results show the usefulness of the hybrid algorithms if the available computation time is not too limited and identify SPEA2 hybridized with very short tabu search runs as the most promising variant.

[1229]
Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization. In T. Bartz-Beielstein, M. Chiarandini, L. Paquete, and M. Preuss, editors, Experimental Methods for the Analysis of Optimization Algorithms, pages 209–222. Springer, Berlin, Germany, 2010.
bib | DOI ]
This chapter introduces two Perl programs that implement graphical tools for exploring the performance of stochastic local search algorithms for biobjective optimization problems. These tools are based on the concept of the empirical attainment function (EAF), which describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space. In particular, we consider the visualization of attainment surfaces and differences between the first-order EAFs of the outcomes of two algorithms. This visualization allows us to identify certain algorithmic behaviors in a graphical way. We explain the use of these visualization tools and illustrate them with examples arising from practice.

[1230]
Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle. EAF Graphical Tools. http://lopez-ibanez.eu/eaftools, 2010. These tools are described in the book chapter “Exploratory analysis of stochastic local search algorithms in biobjective optimization” [1229].
bib ]
Please cite the book chapter, not this.
[1231]
Manuel López-Ibáñez, Leslie Pérez Cáceres, Jérémie Dubois-Lacoste, Thomas Stützle, and Mauro Birattari. The irace package: User Guide. Technical Report TR/IRIDIA/2016-004, IRIDIA, Université Libre de Bruxelles, Belgium, 2016.
bib | http ]
[1232]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Parallel Optimisation Of Pump Schedules With A Thread-Safe Variant Of EPANET Toolkit. In J. E. van Zyl, A. A. Ilemobade, and H. E. Jacobs, editors, Proceedings of the 10th Annual Water Distribution Systems Analysis Conference (WDSA 2008). ASCE, August 2008.
bib | DOI | pdf ]
[1233]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Ant Colony Optimisation for the Optimal Control of Pumps in Water Distribution Networks. Journal of Water Resources Planning and Management, ASCE, 134(4):337–346, 2008.
bib | DOI | http | pdf ]
Reducing energy consumption of water distribution networks has never had more significance than today. The greatest energy savings can be obtained by careful scheduling of operation of pumps. Schedules can be defined either implicitly, in terms of other elements of the network such as tank levels, or explicitly by specifying the time during which each pump is on/off. The traditional representation of explicit schedules is a string of binary values with each bit representing pump on/off status during a particular time interval. In this paper a new explicit representation is presented. It is based on time controlled triggers, where the maximum number of pump switches is specified beforehand. In this representation a pump schedule is divided into a series of integers with each integer representing the number of hours for which a pump is active/inactive. This reduces the number of potential schedules (search space) compared to the binary representation. Ant colony optimization (ACO) is a stochastic meta-heuristic for combinatorial optimization problems that is inspired by the foraging behavior of some species of ants. In this paper, an application of the ACO framework was developed for the optimal scheduling of pumps. The proposed representation was adapted to an ant colony Optimization framework and solved for the optimal pump schedules. Minimization of electrical cost was considered as the objective, while satisfying system constraints. Instead of using a penalty function approach for constraint violations, constraint violations were ordered according to their importance and solutions were ranked based on this order. The proposed approach was tested on a small test network and on a large real-world network. Results are compared with those obtained using a simple genetic algorithm based on binary representation and a hybrid genetic algorithm that uses level-based triggers.

[1234]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Representations and Evolutionary Operators for the Scheduling of Pump Operations in Water Distribution Networks. Evolutionary Computation, 19(3):429–467, 2011.
bib | DOI ]
Reducing the energy consumption of water distribution networks has never had more significance. The greatest energy savings can be obtained by carefully scheduling the operations of pumps. Schedules can be defined either implicitly, in terms of other elements of the network such as tank levels, or explicitly by specifying the time during which each pump is on/off. The traditional representation of explicit schedules is a string of binary values with each bit representing pump on/off status during a particular time interval. In this paper, we formally define and analyze two new explicit representations based on time-controlled triggers, where the maximum number of pump switches is established beforehand and the schedule may contain less switches than the maximum. In these representations, a pump schedule is divided into a series of integers with each integer representing the number of hours for which a pump is active/inactive. This reduces the number of potential schedules compared to the binary representation, and allows the algorithm to operate on the feasible region of the search space. We propose evolutionary operators for these two new representations. The new representations and their corresponding operations are compared with the two most-used representations in pump scheduling, namely, binary representation and level-controlled triggers. A detailed statistical analysis of the results indicates which parameters have the greatest effect on the performance of evolutionary algorithms. The empirical results show that an evolutionary algorithm using the proposed representations improves over the results obtained by a recent state-of-the-art Hybrid Genetic Algorithm for pump scheduling using level-controlled triggers.

[1235]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Solving Optimal Pump Control Problem using Max-Min Ant System. In D. Thierens et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2007, volume 1, page 176. ACM Press, New York, NY, 2007.
bib | DOI | pdf ]
[1236]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Multi-objective Optimisation of the Pump Scheduling Problem using SPEA2. In Proceedings of the 2005 Congress on Evolutionary Computation (CEC 2005), volume 1, pages 435–442. IEEE Press, Piscataway, NJ, September 2005.
bib | DOI ]
[1237]
Manuel López-Ibáñez, T. Devi Prasad, and Ben Paechter. Optimal Pump Scheduling: Representation and Multiple Objectives. In D. A. Savic, G. A. Walters, R. King, and S. Thiam-Khu, editors, Proceedings of the Eighth International Conference on Computing and Control for the Water Industry (CCWI 2005), volume 1, pages 117–122, University of Exeter, UK, September 2005.
bib | pdf ]
[1238]
Manuel López-Ibáñez and Thomas Stützle. An Analysis of Algorithmic Components for Multiobjective Ant Colony Optimization: A Case Study on the Biobjective TSP. In P. Collet, N. Monmarché, P. Legrand, M. Schoenauer, and E. Lutton, editors, Artificial Evolution: 9th International Conference, Evolution Artificielle, EA, 2009, volume 5975 of Lecture Notes in Computer Science, pages 134–145. Springer, Heidelberg, Germany, 2010.
bib | DOI ]
[1239]
Manuel López-Ibáñez and Thomas Stützle. Automatic Configuration of Multi-Objective ACO Algorithms. In M. Dorigo et al., editors, Swarm Intelligence, 7th International Conference, ANTS 2010, volume 6234 of Lecture Notes in Computer Science, pages 95–106. Springer, Heidelberg, Germany, 2010.
bib | DOI ]
In the last few years a significant number of ant colony optimization (ACO) algorithms have been proposed for tackling multi-objective optimization problems. In this paper, we propose a software framework that allows to instantiate the most prominent multi-objective ACO (MOACO) algorithms. More importantly, the flexibility of this MOACO framework allows the application of automatic algorithm configuration techniques. The experimental results presented in this paper show that such an automatic configuration of MOACO algorithms is highly desirable, given that our automatically configured algorithms clearly outperform the best performing MOACO algorithms that have been proposed in the literature. As far as we are aware, this paper is also the first to apply automatic algorithm configuration techniques to multi-objective stochastic local search algorithms.

[1240]
Manuel López-Ibáñez and Thomas Stützle. The impact of design choices of multi-objective ant colony optimization algorithms on performance: An experimental study on the biobjective TSP. In M. Pelikan and J. Branke, editors, Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2010, pages 71–78. ACM Press, New York, NY, 2010.
bib | DOI ]
Over the last few years, there have been a number of proposals of ant colony optimization (ACO) algorithms for tackling multiobjective combinatorial optimization problems. These proposals adapt ACO concepts in various ways, for example, some use multiple pheromone matrices and multiple heuristic matrices and others use multiple ant colonies.
In this article, we carefully examine several of the most prominent of these proposals. In particular, we identify commonalities among the approaches by recasting the original formulation of the algorithms in different terms. For example, several proposals described in terms of multiple colonies can be cast equivalently using a single ant colony, where ants use different weights for aggregating the pheromone and/or the heuristic information. We study algorithmic choices for the various proposals and we identify previously undetected trade-offs in their performance.

[1241]
Manuel López-Ibáñez and Thomas Stützle. The impact of design choices of multi-objective ant colony optimization algorithms on performance: An experimental study on the biobjective TSP. http://iridia.ulb.ac.be/supp/IridiaSupp2010-003/, 2010. Supplementary material of [1240].
bib ]
[1242]
Manuel López-Ibáñez and Thomas Stützle. The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms: Supplementary material, 2011.
bib | http ]
[1243]
Manuel López-Ibáñez and Thomas Stützle. An experimental analysis of design choices of multi-objective ant colony optimization algorithms: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2012-006/, 2012.
bib ]
[1244]
Manuel López-Ibáñez and Thomas Stützle. An experimental analysis of design choices of multi-objective ant colony optimization algorithms. Swarm Intelligence, 6(3):207–232, 2012.
bib | DOI | supplementary material ]
[1245]
Manuel López-Ibáñez and Thomas Stützle. The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms. IEEE Transactions on Evolutionary Computation, 16(6):861–875, 2012.
bib | DOI ]
Multi-objective optimization problems are problems with several, typically conflicting criteria for evaluating solutions. Without any a priori preference information, the Pareto optimality principle establishes a partial order among solutions, and the output of the algorithm becomes a set of nondominated solutions rather than a single one. Various ant colony optimization (ACO) algorithms have been proposed in recent years for solving such problems. These multi-objective ACO (MOACO) algorithms exhibit different design choices for dealing with the particularities of the multi-objective context. This paper proposes a formulation of algorithmic components that suffices to describe most MOACO algorithms proposed so far. This formulation also shows that existing MOACO algorithms often share equivalent design choices but they are described in different terms. Moreover, this formulation is synthesized into a flexible algorithmic framework, from which not only existing MOACO algorithms may be instantiated, but also combinations of components that were never studied in the literature. In this sense, this paper goes beyond proposing a new MOACO algorithm, but it rather introduces a family of MOACO algorithms. The flexibility of the proposed MOACO framework facilitates the application of automatic algorithm configuration techniques. The experimental results presented in this paper show that the automatically configured MOACO framework outperforms the MOACO algorithms that inspired the framework itself. This paper is also among the first to apply automatic algorithm configuration techniques to multi-objective algorithms.

[1246]
Manuel López-Ibáñez and Thomas Stützle. Automatically Improving the Anytime Behaviour of Optimisation Algorithms. European Journal of Operational Research, 235(3):569–582, 2014.
bib | DOI | pdf | supplementary material ]
Optimisation algorithms with good anytime behaviour try to return as high-quality solutions as possible independently of the computation time allowed. Designing algorithms with good anytime behaviour is a difficult task, because performance is often evaluated subjectively, by plotting the trade-off curve between computation time and solution quality. Yet, the trade-off curve may be modelled also as a set of mutually nondominated, bi-objective points. Using this model, we propose to combine an automatic configuration tool and the hypervolume measure, which assigns a single quality measure to a nondominated set. This allows us to improve the anytime behaviour of optimisation algorithms by means of automatically finding algorithmic configurations that produce the best nondominated sets. Moreover, the recently proposed weighted hypervolume measure is used here to incorporate the decision-maker's preferences into the automatic tuning procedure. We report on the improvements reached when applying the proposed method to two relevant scenarios: (i) the design of parameter variation strategies for MAX-MIN Ant System and (ii) the tuning of the anytime behaviour of SCIP, an open-source mixed integer programming solver with more than 200 parameters.

[1247]
Manuel López-Ibáñez, Thomas Stützle, and Marco Dorigo. Ant Colony Optimization: A Component-Wise Overview. In R. Martí, P. M. Pardalos, and M. G. C. Resende, editors, Handbook of Heuristics, pages 371–407. Springer International Publishing, 2018.
bib | DOI | supplementary material ]
[1248]
Eunice López-Camacho, Hugo Terashima-Marin, Peter Ross, and Gabriela Ochoa. A unified hyper-heuristic framework for solving bin packing problems. Expert Systems with Applications, 41(15):6876–6889, 2014.
bib | DOI ]
[1249]
Manuel López-Ibáñez. Multi-objective Ant Colony Optimization. Diploma thesis, Intellectics Group, Computer Science Department, Technische Universität Darmstadt, Germany, 2004.
bib | pdf ]
[1250]
Manuel López-Ibáñez. Operational Optimisation of Water Distribution Networks. PhD thesis, School of Engineering and the Built Environment, Edinburgh Napier University, UK, 2009.
bib | http ]
[1251]
Ilya Loshchilov, Marc Schoenauer, and Michèle Sebag. Alternative Restart Strategies for CMA-ES. In C. A. Coello Coello et al., editors, Parallel Problem Solving from Nature, PPSN XII, volume 7491 of Lecture Notes in Computer Science, pages 296–305. Springer, Heidelberg, Germany, 2012.
bib | DOI ]
[1252]
A. V. Lotov and Kaisa Miettinen. Visualizing the Pareto Frontier. In J. Branke, K. Deb, K. Miettinen, and R. Slowiński, editors, Multi-objective Optimization: Interactive and Evolutionary Approaches, volume 5252 of Lecture Notes in Computer Science, pages 213–243. Springer, Heidelberg, Germany, 2008.
bib ]
[1253]
Samir Loudni and Patrice Boizumault. Combining VNS with constraint programming for solving anytime optimization problems. European Journal of Operational Research, 191:705–735, 2008.
bib | DOI ]
[1254]
Helena R. Lourenço, Olivier Martin, and Thomas Stützle. Iterated Local Search. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics, pages 321–353. Kluwer Academic Publishers, Norwell, MA, 2002.
bib | DOI ]
[1255]
Helena R. Lourenço, Olivier Martin, and Thomas Stützle. Iterated Local Search: Framework and Applications. In M. Gendreau and J.-Y. Potvin, editors, Handbook of Metaheuristics, volume 146 of International Series in Operations Research & Management Science, chapter 9, pages 363–397. Springer, New York, NY, 2 edition, 2010.
bib | DOI ]
[1256]
Helena R. Lourenço, Olivier Martin, and Thomas Stützle. Iterated Local Search: Framework and Applications. In M. Gendreau and J.-Y. Potvin, editors, Handbook of Metaheuristics, volume 272 of International Series in Operations Research & Management Science, chapter 5, pages 129–168. Springer, 2019.
bib | DOI ]
[1257]
Helena R. Lourenço. Job-Shop Scheduling: Computational Study of Local Search and Large-Step Optimization Methods. European Journal of Operational Research, 83(2):347–364, 1995.
bib ]
[1258]
Antonio Lova and Pilar Tormos. Analysis of Scheduling Schemes and Heuristic Rules Performance in Resource-Constrained Multiproject Scheduling. Annals of Operations Research, 102(1-4):263–286, February 2001.
bib | DOI ]
Frequently, the availability of resources assigned to a project is limited and not sufficient to execute all the concurrent activities. In this situation, decision making about their schedule is necessary. Many times this schedule supposes an increase in the project completion time. Additionally, companies commonly manage various projects simultaneously, sharing a pool of renewable resources. Given these resource constraints, we often can only apply heuristic methods to solve the scheduling problem. In this work the effect of the schedule generation schemes - serial or parallel - and priority rules - MINLFT, MINSLK, MAXTWK, SASP or FCFS - with two approaches - multi-project and single-project - are analysed. The time criteria considered are the mean project delay and the multiproject duration increase. Through an extensive computational study, results show that with the parallel scheduling generation scheme and the multi-project approach the project manager can obtain a good multiproject schedule with the time criterion selected: minimising mean project delay or minimising multiproject duration increase. New heuristics - based on priority rules with a two-phase approach - that outperform classical ones are proposed to minimise mean project delay with a multi-project approach. Finally, the best heuristics analysed are evaluated together with a representative sample of commercial project management software.

Keywords: Combinatorics, heuristic based on priority rules, Multiproject scheduling, Operation Research/Decision Theory, Project management, project management software, Resource allocation, Theory of Computation
[1259]
Antonio Lova, Pilar Tormos, Mariamar Cervantes, and Federico Barber. An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes. International Journal of Production Economics, 117(2):302–316, 2009.
bib | DOI ]
Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) aims at finding the start times and execution modes for the activities of a project that optimize a given objective function while verifying a set of precedence and resource constraints. In this paper, we focus on this problem and develop a hybrid Genetic Algorithm (MM-HGA) to solve it. Its main contributions are the mode assignment procedure, the fitness function and the use of a very efficient improving method. Its performance is demonstrated by extensive computational results obtained on a set of standard instances and against the best currently available algorithms.

Keywords: genetic algorithm, multi-mode resource-constrained project scheduling
[1260]
Manuel Lozano, Fred Glover, Carlos García-Martínez, Francisco J. Rodríguez, and Rafael Martí. Tabu Search with Strategic Oscillation for the Quadratic Minimum Spanning Tree. IIE Transactions, 46(4):414–428, 2014.
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[1261]
Manuel Lozano, Daniel Molina, and Carlos García-Martínez. Iterated Greedy for the Maximum Diversity Problem. European Journal of Operational Research, 214(1):31–38, 2011.
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[1262]
Zhipeng Lü, Fred Glover, and Jin-Kao Hao. A hybrid metaheuristic approach to solving the UBQP problem. European Journal of Operational Research, 207(3):1254–1262, 2010.
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[1263]
M. Lundy and A. Mees. Convergence of an Annealing Algorithm. Mathematical Programming, 34(1):111–124, 1986.
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[1264]
T. Lust and Jacques Teghem. Two-phase Pareto local search for the biobjective traveling salesman problem. Journal of Heuristics, 16(3):475–510, 2010.
bib | DOI ]
In this work, we present a method, called Two-Phase Pareto Local Search, to find a good approximation of the efficient set of the biobjective traveling salesman problem. In the first phase of the method, an initial population composed of a good approximation of the extreme supported efficient solutions is generated. We use as second phase a Pareto Local Search method applied to each solution of the initial population. We show that using the combination of these two techniques: good initial population generation plus Pareto Local Search gives better results than state-of-the-art algorithms. Two other points are introduced: the notion of ideal set and a simple way to produce near-efficient solutions of multiobjective problems, by using an efficient single-objective solver with a data perturbation technique.

[1265]
T. Lust and Jacques Teghem. The multiobjective traveling salesman problem: A survey and a new approach. In C. A. Coello Coello, C. Dhaenens, and L. Jourdan, editors, Advances in Multi-Objective Nature Inspired Computing, volume 272 of Studies in Computational Intelligence, pages 119–141. Springer, 2010.
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[1266]
T. Lust and Jacques Teghem. The multiobjective multidimensional knapsack problem: a survey and a new approach. Arxiv preprint arXiv:1007.4063, 2010.
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Published as [1267]
[1267]
T. Lust and Jacques Teghem. The multiobjective multidimensional knapsack problem: a survey and a new approach. International Transactions in Operational Research, 19(4):495–520, 2012.
bib | DOI ]
[1268]
T. Lust and Andrzej Jaszkiewicz. Speed-up techniques for solving large-scale biobjective TSP. Computers & Operations Research, 37(3):521–533, 2010.
bib | DOI ]
Keywords: Multiobjective combinatorial optimization, Hybrid metaheuristics, TSP, Local search, Speed-up techniques
[1269]
C. von Lücken, Benjamín Barán, and Carlos Brizuela. A survey on multi-objective evolutionary algorithms for many-objective problems. Computational Optimization and Applications, 58(3):707–756, 2014.
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Qingfu Zhang. MOEA/D homepage. https://dces.essex.ac.uk/staff/zhang/webofmoead.htm, 2007.
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Gunther Mäckle, Dragan A. Savic, and Godfrey A. Walters. Application of Genetic Algorithms to Pump Scheduling for Water Supply. In Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA'95, volume 414, pages 400–405, Sheffield, UK, September 1995. IEE Conference Publication.
bib | http ]
A simple Genetic Algorithm has been applied to the scheduling of multiple pumping units in a water supply system with the objective of minimising the overall cost of the pumping operation, taking advantage of storage capacity in the system and the availability of off peak electricity tariffs. A simple example shows that the method is easy to apply and has produced encouraging preliminary results

[1272]
Nateri K. Madavan. Multiobjective optimization using a Pareto differential evolution approach. In D. B. Fogel et al., editors, Proceedings of the 2002 World Congress on Computational Intelligence (WCCI 2002), pages 1145–1150, Piscataway, NJ, 2002. IEEE Press.
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Sam Madden. From Databases to Big Data. IEEE Internet Computing, 16(3), 2012.
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[1274]
M. Mahdavi, M. Fesanghary, and E. Damangir. An improved harmony search algorithm for solving optimization problems. Applied Mathematics and Computation, 188(2):1567–1579, 2007.
bib | DOI ]
This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm has been successfully applied to various benchmarking and standard engineering optimization problems. Numerical results reveal that the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems.

Keywords: Global optimization, Heuristics, Harmony search algorithm, Mathematical programming
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Guilherme B. Mainieri and Débora P. Ronconi. New heuristics for total tardiness minimization in a flexible flowshop. Optimization Letters, pages 1–20, 2012.
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D. R. Broad, Graeme C. Dandy, and Holger R. Maier. A Metamodeling Approach to Water Distribution System Optimization. In 6th Annual Symposium on Water Distribution Systems Analysis. ASCE, June 2004.
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Holger R. Maier, Angus R. Simpson, Aaron C. Zecchin, Wai Kuan Foong, Kuang Yeow Phang, Hsin Yeow Seah, and Chan Lim Tan. Ant Colony Optimization for Design of Water Distribution Systems. Journal of Water Resources Planning and Management, ASCE, 129(3):200–209, May / June 2003.
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Yuri Malitsky and Meinolf Sellmann. Instance-specific algorithm configuration as a method for non-model-based portfolio generation. In N. Beldiceanu, N. Jussien, and E. Pinson, editors, Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimization Problems, volume 7298 of Lecture Notes in Computer Science, pages 244–259. Springer, Heidelberg, Germany, 2012.
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Yuri Malitsky, Deepak Mehta, Barry O’Sullivan, and Helmut Simonis. Tuning parameters of large neighborhood search for the machine reassignment problem. In G. C. and S. M., editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2010, volume 7874 of Lecture Notes in Computer Science, pages 176–192. Springer, Heidelberg, Germany, 2013.
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Vittorio Maniezzo. Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem. INFORMS Journal on Computing, 11(4):358–369, 1999.
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Vittorio Maniezzo, M. Boschetti, and M. Jelasity. An Ant Approach to Membership Overlay Design. In M. Dorigo et al., editors, Ant Colony Optimization and Swarm Intelligence, 4th International Workshop, ANTS 2004, volume 3172 of Lecture Notes in Computer Science, pages 37–48. Springer, Heidelberg, Germany, 2004.
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Vittorio Maniezzo and A. Carbonaro. An ANTS Heuristic for the Frequency Assignment Problem. Future Generation Computer Systems, 16(8):927–935, 2000.
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Vittorio Maniezzo and Alberto Colorni. The Ant System Applied to the Quadratic Assignment Problem. IEEE Transactions on Knowledge and Data Engineering, 11(5):769–778, 1999.
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Vittorio Maniezzo and M. Milandri. An Ant-Based Framework for Very Strongly Constrained Problems. In M. Dorigo et al., editors, Ant Algorithms, Third International Workshop, ANTS 2002, volume 2463 of Lecture Notes in Computer Science, pages 222–227. Springer, Heidelberg, Germany, 2002.
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Christopher D. Manning, Mihai Surdeanu, John Bauer, Jenny Rose Finkel, Steven J. Bethard, and David McClosky. The Stanford CoreNLP Natural Language Processing Toolkit. In Association for Computational Linguistics (ACL) System Demonstrations, pages 55–60, 2014.
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F. Martínez, V. Bou, V. Hernández, F. Alvarruiz, and J. M. Alonso. ANN Architectures for Simulating Water Distribution Networks. In D. A. Savic, G. A. Walters, R. King, and S. Thiam-Khu, editors, Proceedings of the Eighth International Conference on Computing and Control for the Water Industry (CCWI 2005), volume 1, pages 251–256, University of Exeter, UK, September 2005.
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Marie-Eléonore Marmion, Franco Mascia, Manuel López-Ibáñez, and Thomas Stützle. Automatic Design of Hybrid Stochastic Local Search Algorithms. In M. J. Blesa, C. Blum, P. Festa, A. Roli, and M. Sampels, editors, Hybrid Metaheuristics, volume 7919 of Lecture Notes in Computer Science, pages 144–158. Springer, Heidelberg, Germany, 2013.
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Oded Maron and Andrew W. Moore. Hoeffding races: Accelerating model selection search for classification and function approximation. In J. D. Cowan, G. Tesauro, and J. Alspector, editors, Advances in Neural Information Processing Systems, volume 6, pages 59–66. Morgan Kaufmann Publishers, San Francisco, CA, 1994.
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Federico Pagnozzi and Thomas Stützle. Automatic Design of Hybrid Stochastic Local Search Algorithms for Permutation Flowshop Problems. Technical Report TR/IRIDIA/2018-005, IRIDIA, Université Libre de Bruxelles, Belgium, April 2018.
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Federico Pagnozzi and Thomas Stützle. Automatic Design of Hybrid Stochastic Local Search Algorithms for Permutation Flowshop Problems: Supplementary Material. http://iridia.ulb.ac.be/supp/IridiaSupp2018-002/, 2018.
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Federico Pagnozzi and Thomas Stützle. Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems. European Journal of Operational Research, 276:409–421, 2019.
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Federico Pagnozzi and Thomas Stützle. Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems with additional constraints. http://iridia.ulb.ac.be/supp/IridiaSupp2018-002/, 2019.
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[1501]
Luís Paquete. Algoritmos Evolutivos Multiobjectivo para Afectação de Recursos e sua Aplicação à Geração de Horários em Universidades (Multiobjective Evolutionary Algorithms for Resource Allocation and their Application to University Timetabling). Master's thesis, University of Algarve, 2001. In Portuguese.
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The aim of this study is the application of multiobjective evolutionary algorithms to resource allocation problems, such as university examination timetabling and course timetabling problems. Usually, these problems are characterized by multiple conflicting objectives. A multiobjective formalization of these problems is presented, based on goals and priorities. Various aspects of evolutionary algorithms are proposed and studied for these problems, particulary, selection methods and types and parameters of mutation operator. The choice of both representation and operators is made so as not to favour excessively certain objectives with respect to others at the level of the exploration mechanism. A comparative study of performance is presented for the proposed algorithms by means of statistical inference, based on real problems of the University of Algarve. The notion of attainment functions is used as a base for the assessment of performance of multiobjective evolutionary algorithms. Finally, the evolution of the solution cost during the runs is analysed by means of attainment functions, as well.

[1502]
Luís Paquete. Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: Methods and Analysis. PhD thesis, FB Informatik, TU Darmstadt, Germany, 2005.
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Luís Paquete, Marco Chiarandini, and Thomas Stützle. Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study. In X. Gandibleux, M. Sevaux, K. Sörensen, and V. T'Kindt, editors, Metaheuristics for Multiobjective Optimisation, volume 535 of Lecture Notes in Economics and Mathematical Systems, pages 177–199. Springer, Berlin, Germany, 2004.
bib | DOI ]
In this article, we study Pareto local optimum sets for the biobjective Traveling Salesman Problem applying straightforward extensions of local search algorithms for the single objective case. The performance of the local search algorithms is illustrated by experimental results obtained for well known benchmark instances and comparisons to methods from literature. In fact, a 3-opt local search is able to compete with the best performing metaheuristics in terms of solution quality. Finally, we also present an empirical study of the features of the solutions found by 3-opt on a set of randomly generated instances. The results indicate the existence of several clusters of near-optimal solutions that are separated by only a few edges.

Keywords: Pareto local search, PLS
[1504]
Luís Paquete, Carlos M. Fonseca, and Manuel López-Ibáñez. An optimal algorithm for a special case of Klee's measure problem in three dimensions. Technical Report CSI-RT-I-01/2006, CSI, Universidade do Algarve, 2006. Superseded by paper in IEEE Transactions on Evolutionary Computation [172].
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The measure of the region dominated by (the maxima of) a set of n points in the positive d-orthant has been proposed as an indicator of performance in multiobjective optimization, known as the hypervolume indicator, and the problem of computing it efficiently is attracting increasing attention. In this report, this problem is formulated as a special case of Klee's measure problem in d dimensions, which immediately establishes O(nd/2logn) as a, possibly conservative, upper bound on the required computation time. Then, an O(n log n) algorithm for the 3-dimensional version of this special case is constructed, based on an existing dimension-sweep algorithm for the related maxima problem. Finally, O(n log n) is shown to remain a lower bound on the time required by the hypervolume indicator for d>1, which attests the optimality of the algorithm proposed.

Proof of Theorem 3.1 is incorrect
[1505]
Luís Paquete, Tommaso Schiavinotto, and Thomas Stützle. On Local Optima in Multiobjective Combinatorial Optimization Problems. Annals of Operations Research, 156:83–97, 2007.
bib | DOI ]
In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.

Keywords: Pareto local search, PLS
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Luís Paquete and Thomas Stützle. A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. European Journal of Operational Research, 169(3):943–959, 2006.
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Luís Paquete and Thomas Stützle. Clusters of non-dominated solutions in multiobjective combinatorial optimization: An experimental analysis. In V. Barichard, M. Ehrgott, X. Gandibleux, and V. T'Kindt, editors, Multiobjective Programming and Goal Programming: Theoretical Results and Practical Applications, volume 618 of Lecture Notes in Economics and Mathematical Systems, pages 69–77. Springer, Berlin, 2009.
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[1508]
Luís Paquete and Thomas Stützle. Design and analysis of stochastic local search for the multiobjective traveling salesman problem. Computers & Operations Research, 36(9):2619–2631, 2009.
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[1509]
Luís Paquete and Thomas Stützle. An Experimental Investigation of Iterated Local Search for Coloring Graphs. In S. Cagnoni et al., editors, Applications of Evolutionary Computing, Proceedings of EvoWorkshops 2002, volume 2279 of Lecture Notes in Computer Science, pages 122–131. Springer, Heidelberg, Germany, 2002.
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Luís Paquete and Thomas Stützle. A Two-Phase Local Search for the Biobjective Traveling Salesman Problem. In C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors, Evolutionary Multi-criterion Optimization, EMO 2003, volume 2632 of Lecture Notes in Computer Science, pages 479–493. Springer, Heidelberg, Germany, 2003.
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Luís Paquete, Thomas Stützle, and Manuel López-Ibáñez. On the design and analysis of SLS algorithms for multiobjective combinatorial optimization problems. Technical Report TR/IRIDIA/2005-029, IRIDIA, Université Libre de Bruxelles, Belgium, 2005.
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Effective Stochastic Local Search (SLS) algorithms can be seen as being composed of several algorithmic components, each of which plays some specific role with respect to overall performance. In this article, we explore the application of experimental design techniques to analyze the effect of different choices for these algorithmic components on SLS algorithms applied to Multiobjective Combinatorial Optimization Problems that are solved in terms of Pareto optimality. This analysis is done using the example application of SLS algorithms to the biobjective Quadratic Assignment Problem and we show also that the same choices for algorithmic components can lead to different behavior in dependence of various instance features, such as the structure of input data and the correlation between objectives.

[1512]
Luís Paquete, Thomas Stützle, and Manuel López-Ibáñez. Towards the Empirical Analysis of SLS Algorithms for Multiobjective Combinatorial Optimization Problems through Experimental Design. In K. F. Doerner, M. Gendreau, P. Greistorfer, W. J. Gutjahr, R. F. Hartl, and M. Reimann, editors, 6th Metaheuristics International Conference (MIC 2005), pages 739–746, Vienna, Austria, 2005.
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Stochastic Local Search (SLS) algorithms for Multiobjective Combinatorial Optimization Problems (MCOPs) typically involve the selection and parameterization of many algorithm components whose role with respect to their overall performance and relation to certain instance features is often not clear. In this abstract, we use a modular approach for the design of SLS algorithms for MCOPs defined in terms of Pareto optimality and we present an extensive analysis of SLS algorithms through experimental design techniques, where each algorithm component is considered a factor. The experimental analysis is based on a sound experimental methodology for analyzing the output of algorithms for MCOPs. We show that different choices for algorithm components can lead to different behavior in dependence of various instance features.

[1513]
Luís Paquete, Thomas Stützle, and Manuel López-Ibáñez. Using experimental design to analyze stochastic local search algorithms for multiobjective problems. In K. F. Doerner, M. Gendreau, P. Greistorfer, W. J. Gutjahr, R. F. Hartl, and M. Reimann, editors, Metaheuristics: Progress in Complex Systems Optimization, volume 39 of Operations Research / Computer Science Interfaces, pages 325–344. Springer, New York, NY, 2007.
bib | DOI ]
Stochastic Local Search (SLS) algorithms can be seen as being composed of several algorithmic components, each playing some specific role with respect to overall performance. This article explores the application of experimental design techniques to analyze the effect of components of SLS algorithms for Multiobjective Combinatorial Optimization problems, in particular for the Biobjective Quadratic Assignment Problem. The analysis shows that there exists a strong dependence between the choices for these components and various instance features, such as the structure of the input data and the correlation between the objectives.

Post-Conference Proceedings of the 6th Metaheuristics International Conference (MIC 2005)
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Paola Pellegrini, Thomas Stützle, and Mauro Birattari. Off-line vs. On-line Tuning: A Study on Max-Min Ant System for the TSP. In M. Dorigo et al., editors, Swarm Intelligence, 7th International Conference, ANTS 2010, volume 6234 of Lecture Notes in Computer Science, pages 239–250. Springer, Heidelberg, Germany, 2010.
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Leslie Pérez Cáceres, Bernd Bischl, and Thomas Stützle. Evaluating random forest models for irace. In P. A. N. Bosman, editor, GECCO'17 Companion, pages 1146–1153, New York, NY, 2017. ACM Press.
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Leslie Pérez Cáceres, Manuel López-Ibáñez, Holger H. Hoos, and Thomas Stützle. An experimental study of adaptive capping in irace. In R. Battiti, D. E. Kvasov, and Y. D. Sergeyev, editors, Learning and Intelligent Optimization, 11th International Conference, LION 11, volume 10556 of Lecture Notes in Computer Science, pages 235–250. Springer, Cham, Switzerland, 2017.
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Leslie Pérez Cáceres, Manuel López-Ibáñez, and Thomas Stützle. An Analysis of Parameters of irace. In C. Blum and G. Ochoa, editors, Proceedings of EvoCOP 2014 – 14th European Conference on Evolutionary Computation in Combinatorial Optimization, volume 8600 of Lecture Notes in Computer Science, pages 37–48. Springer, Heidelberg, Germany, 2014.
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Leslie Pérez Cáceres, Manuel López-Ibáñez, and Thomas Stützle. Ant Colony Optimization on a Budget of 1000: Supplementary material, 2015.
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Leslie Pérez Cáceres, Manuel López-Ibáñez, and Thomas Stützle. Ant colony optimization on a limited budget of evaluations. Swarm Intelligence, 9(2-3):103–124, 2015.
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Leslie Pérez Cáceres, Federico Pagnozzi, Alberto Franzin, and Thomas Stützle. Automatic Configuration of GCC Using Irace. In E. Lutton, P. Legrand, P. Parrend, N. Monmarché, and M. Schoenauer, editors, EA 2017: Artificial Evolution, volume 10764 of Lecture Notes in Computer Science, pages 202–216. Springer, Heidelberg, Germany, 2017.
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Automatic algorithm configuration techniques have proved to be successful in finding performance-optimizing parameter settings of many search-based decision and optimization algorithms. A recurrent, important step in software development is the compilation of source code written in some programming language into machine-executable code. The generation of performance-optimized machine code itself is a difficult task that can be parametrized in many different possible ways. While modern compilers usually offer different levels of optimization as possible defaults, they have a larger number of other flags and numerical parameters that impact properties of the generated machine-code. While the generation of performance-optimized machine code has received large attention and is dealt with in the research area of auto-tuning, the usage of standard automatic algorithm configuration software has not been explored, even though, as we show in this article, the performance of the compiled code has significant stochasticity, just as standard optimization algorithms. As a practical case study, we consider the configuration of the well-known GNU compiler collection (GCC) for minimizing the run-time of machine code for various heuristic search methods. Our experimental results show that, depending on the specific code to be optimized, improvements of up to 40% of execution time when compared to the -O2 and -O3 optimization flags is possible.

[1543]
Leslie Pérez Cáceres, Federico Pagnozzi, Alberto Franzin, and Thomas Stützle. Automatic configuration of GCC using irace: Supplementary material. http://iridia.ulb.ac.be/supp/IridiaSupp2017-009/, 2017.
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Matias Péres, Germán Ruiz, Sergio Nesmachnow, and Ana C. Olivera. Multiobjective evolutionary optimization of traffic flow and pollution in Montevideo, Uruguay. Applied Soft Computing, 70:472–485, 2018.
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Keywords: Multiobjective evolutionary algorithms,Pollution,Simulation,Traffic flow
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Pedro Pinto, Thomas Runkler, and João Sousa. Ant Colony Optimization and its Application to Regular and Dynamic MAX-SAT Problems. In Advances in Biologically Inspired Information Systems, volume 69 of Studies in Computational Intelligence, pages 285–304. Springer, Berlin, Germany, 2007.
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In this chapter we discuss the ant colony optimization meta-heuristic (ACO) and its application to static and dynamic constraint satisfaction optimization problems, in particular the static and dynamic maximum satisfiability problems (MAX-SAT). In the first part of the chapter we give an introduction to meta-heuristics in general and ant colony optimization in particular, followed by an introduction to constraint satisfaction and static and dynamic constraint satisfaction optimization problems. Then, we describe how to apply the ACO algorithm to the problems, and do an analysis of the results obtained for several benchmarks. The adapted ant colony optimization accomplishes very well the task of dealing with systematic changes of dynamic MAX-SAT instances derived from static problems.

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Rapeepan Pitakaso, Christian Almeder, Karl F. Doerner, and Richard F. Hartl. Combining exact and population-based methods for the Constrained Multilevel Lot Sizing Problem. International Journal of Production Research, 44(22):4755–4771, 2006.
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Rapeepan Pitakaso, Christian Almeder, Karl F. Doerner, and Richard F. Hartl. A Max-Min Ant System for unconstrained multi-level lot-sizing problems. Computers & Operations Research, 34(9):2533–2552, 2007.
bib | DOI ]
In this paper, we present an ant-based algorithm for solving unconstrained multi-level lot-sizing problems called ant system for multi-level lot-sizing algorithm (ASMLLS). We apply a hybrid approach where we use ant colony optimization in order to find a good lot-sizing sequence, i.e. a sequence of the different items in the product structure in which we apply a modified Wagner-Whitin algorithm for each item separately. Based on the setup costs each ant generates a sequence of items. Afterwards a simple single-stage lot-sizing rule is applied with modified setup costs. This modification of the setup costs depends on the position of the item in the lot-sizing sequence, on the items which have been lot-sized before, and on two further parameters, which are tried to be improved by a systematic search. For small-sized problems ASMLLS is among the best algorithms, but for most medium- and large-sized problems it outperforms all other approaches regarding solution quality as well as computational time.

Keywords: Ant colony optimization, Material requirements planning, Multi-level lot-sizing, Wagner-Whitin algorithm
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This paper presents a scenario-based Multi-Objective structure to handle decision problems under deep uncertainty. Most of the decisions in real-life problems need to be made in the absence of complete knowledge about the consequences of the decision and/or are characterised by uncertainties about the future which is unpredictable. These uncertainties are almost impossible to reduce by gathering more information and are not statistical in nature. Therefore, classical probability-based approaches, such as stochastic programming, do not address these problems; as they require a correctly-defined complete sample space, strong assumptions (e.g. normality), or both. The proposed method extends the concept of two-stage stochastic programming with recourse to address the capability of dealing with deep uncertainty through the use of scenario planning rather than statistical expectation. In this research, scenarios are used as a dimension of preference to avoid problems relating to the assessment and use of probabilities under deep uncertainty. Such scenario-based thinking involved a multi-objective representation of performance under different future conditions as an alternative to expectation. To the best of our knowledge, this is the first attempt of performing a multi-criteria evaluation under deep uncertainty through a structured optimisation model. The proposed structure replacing probabilities (in dynamic systems with deep uncertainties) by aspirations within a goal programming structure. In fact, this paper also proposes an extension of the goal programming paradigm to deal with deep uncertainty. Furthermore, we will explain how this structure can be modelled, implemented, and solved by Goal Programming using some simple, but not trivial, examples. Further discussion and comparisons with some popular existing methods will also provided to highlight the superiorities of the proposed structure.

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Operation of pumping stations represents high costs to water supply companies. Therefore, reducing such costs through an optimal pump scheduling becomes an important issue. This work presents the use of Multiobjective Evolutionary Algorithms (MOEAs) to solve an optimal pump-scheduling problem. For the first time, six different approaches were implemented and compared. These algorithms aim to minimise four objectives: electric energy cost, pumps' maintenance cost, maximum power peak, and level variation in the reservoir. In order to consider hydraulic and technical constrains, a heuristic constrain algorithm was developed and combined with each MOEA utilised. Evaluation of experimental results of a set of metrics shows that the Strength Pareto Evolutionary Algorithm (SPEA) achieves the best performance for this problem. Moreover, SPEA's set of solutions provide pumping station operation engineers with a wide range of optimal pump schedules to chose from.

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We consider the resource-constrained project scheduling problem (RCPSP). The focus of the paper is on a formal definition of semi-active, active, and non-delay schedules. Traditionally these schedules establish basic concepts within the job shop scheduling literature. There they are usually defined in a rather informal way which does not create any substantial problems. Using these concepts in the more general RCPSP without giving a formal definition may cause serious problems. After providing a formal definition of semi-active, active, and non-delay schedules for the RCPSP we outline some of these problems occurring within the disjunctive arc concept.

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This article presents an innovative approach to solve one of the most relevant problems related to smart mobility: the reduction of vehicles' travel time. Our original approach, called Red Swarm, suggests a potentially customized route to each vehicle by using several spots located at traffic lights in order to avoid traffic jams by using {V2I} communications. That is quite different from other existing proposals, as it deals with real maps and actual streets, as well as several road traffic distributions. We propose an evolutionary algorithm (later efficiently parallelized) to optimize our case studies which have been imported from OpenStreetMap into {SUMO} as they belong to a real city. We have also developed a Rerouting Algorithm which accesses the configuration of the Red Swarm and communicates the route chosen to vehicles, using the spots (via WiFi link). Moreover, we have developed three competing algorithms in order to compare their results to those of Red Swarm and have observed that Red Swarm not only achieved the best results, but also outperformed the experts' solutions in a total of 60 scenarios tested, with up to 19% shorter travel times.

Keywords: Evolutionary algorithm,Road traffic,Smart city,Smart mobility,Traffic light,WiFi connections
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In this article we present a strategy based on an evolution- ary algorithm to calculate the real vehicle flows in cities according to data from sensors placed in the streets. We have worked with a map imported from OpenStreetMap into the SUMO traffic simulator so that the resulting scenarios can be used to perform different optimizations with the confidence of being able to work with a traffic distribution close to reality. We have compared the results of our algorithm to other competitors and achieved results that replicate the real traffic distribution with a precision higher than 90%.

Keywords: Evolutionary algorithm,SUMO,Smart city,Smart mobility,Traffic simulation
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Thomas Stützle and Holger H. Hoos. Max-Min Ant System. Future Generation Computer Systems, 16(8):889–914, 2000.
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Thomas Stützle and Holger H. Hoos. The Max-Min Ant System and Local Search for the Traveling Salesman Problem. In T. Bäck, Z. Michalewicz, and X. Yao, editors, Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC'97), pages 309–314. IEEE Press, Piscataway, NJ, 1997.
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Thomas Stützle and Holger H. Hoos. Max-Min Ant System and Local Search for Combinatorial Optimization Problems. In S. Voß, S. Martello, I. H. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 137–154. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
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Thomas Stützle and Manuel López-Ibáñez. Automatic (Offline) Configuration of Algorithms. In J. L. J. Laredo, S. Silva, and A. I. Esparcia-Alcázar, editors, GECCO (Companion), pages 681–702. ACM Press, New York, NY, 2015.
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Thomas Stützle and Manuel López-Ibáñez. Automated Offline Design of Algorithms. In P. A. N. Bosman, editor, GECCO'17 Companion, pages 1038–1065. ACM Press, New York, NY, 2017.
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Thomas Stützle and Manuel López-Ibáñez. Automated Design of Metaheuristic Algorithms. In M. Gendreau and J.-Y. Potvin, editors, Handbook of Metaheuristics, volume 272 of International Series in Operations Research & Management Science, pages 541–579. Springer, 2019.
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Thomas Stützle, Manuel López-Ibáñez, and Marco Dorigo. A Concise Overview of Applications of Ant Colony Optimization. In J. J. Cochran, editor, Wiley Encyclopedia of Operations Research and Management Science, volume 2, pages 896–911. John Wiley & Sons, 2011.
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Thomas Stützle and Rubén Ruiz. Iterated Greedy. In R. Martí, P. M. Pardalos, and M. G. C. Resende, editors, Handbook of Heuristics, pages 1–31. Springer International Publishing, 2018.
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Thomas Stützle and Rubén Ruiz. Iterated Local Search. In R. Martí, P. M. Pardalos, and M. G. C. Resende, editors, Handbook of Heuristics, pages 1–27. Springer International Publishing, 2018.
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Thomas Stützle. Local Search Algorithms for Combinatorial Problems — Analysis, Improvements, and New Applications. PhD thesis, FB Informatik, TU Darmstadt, Germany, 1998.
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We consider sequential decision problems under uncertainty, where we seek to optimize an unknown function from noisy samples. This requires balancing exploration (learning about the objective) and exploitation (localizing the maximum), a problem well-studied in the multi-armed bandit literature. In many applications, however, we require that the sampled function values exceed some prespecified "safety" threshold, a requirement that existing algorithms fail to meet. Examples include medical applications where patient comfort must be guaranteed, recommender systems aiming to avoid user dissatisfaction, and robotic control, where one seeks to avoid controls causing physical harm to the platform. We tackle this novel, yet rich, set of problems under the assumption that the unknown function satisfies regularity conditions expressed via a Gaussian process prior. We develop an efficient algorithm called SafeOpt, and theoretically guarantee its convergence to a natural notion of optimum reachable under safety constraints. We evaluate SafeOpt on synthetic data, as well as two real applications: movie recommendation, and therapeutic spinal cord stimulation.

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Enforcing safety is a key aspect of many problems pertaining to sequential decision making under uncertainty, which require the decisions made at every step to be both informative of the optimal decision and also safe. For example, we value both efficacy and comfort in medical therapy, and efficiency and safety in robotic control. We consider this problem of optimizing an unknown utility function with absolute feedback or preference feedback subject to unknown safety constraints. We develop an efficient safe Bayesian optimization algorithm, StageOpt, that separates safe region expansion and utility function maximization into two distinct stages. Compared to existing approaches which interleave between expansion and optimization, we show that StageOpt is more efficient and naturally applicable to a broader class of problems. We provide theoretical guarantees for both the satisfaction of safety constraints as well as convergence to the optimal utility value. We evaluate StageOpt on both a variety of synthetic experiments, as well as in clinical practice. We demonstrate that StageOpt is more effective than existing safe optimization approaches, and is able to safely and effectively optimize spinal cord stimulation therapy in our clinical experiments.

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The application of multi-objective optimisation to evolutionary robotics is receiving increasing attention. A survey of the literature reveals the different possibilities it offers to improve the automatic design of efficient and adaptive robotic systems, and points to the successful demonstrations available for both task-specific and task-agnostic approaches (i.e., with or without reference to the specific design problem to be tackled). However, the advantages of multi-objective approaches over single-objective ones have not been clearly spelled out and experimentally demonstrated. This paper fills this gap for task-specific approaches: starting from well-known results in multi-objective optimisation, we discuss how to tackle commonly recognised problems in evolutionary robotics. In particular, we show that multi-objective optimisation (i) allows evolving a more varied set of behaviours by exploring multiple trade-offs of the objectives to optimise, (ii) supports the evolution of the desired behaviour through the introduction of objectives as proxies, (iii) avoids the premature convergence to local optima possibly introduced by multi-component fitness functions, and (iv) solves the bootstrap problem exploiting ancillary objectives to guide evolution in the early phases. We present an experimental demonstration of these benefits in three different case studies: maze navigation in a single robot domain, flocking in a swarm robotics context, and a strictly collaborative task in collective robotics.

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We present a reinforcement learning approach to explore and optimize a safety-constrained Markov Decision Process(MDP). In this setting, the agent must maximize discounted cumulative reward while constraining the probability of entering unsafe states, defined using a safety function being within some tolerance. The safety values of all states are not known a priori, and we probabilistically model them via a Gaussian Process (GP) prior. As such, properly behaving in such an environment requires balancing a three-way trade-off of exploring the safety function, exploring the reward function, and exploiting acquired knowledge to maximize reward. We propose a novel approach to balance this trade-off. Specifically, our approach explores unvisited states selectively; that is, it prioritizes the exploration of a state if visiting that state significantly improves the knowledge on the achievable cumulative reward. Our approach relies on a novel information gain criterion based on Gaussian Process representations of the reward and safety functions. We demonstrate the effectiveness of our approach on a range of experiments, including a simulation using the real Martian terrain data.

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