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Hybrid Metaheuristics for Multi-objective Combinatorial Optimization

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Hybrid Metaheuristics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 114))

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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References

  1. P. Agrell, M. Sun, and A. Stam. A tabu search multi-criteria decision model for facility location planning. In Proceedings of the 1997 DSI Annual Meeting, San Diego, California, volume 2, pages 908–910. Decision Sciences Institute, Atlanta, GA, 1997.

    Google Scholar 

  2. M. J. Alves and J. Climaco. An interactive method for 0–1 multiobjective problems using simulated annealing and tabu search. Journal of Heuristics, 6(3):385–403, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Angel, E. Bampis, and L. Gourvès. Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem. Theoretical Computer Science, 310:135–146, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  4. V. A. Armentano and J. E. C. Arroyo. An application of a multi-objective tabu search algorithm to a bicriteria flowshop problem. Journal of Heuristics, 10:463–481, 2004.

    Article  MATH  Google Scholar 

  5. V. Barichard and J.-K. Hao. Un algorithme hybride pour le problème de sac à dos multi-objectifs. In Huitièmes Journées Nationales sur la Résolution Pratique de Problèmes NP-Complets JNPC’2002 Proceedings, 2002. Nice, France, 27–29 May.

    Google Scholar 

  6. V. Barichard and J.-K. Hao. A population and interval constraint propagation algorithm. In G. Goos, J. Hartmanis, and J. van Leeuwen, editors, Evolutionary Multi-Criterion Optimization: Second International Conference, EMO 2003, Faro, Portugal, April 8–11, 2003. Proceedings, volume 2632 of Lecture Notes in Computer Science, pages 88–101. Springer-Verlag, Berlin, Germany, 2003.

    Google Scholar 

  7. V. Barichard and J.-K. Hao. A population and interval constraint propagation algorithm for mulitobjective optimization. In Proceedings of The Fifth Metaheuristics International Conference MIC’03, paper ID MIC03–04. CD ROM, 2003.

    Google Scholar 

  8. R. Beausoleil. Multiple criteria scatter search. In J. P. de Sousa, editor, MIC 2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16-20, 2001, volume 2, pages 539–543, 2001.

    Google Scholar 

  9. F. Ben Abdelaziz, J. Chaouachi, and S. Krichen. A hybrid heuristic for multiobjective knapsack problems. In S. Voß, S. Martello, I. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 205–212. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.

    Google Scholar 

  10. W. M. Carlyle, J. W. Fowler, E. S. Gel, and B. Kim. Quantitative comparison of approximate solution sets for bi-criteria optimization problems. Decision Sciences, 34(1):63–82, 2003.

    Article  Google Scholar 

  11. R. L. Carraway, T. L. Morin, and H. Moskovitz. Generalized dynamic programming for multicriteria optimization. European Journal of Operational Research, 44:95–104, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Chen, K. Subprasom, and Z. Ji. A simulation-based multi-objective genetic algorithm (SMOGA) procedure for BOT network design. Optimization and Engineering, 7:225–247, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. A. Coello. A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowledge and Information Systems, 1(3):269–308, 1999.

    Google Scholar 

  14. C. A. Coello. An updated survey of GA-based multiobjective optimization techniques. ACM Computing Surveys, 32(2):109–143, 2000.

    Article  Google Scholar 

  15. Y. Collette and P. Siarry. Three new metrics to measure the convergence of metaheuristics towards the Pareto frontier and the aesthetic of a set of solutions in biobjcetive optimization. Computers and Operations Research, 32:773–792, 2005.

    Article  MATH  Google Scholar 

  16. P. Czyżak and A. Jaszkiewicz. A multiobjective metaheuristic approach to the localization of a chain of petrol stations by the capital budgeting model. Control and Cybernetics, 25(1):177–187, 1996.

    MATH  Google Scholar 

  17. P. Czyżak and A. Jaszkiewicz. Pareto simulated annealing. In G. Fandel and T. Gal, editors, Multiple Criteria Decision Making. Proceedings of the XIIth International Conference, Hagen (Germany), volume 448 of Lecture Notes in Economics and Mathematical Systems, pages 297–307. Springer-Verlag, Berlin, Germany, 1997.

    Google Scholar 

  18. P. Czyżak and A. Jaszkiewicz. Pareto simulated annealing – A metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7(1):34–47, 1998.

    Article  MATH  Google Scholar 

  19. X. Delorme, X. Gandibleux, and F. Degoutin. Evolutionary, constructive and hybrid procedures for the biobjective set packing problem. September 2005. In revision (European Journal of Operational Research) Research report EMSE 2005-500-011, Ecole des Mines de Saint-Etienne, 2005.

    Google Scholar 

  20. X. Delorme, X. Gandibleux, and J. Rodriguez. Résolution d’un problème d’évaluation de capacité d’infrastructure ferroviaire. In Actes du colloque sur l’innovation technologique pour les transports terrestres (TILT), volume 2, pages 647–654. GRRT Lille, 2003.

    Google Scholar 

  21. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer. Ant colony optimization in multiobjective portfolio selection. In J. P. de Sousa, editor, MIC’2001 Proceedings of the 4th Metaheurstics International Conference, Porto, July16-20, 2001, volume 1, pages 243–248, 2001.

    Google Scholar 

  22. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer. Investitionsentscheidungen bei mehrfachen Zielsetzungen und künstliche Ameisen. In P. Chamoni, R. Leisten, A. Martin, J. Minnemann, and H. Stadtler, editors, Operations Research Proceedings 2001, Selected Papers of OR 2001, pages 355–362. Springer-Verlag, Berlin, Germany, 2002.

    Google Scholar 

  23. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer. Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Annals of Operations Research, 131:79–99, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  24. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer. Pareto ant colony optimization with ILP preprocessing in multiobjective portfolio selection. European Journal of Operational Research, 171:830–841, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  25. K. Doerner, R. F. Hartl, and M. Reimann. Are COMPETants more competent for problem solving? The case of a multiple objective transportation problem. In L. Lee Spector, A. D. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M. H. Garzon, and E. Burke, editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), page 802. Morgan Kaufmann, San Francisco, CA, 2001.

    Google Scholar 

  26. M. Ehrgott. Approximation algorithms for combinatorial multicriteria optimization problems. International Transcations in Operational Research, 7:5–31, 2000.

    Article  MathSciNet  Google Scholar 

  27. M. Ehrgott and X. Gandibleux. A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum, 22:425–460, 2000.

    MATH  MathSciNet  Google Scholar 

  28. M. Ehrgott and X. Gandibleux. Multiobjective combinatorial optimization. In M. Ehrgott and X. Gandibleux, editors, Multiple Criteria Optimization – State of the Art Annotated Bibliographic Surveys, volume 52 of Kluwer’s International Series in Operations Research & Management Science, pages 369–444. Kluwer Academic Publishers, Boston, MA, 2002.

    Google Scholar 

  29. M. Ehrgott and X. Gandibleux, editors. Multiple Criteria Optimization – State of the Art Annotated Bibliographic Surveys, volume 52 of Kluwer’s International Series in Operations Research and Management Science. Kluwer Academic Publishers, Boston, MA, 2002.

    MATH  Google Scholar 

  30. M. Ehrgott and X. Gandibleux. Approximative solution methods for multiobjective combinatorial optimization. TOP, 12(1):1–88, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  31. M. Ehrgott and X. Gandibleux. Bound sets for biobjective combinatorial optimization problems. Computers & Operations Research, 34:2674–2694, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  32. M. Ehrgott, K. Klamroth, and S. Schwehm. An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3):752–770, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  33. M. Ehrgott and D. M. Ryan. Constructing robust crew schedules with bicriteria optimization. Journal of Multi-Criteria Decision Analysis, 11:139–150, 2002.

    Article  MATH  Google Scholar 

  34. M. Ehrgott and D. Tenfelde-Podehl. Computation of ideal and nadir values and implications for their use in MCDM methods. European Journal of Operational Research, 151(1):119–131, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  35. M. Ehrgott and M. Wiecek. Multiobjective programming. In J. Figueira, S. Greco, and M. Ehrgott, editors, Multicriteria Decision Analysis: State of the Art Surveys, pages 667–722. Springer Science + Business Media, New York, 2005.

    Google Scholar 

  36. P. Engrand. A multi-objective approach based on simulated annealing and its application to nuclear fuel management. In Proceedings of the 5th ASME/SFEN/JSME International Conference on Nuclear Engineering. Icone 5, Nice, France 1997, pages 416–423. American Society of Mechanical Engineers, New York, NY, 1997.

    Google Scholar 

  37. P. Engrand and X. Mouney. Une méthode originale d’optimisation multi-objectif. Technical Report 98NJ00005, EDF-DER Clamart, France, 1998.

    Google Scholar 

  38. T. Erlebach, H. Kellerer, and U. Pferschy. Approximating multiobjective knapsack problems. Management Science, 48(12):1603–1612, 2002.

    Article  Google Scholar 

  39. E. Fernández and J. Puerto. Multiobjective solution of the uncapacitated plant location problem. European Journal of Operational Research, 145(3):509–529, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  40. C. M. Fonseca and P. J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, California, 1993. University of Illinois at Urbana-Champaign, pages 416–423. Morgan Kaufmann, San Francisco, CA, 1993.

    Google Scholar 

  41. C. M. Fonseca and P. J. Fleming. An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation, 3(1):1–16, 1995.

    Article  Google Scholar 

  42. M. P. Fourman. Compaction of Symbolic Layout using Genetic Algorithms. In Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, pages 141–153. Lawrence Erlbaum, 1985.

    Google Scholar 

  43. L. M. Gambardella, E. Taillard, and G. Agazzi. MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 63–76. McGraw-Hill, London, 1999.

    Google Scholar 

  44. X. Gandibleux, F. Beugnies, and S. Randriamasy. Martins’ algorithm revisited for multi-objective shortest path problems with a maxmin cost function. 4OR: Quarterly Journal of Operations Research, 4(1):47–59, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  45. X. Gandibleux and A. Fréville. Tabu search based procedure for solving the 0/1 multiobjective knapsack problem: The two objective case. Journal of Heuristics, 6(3):361–383, 2000.

    Article  MATH  Google Scholar 

  46. X. Gandibleux, N. Mezdaoui, and A. Fréville. A tabu search procedure to solve multiobjective combinatorial optimization problems. In R. Caballero, F. Ruiz, and R. Steuer, editors, Advances in Multiple Objective and Goal Programming, volume 455 of Lecture Notes in Economics and Mathematical Systems, pages 291–300. Springer-Verlag, Berlin, Germany, 1997.

    Google Scholar 

  47. X. Gandibleux, H. Morita, and N. Katoh. A genetic algorithm for 0-1 multiobjective knapsack problem. In International Conference on Nonlinear Analysis and Convex Analysis (NACA98) Proceedings, 1998. July 28-31 1998, Niigata, Japan.

    Google Scholar 

  48. X. Gandibleux, H. Morita, and N. Katoh. The supported solutions used as a genetic information in a population heuristic. In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, volume 1993 of Lecture Notes in Computer Science, pages 429–442. Springer-Verlag, Berlin, Germany, 2001.

    Chapter  Google Scholar 

  49. X. Gandibleux, H. Morita, and N. Katoh. Impact of clusters, path-relinking and mutation operators on the heuristic using a genetic heritage for solving assignment problems with two objectives. In Proceedings of The Fifth Metaheuristics International Conference MIC’03, pages Paper ID MIC03–23. CD ROM, 2003.

    Google Scholar 

  50. X. Gandibleux, H. Morita, and N. Katoh. A population-based metaheuristic for solving assignment problems with two objectives. Technical Report no7/2003/ROI, LAMIH, Université de Valenciennes, 2003.

    Google Scholar 

  51. X. Gandibleux, H. Morita, and N. Katoh. Evolutionary operators based on elite solutions for biobjective combinatorial optimization. In C. Coello Coello and G. Lamont, editors, Applications of Multi-Objective Evolutionary Algorithms, chapter 23, pages 555–579. World Scientific, Singapore, 2004.

    Google Scholar 

  52. X. Gandibleux, D. Vancoppenolle, and D. Tuyttens. A first making use of GRASP for solving MOCO problems. Technical report, University of Valenciennes, France, 1998. Paper presented at MCDM 14, June 8-12 1998, Charlottesville, VA.

    Google Scholar 

  53. F. Glover and M. Laguna. Tabu Search. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.

    MATH  Google Scholar 

  54. F. Glover, M. Laguna, and R. Martí. Fundamentals of scatter search and path relinking. Control and Cybernetics, 39(3):653–684, 2000.

    Google Scholar 

  55. D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Co., Reading, MA, 1989.

    MATH  Google Scholar 

  56. C. Gomes da Silva, J. Climaco, and J. Figueira. A scatter search method for bi-criteria {0, 1}-knapsack problems. European Journal of Operational Research, 169:373–391, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  57. C. Gomes da Silva, J. Figueira, and J. Clímaco. Integrating partial optimization with scatter search for solving bi-criteria {0, 1}-knapsack problems. European Journal of Operational Research, 177:1656–1677, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  58. L. Gourvès. Approximation polynomiale et optimisation combinatoire multicritère. PhD thesis, Université dÉvry Val d’Essone, 2005.

    Google Scholar 

  59. M. Gravel, W. L. Price, and C. Gagné. Scheduling continuous casting of aluminium using a multiple objective ant colony optimization metaheuristic. European Journal of Operational Research, 143(1):218–229, 2002.

    Article  MATH  Google Scholar 

  60. J. J. Grefenstette. GENESIS: A system for using genetic search procedures. In Proceedings of the 1984 Conference on Intelligent Systems and Machines, pages 161–165. Oakland University, Rochester, MI, 1984.

    Google Scholar 

  61. P. Hajela and C. Y. Lin. Genetic search strategies in multicriterion optimal design. Structural Optimization, 4:99–107, 1992.

    Article  Google Scholar 

  62. H. W. Hamacher and K.-H. Küfer. Inverse radiation therapy planing – A multiple objective optimization approach. Discrete Applied Mathematics, 118(1–2):145–161, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  63. M. P. Hansen. Metaheuristics for multiple objective combinatorial optimization. PhD thesis, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby (Denmark), 1998. Report IMM-PHD-1998-45.

    Google Scholar 

  64. M. P. Hansen. Tabu search for multiobjective combinatorial optimization: TAMOCO. Control and Cybernetics, 29(3):799–818, 2000.

    MATH  MathSciNet  Google Scholar 

  65. M. Hapke, A. Jaszkiewicz, and R. Slowinski. Interactive analysis of multiple-criteria project scheduling problems. European Journal of Operational Research, 107(2):315–324, 1998.

    Article  MATH  Google Scholar 

  66. C. Haubelt, J. Gamenik, and J. Teich. Initial population construction for convergence improvement of MOEAs. In C. Coello Coello, A. Hernández Aguirre, and E. Zitzler, editors, Evolutionary Multi-Criterion Optimization, volume 3410 of Lecture Notes in Computer Sciences, pages 191–205. Springer-Verlag, Berlin, Germany, 2005.

    Google Scholar 

  67. J. Horn, N. Nafpliotis, and D. E. Goldberg. A niched Pareto genetic algorithm for multiobjective optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, Orlando, FL, 29 June – 1 July 1994, volume 1, pages 82–87. IEEE Service Center, Piscataway, NJ, 1994.

    Google Scholar 

  68. S. Iredi, D. Merkle, and M. Middendorf. Bi-criterion optimization with multi colony ant algorithms. In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, volume 1993 of Lecture Notes in Computer Science, pages 359–372. Springer-Verlag, Berlin, Germany, 2001.

    Chapter  Google Scholar 

  69. A. Jaszkiewicz. Multiple objective genetic local search algorithm. In M. Köksalan and S. Zionts, editors, Multiple Criteria Decision Making in the New Millennium, volume 507 of Lecture Notes in Economics and Mathematical Systems, pages 231–240. Springer-Verlag, Berlin, Germany, 2001.

    Google Scholar 

  70. A. Jaszkiewicz. Multiple objective metaheuristic algorithms for combinatorial optimization. Habilitation thesis, Poznan University of Technology, Poznan (Poland), 2001.

    Google Scholar 

  71. A. Jaszkiewicz. A comparative study of multiple-objective metaheuristics on the bi-objective set covering problem and the Pareto memetic algorithm. Annals of Operations Research, 131:135–158, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  72. D. Jones, S. K. Mirrazavi, and M. Tamiz. Multi-objective meta-heuristics: An overview of the current state-of-the-art. European Journal of Operational Research, 137(1):1–9, 2002.

    Article  MATH  Google Scholar 

  73. N. Jozefowiez. Modélisation et résolution approchée de problèmes de tournées multi-objectif. PhD thesis, Université de Lille 1, France, 2004.

    Google Scholar 

  74. N. Jozefowiez, F. Glover, and M. Laguna. A hybrid meta-heuristic for the traveling salesman problem with profits. Technical report, Leeds School of Business, University of Colorado at Boulder, 2006.

    Google Scholar 

  75. N. Jozefowiez, F. Semet, and E. G. Talbi. The bi-objective covering tour problem. Computers and Operations Research, 34:1929–1942, 2007.

    Article  MATH  Google Scholar 

  76. J. Kennedy and R. C. Eberhart. Particle swarm optimization. In Proceedings of the 1995 IEEE International Conference on Neural Networks, volume IV, pages 1942–1948. IEEE Service Center, Piscataway, NJ, 1995.

    Google Scholar 

  77. J. D. Knowles and D. W. Corne. The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimisation. In Proceedings of the 1999 Congress on Evolutionary Computation. Washington, D.C., pages 98–105. IEEE Service Center, Piscataway, NJ, 1999.

    Google Scholar 

  78. F. Kursawe. Evolution strategies for vector optimization. In Proceedings of the 10th International Conference on Multiple Criteria Decision Making, Taipei-Taiwan, volume III, pages 187–193, 1992.

    Google Scholar 

  79. P. Lacomme, C. Prins, and M. Sevaux. A genetic algorithm for a bi-objective arc routing problem. Computers and Operations Research, 33:3473–3493, 2006.

    Article  MATH  Google Scholar 

  80. M. Laumanns, L. Thiele, and E. Zitzler. An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research, 169:932–942, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  81. M. Laumanns, E. Zitzler, and L. Thiele. On the effect of archiving, elitism, and density based selection in evolutionary multi-objective optimization. In Evolutionary Multi-Criteria Optimization. First International Conference, EMO 2001. Zürich, Switzerland, March 7–9, 2001. Proceedings, volume 1993 of Lecture Notes in Computer Science, pages 181–196. Springer-Verlag, Berlin, Germany, 2001.

    Google Scholar 

  82. H. Lee and P. S. Pulat. Bicriteria network flow problems: Integer case. European Journal of Operational Research, 66:148–157, 1993.

    Article  MATH  Google Scholar 

  83. M. López-Ibáñez, L. Paquete, and T. Stützle. Hybrid population-based algorithms for the biobjective quadratic assignment problem. Technical report, Computer Science Department, Darmstadt University of Technology, 2004.

    Google Scholar 

  84. P. Lučić and D. Teodorović. Simulated annealing for the multi-objective aircrew rostering problem. Transportation Research A: Policy and Practice, 33(1):19–45, 1999.

    Article  Google Scholar 

  85. B. Manthey and L. S. Ram. Approximation algorithms for multi-criteria traveling salesman problems. In T. Erlebach and C. Kaklamanis, editors, Approximation and Online Algorithms, volume 4368 of Lecture Notes in Computer Science, pages 302–315. Springer-Verlag, Berlin, Germany, 2007.

    Chapter  Google Scholar 

  86. C. E. Mariano and E. Morales. MOAQ and ant-Q algorithm for multiple objective optimization problems. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, Florida, USA, 13–17 July 1999, volume 1, pages 894–901. Morgan Kaufmann, San Francisco, CA, 1999.

    Google Scholar 

  87. C. E. Mariano and E. Morales. A multiple objective ant-q algorithm for the design of water distribution irrigation networks. Technical Report HC-9904, Instituto Mexicano de Tecnología del Agua, 1999.

    Google Scholar 

  88. G. Mavrotas and D. Diakoulaki. A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research, 107(3):530–541, 1998.

    Article  MATH  Google Scholar 

  89. P. R. McMullen. An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives. Artificial Intelligence in Engineering, 15:309–317, 2001.

    Article  Google Scholar 

  90. P. R. McMullen and G. V. Frazier. Using simulated annealing to solve a multiobjective assembly line balancing problem with parallel workstations. International Journal of Production Research, 36(10):2717–2741, 1999.

    Google Scholar 

  91. K. Miettinen. Nonlinear Multiobjective Optimization, volume 12 of International Series in Operations Research and Management Science. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.

    MATH  Google Scholar 

  92. J. Moore and R. Chapman. Application of particle swarm to multiobjective optimization. Technical report, Department of Computer Science and Software Engineering, Auburn University, 1999.

    Google Scholar 

  93. H. Morita, X. Gandibleux, and N. Katoh. Experimental feedback on biobjective permutation scheduling problems solved with a population heuristic. Foundations of Computing and Decision Sciences Journal, 26(1):23–50, 2001.

    Google Scholar 

  94. T. Murata and H. Ishibuchi. MOGA: Multi-objective genetic algorithms. In Proceedings of the 2nd IEEE International Conference on Evolutionary Computing, Perth, Australia, pages 289–294. IEEE Service Center, Piscataway, NJ, 1995.

    Google Scholar 

  95. D. Nam and C. H. Park. Multiobjective simulated annealing: A comparative study to evolutionary algorithms. International Journal of Fuzzy Systems, 2(2):87–97, 2000.

    Google Scholar 

  96. C. H. Papadimitriou and M. Yannakakis. On the approximability of trade-offs and optimal access to web sources. In Proceedings of the 41st Annual Symposium on the Foundation of Computer Science FOCS00, pages 86–92. IEEE Computer Society, Los Alamitos, CA, 2000.

    Chapter  Google Scholar 

  97. L. Paquete and T. 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 – Second International Conference, EMO 2003, Faro, Portugal, April 8-11, 2003, Proceedings, volume 2632 of Lecture Notes in Computer Science, pages 479–493. Springer-Verlag, Berlin, Germany, 2003.

    Chapter  Google Scholar 

  98. L. Paquete and T. Stützle. A study of stochastic local search for the biobjective QAP with correlated flow matrices. European Journal of Operational Research, 169:943–959, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  99. L. F. Paquete. Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: Methods and Analysis. PhD thesis, Department of Computer Science, Technical University of Darmstadt, 2005.

    Google Scholar 

  100. G. Parks and A. Suppapitnarm. Multiobjective optimization of PWR reload core designs using simulated annealing. In Proceedings of the International Conference on Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications. Madrid, Spain, September 1999, volume 2, pages 1435–1444. Senda Editorial S. A., Madrid, Spain, 1999.

    Google Scholar 

  101. J. M. Pasia, X. Gandibleux, K. F. Doerner, and R. F. Hartl. Local search guided by path relinking and heuristic bounds. In S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, editors, Evolutionary Multi-Criterion Optimization, volume 4403 of Lecture Notes in Computer Science, pages 501–515. Springer-Verlag, Berlin, Germany, 2007.

    Chapter  Google Scholar 

  102. A. Przybylski, X. Gandibleux, and M. Ehrgott. Recursive algorithms for finding all nondominated extreme points in the outcome set of a multiobjective integer program. Technical report, LINA, Université de Nantes, 2007. Submitted for publication.

    Google Scholar 

  103. A. Przybylski, X. Gandibleux, and M. Ehrgott. A two phase method for multiobjective integer programming and its application to the assignment problem with three objectives. Technical report, LINA – Laboratoire d’Informatique de Nantes Atlantique, 2007.

    Google Scholar 

  104. A. Przybylski, X. Gandibleux, and M. Ehrgott. Two phase algorithms for the biobjective assignment problem. European Journal of Operational Research, 185:509–533, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  105. A. R. Rahimi-Vahed and S. M. Mirghorbani. A multi-objective particle swarm for a flow shop scheduling problem. Journal of Combinatorial Optimization, 13:79–102, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  106. R. M. Ramos, S. Alonso, J. Sicilia, and C. González. The problem of the optimal biobjective spanning tree. European Journal of Operational Research, 111:617–628, 1998.

    Article  MATH  Google Scholar 

  107. S. Randriamasy, X. Gandibleux, J. Figueira, and P. Thomin. Device and a method for determining routing paths in a communication network in the presence of selection attributes. Patent 11/25/04. #20040233850. Washington, DC, USA. www.freepatentsonline.com/20040233850.htm, 2004.

  108. S. Sayın. Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Mathematical Programming, 87:543–560, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  109. J. D. Schaffer. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. PhD thesis, Vanderbilt University, Nashville, TN (USA), 1984.

    Google Scholar 

  110. J. D. Schaffer. Multiple objective optimization with vector evaluated genetic algorithms. In J. J. Grefenstette, editor, Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, pages 93–100. Lawrence Erlbaum, Pittsburgh, PA, 1985.

    Google Scholar 

  111. P. Serafini. Simulated annealing for multiobjective optimization problems. In Proceedings of the 10th International Conference on Multiple Criteria Decision Making, Taipei-Taiwan, volume I, pages 87–96, 1992.

    Google Scholar 

  112. P. S. Shelokar, V. K. Jarayaman, and B. D. Kulkarni. Ant algorithm for single and multiobjective reliability optimization problems. Quality and Reliability Engineering International, 18(6):497–514, 2002.

    Article  Google Scholar 

  113. P. S. Shelokar, V. K. Jayarama, and B. D. Kulkarni. Multiobjective optimization of reactor-regenerator system using ant algorithm. Petroleum Science and Technology, 21(7&8):1167–1184, 2003.

    Google Scholar 

  114. P. S. Shelokar, S. Adhikari, R. Vakil, V. K. Jayaraman, and B. D. Kulkarni. Multiobjective ant algorithm: Combination of strength Pareto fitness assignment and thermodynamic clustering. Foundations of Computing and Decision Sciences, 25(4):213–230, 2000.

    Google Scholar 

  115. K. Sörensen. Multi-objective optimization of mobile phone keymaps for typing messages using a word list. European Journal of Operational Research, 179:838–846, 2007.

    Article  MATH  Google Scholar 

  116. F. Sourd, O. Spanjaard, and P. Perny. Multi-objective branch and bound. application to the bi-objective spanning tree problem. Technical report, Department of Decision, Intelligent Systems and Operations Research Université Pierre et Marie Curie, Paris, 2006.

    Google Scholar 

  117. N. Srinivas and K. Deb. Multiobjective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation, 2(3):221–248, 1994.

    Article  Google Scholar 

  118. R. Steuer, J. Silverman, and A. Whisman. A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure. Management Science, 39(10):1255–1260, 1993.

    Article  MATH  Google Scholar 

  119. M. Sun. Applying tabu search to multiple objective combinatorial optimization problems. In Proceedings of the 1997 DSI Annual Meeting, San Diego, California, volume 2, pages 945–947. Decision Sciences Institute, Atlanta, GA, 1997.

    Google Scholar 

  120. A. Suppapitnarm and G. Parks. Simulated annealing: An alternative approach to true multiobjective optimization. In A. S. Wu, editor, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’99). Orlando, Florida. Morgan Kaufmann, San Francisco, CA, 1999.

    Google Scholar 

  121. A. Suppapitnarm, K. Seffen, G. Parks, and P. Clarkson. A simulated annealing algorithm for multiobjective optimization. Engineering Optimization, 33(1):59–85, 2000.

    Article  Google Scholar 

  122. K. C. Tan, C. Y. Cheong, and C. K. Goh. Solving multiobjective vehicel routing problem with stochastic demand via evolutionary computation. European Journal of Operational Research, 177:813–839, 2007.

    Article  MATH  Google Scholar 

  123. K. C. Tan, Y. H. Chew, and L. H. Lee. A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems. European Journal of Operational Research, 172:855–885, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  124. K. C. Tan, Y. H. Chew, and L. H. Lee. A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows. Computational Optimization and Applications, 34:115–151, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  125. J. Teghem, D. Tuyttens, and E. L. Ulungu. An interactive heuristic method for multi-objective combinatorial optimization. Computers and Operations Research, 27(7–8):621–634, 2000.

    Article  MATH  Google Scholar 

  126. D. Tenfelde-Podehl. Facilities Layout Problems: Polyhedral Structure, Multiple Objectives and Robustness. PhD thesis, University of Kaiserslautern, Department of Mathematics, 2002.

    Google Scholar 

  127. M. Thompson. Application of multi objective evolutionary algorithms to analogue filter tuning. In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, volume 1993 of Lecture Notes in Computer Science, pages 546–559. Springer-Verlag, Berlin, Germany, 2001.

    Chapter  Google Scholar 

  128. V. T’kindt, N. Monmarché, F. Tercinet, and D. Laügt. An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem. European Journal of Operational Research, 142(2):250–257, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  129. D. Tuyttens, J. Teghem, P. Fortemps, and K. Van Nieuwenhuyse. Performance of the MOSA method for the bicriteria assignment problem. Journal of Heuristics, 6(3):295–310, 2000.

    Article  MATH  Google Scholar 

  130. E. L. Ulungu. Optimisation combinatoire multicritère: Détermination de l’ensemble des solutions efficaces et méthodes interactives. PhD thesis, Faculté des Sciences, Université de Mons-Hainaut. Mons, Belgium, 1993.

    Google Scholar 

  131. E. L. Ulungu and J. Teghem. The two-phases method: An efficient procedure to solve bi-objective combinatorial optimization problems. Foundations of Computing and Decision Sciences, 20(2):149–165, 1994.

    MathSciNet  Google Scholar 

  132. E. L. Ulungu, J. Teghem, P Fortemps, and D. Tuyttens. MOSA method: A tool for solving multi-objective combinatorial optimization problems. Journal of Multi-Criteria Decision Analysis, 8(4):221–236, 1999.

    Google Scholar 

  133. E. L. Ulungu, J. Teghem, and C. Ost. Efficiency of interactive multi-objective simulated annealing through a case study. Journal of the Operational Research Society, 49:1044–1050, 1998.

    MATH  Google Scholar 

  134. A. Viana and J. Pinho de Sousa. Using metaheuristics in multiobjective ressource constrained project scheduling. European Journal of Operational Research, 120(2):359–374, 2000.

    Google Scholar 

  135. M. Visée, J. Teghem, M. Pirlot, and E. L. Ulungu. Two-phases method and branch and bound procedures to solve the bi-obective knapsack problem. Journal of Global Optimization, 12:139–155, 1998.

    Article  MATH  Google Scholar 

  136. A. Warburton. Approximation of Pareto optima in multiple-objective shortest-path problems. Operations Research, 35(1):70 –79, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  137. H. Yapicioglu, A. E. Smith, and G. Dozier. Solving the semi-desirable facility location problem using bi-objective particle swarm. European Journal of Operational Research, 177:733–749, 2007.

    Article  MATH  Google Scholar 

  138. E. Zitzler and L. Thiele. An evolutionary algorithm for multiobjective optimization: The strength Pareto approach. Technical Report 43, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH), Zürich, Switzerland, May 1998.

    Google Scholar 

  139. E. Zitzler and L. Thiele. Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3(4):257–271, 1999.

    Article  Google Scholar 

  140. E. Ziztler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. Grunert da Fonseca. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117–132, 2003.

    Article  Google Scholar 

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Ehrgott, M., Gandibleux, X. (2008). Hybrid Metaheuristics for Multi-objective Combinatorial Optimization. In: Blum, C., Aguilera, M.J.B., Roli, A., Sampels, M. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78295-7_8

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