Top

, Volume 12, Issue 1, pp 1–63 | Cite as

Approximative solution methods for multiobjective combinatorial optimization

  • Matthias Ehrgott
  • Xavier Gandibleux
Article

Abstract

In this paper we present a review of approximative solution methods, that is, heuristics and metaheuristics designed for the solution of multiobjective combinatorial optimization problems (MOCO). First, we discuss questions related to approximation in this context, such as performance ratios, bounds, and quality measures. We give some examples of heuristics proposed for the solution of MOCO problems. The main part of the paper covers metaheuristics and more precisely non-evolutionary methods. The pioneering methods and their derivatives are described in a unified way. We provide an algorithmic presentation of each of the methods together with examples of applications, extensions, and a bibliographic note. Finally, we outline trends in this area.

Key Words

Multiobjective optimization combinatorial optimization heuristics metaheuristics approximation 

AMS subject classification

90C29 90C27 90C59 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agreell P., Sun M. and Stam A. (1997). A tabu search multi-criteria decision model for facility location planning. Proceedings of the 1997 DSI Annual Meeting, San Diego, California, volume 2, 908–910. Decision Sciences Institute, Atlanta.Google Scholar
  2. Alves M.J. and Climaco J. (2000). An interactive method for 0–1 multiobjective problems using simulated annealing and tabu search.Journal of Heuristics 6, 385–403.CrossRefGoogle Scholar
  3. Andersen K.A., Jørnsten K. and Lind M. (1996). On bicriterion minimal spanning trees: An approximation.Computers and Operations Research 23, 1171–1182.CrossRefGoogle Scholar
  4. Ausiello G., Crescenzi P., Gambosi G., Kann V., Marchetti-Spaccamela A. and Protasi M. (1999).Complexity and Approximation — Combinatorial Optimization Problems and Their Approximability Properties. Springer Verlag.Google Scholar
  5. Bagchi T.P. (1999).Multiobjective Scheduling by Genetic Algorithms. Kluwer Academic Publishers.Google Scholar
  6. Barchard V. and Hao J.K. (2002). Un algorithme hybride pour le problème de sac à dos multi-objectifs. JNPC’2002 Proceedings: Huitièmes Journées Nationales sur la Résolution Pratique de Problèmes NP-Complets, Nice, France, 27–29 May 2002, 19–30.Google Scholar
  7. Baykasoglu A. (2001a). Goal programming using the multiple objective tabu search.Journal of the Operational Research Society 52, 1359–1369.CrossRefGoogle Scholar
  8. Baykasoglu A. (2001b). MOAPPS 1.0: Aggregate production planning using the multiple objective tabu search.International Journal of Production Research 39, 3685–3702.CrossRefGoogle Scholar
  9. Baykasoglu A., Owen S. and Gindy N. (1999). A taboo search based approach to find the Pareto optimal set in multiple objective optimisation.Journal of Engineering Optimization 31, 731–748.Google Scholar
  10. Beausoleil R. (2001). Multiple criteria scatter search. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 2, 539–543.Google Scholar
  11. Ben Abdelaziz F., Chaouachi J. and Krichen S. (1999). A hybrid heuristic for multiobjective knapsack problems. In: Voss S., Martello S., Osman I. and Roucairol C. (eds.),Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, 205–212.Google Scholar
  12. Burkard R.E., Rote G., Ruhe G. and Sieber N. (1989). Algorithmische Untersuchungen zu bikriteriellen kostenminimalen Flüssen in Netzwerken.Wissenschaftliche Zeitung der Technischen Hochschule Leipzig 13, 333–341.Google Scholar
  13. Claro J. and Sousa J.P. de (2001). An object-oriented framework for multiobjective local search. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 231–236.Google Scholar
  14. Coello C.A., Van Veldhuizen D. and Lamont G. (2002).Evolutionary Algorithms for solving multi-objective problems. Kluwer Academic Publishers.Google Scholar
  15. Coello C.A. (1996). An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Designe. Ph.D. Dissertation, Tulane University.Google Scholar
  16. Coello C.A. (1999). A comprehensive survey of evoutionary-based multiobjective optimization techniques.Knowledge and Information Systems 1, 269–308.Google Scholar
  17. Coello C.A. (2000). An updated survey of GA-based multiobjective optimization techniques.ACM Computing Surveys 32, 109–143.CrossRefGoogle Scholar
  18. Coello C.A. (2004). List of references on evolutionary multiobjective optimization. http://www.lania.mx/~ccoello/EMOO/.Google Scholar
  19. Corley H.W. (1985). Efficient spanning trees.Journal of Optimization Theory and Applications 45, 481–485.CrossRefGoogle Scholar
  20. Czyzak P. and Jaszkiewicz A. (1996). A multiobjective metaheuristic approach to the localization of a chain of petrol stations by the capital budgeting model.Control and Cybernetics 25, 177–187.Google Scholar
  21. Czyzak P. and Jaszkiewicz A. (1997). Pareto simulated annealing. In: Fandel G. and Gal T. (eds.),Multiple Criteria Decision Making, Proceedings of the XIIth International Conference, Hagen (Germany), Lecture Notes in Economics and Mathematical Systems 448, 297–307.Google Scholar
  22. Czyzak P. and Jaszkiewicz A. (1998). Pareto simulated annealing — A metaheuristic technique for multiple objective combinatorial optimization.Journal of Multi-Criteria Decision Analysis 7, 34–47.CrossRefGoogle Scholar
  23. Dahl G., Jörnsten K. and Lokketangen A. (1995). A tabu search approach to the channel minimization problem. Proceedings of the International Conference on Optimization Techniques and Applications (ICOTA’95), 5–8 July 1995, Chengdu, China, 369–377.Google Scholar
  24. Mira de Fonseca C. M. (1995). Multiobjective Genetic Algorithms with Applications to Control Engineering Problems. Ph.D. Dissertation, University of Sheffield.Google Scholar
  25. Deb K. (2001).Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley.Google Scholar
  26. Delorme X., Gandibleux X. and Rodriguez J. (2003). Résolution d’un problème d’évaluation de capacité d’infrastructure ferroviaire. Actes du colloque sur l’innovation technologique pour les transports terrestres (TILT) 2, 647–654. GRRT, Lille, France.Google Scholar
  27. Doerner K., Gutjahr W.J., Hartl R.F., Strauss C. and Stummer C. (2001a). Ant colony optimization in multiobjective portfolio selection. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 243–248.Google Scholar
  28. Doerner K., Hartl R.F. and Reimann M. (2001b). Are COMPETants more competent for problem solving? The case of a multiple objective transportation problem. Technical Report 50, Department for Production and Operations Management, University of Vienna.Google Scholar
  29. Doerner K., Gutjahr W.J., Hartl R.F., Strauss C. and Stummer C. (2002). Investi-tionsentscheidungen bei mehrfachen Zielsetzungen und künstliche Ameisen. In: Chamoni P., Leisten R., Martin A., Minnemann J. and Stadtler H. (eds.),Operations Research Proceedings 2001, Selected Papers of OR 2001. Springer Verlag, 355–362.Google Scholar
  30. Doerner K., Gutjahr W.J., Hartl R.F., Strauss C. and Stummer C. (2003). Pareto ant colony optimization in multiobjective portfolio selection with LP preprocessing. Technical Report 2003-06, Center for Business Studies, University of Vienna.Google Scholar
  31. Doerner K., Gutjahr W.J., Hartl R.F., Strauss C. and Stummer C. (2004). Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection.Annals of Operations Research (to appear).Google Scholar
  32. Dorigo (1992).Optimization, Learning and Natural Algorithms. Ph.D. Dissertation, Politecnico di Milano. (in Italian).Google Scholar
  33. Dorigo M., Colorni A. and Maniezzo V. (1996). The ant system: Optimization by a colony of cooperating agents.IEEE Transactions on Systems, Man and Cybernetics Part B 26, 29–41.CrossRefGoogle Scholar
  34. Dorigo M., Di Caro G. and Gambardella L.M. (1997). Ant algorithms for discrete optimization.Artificial Life 5, 137–172.CrossRefGoogle Scholar
  35. Ehrgott M. (1999). Integer solutions of multicriteria network flow problems.Investigação Operacional 19, 229–243.Google Scholar
  36. Ehrgott M. (2000). Approximation algorithms for combinatorial multicriteria optimization problems.International Transactions in Operational Research 7, 5–31.CrossRefGoogle Scholar
  37. Ehrgott M. and Gandibleux X. (2000). A survey and annotated bibliography of multiobjective combinatorial optimization.OR Spektrum 22, 425–460.Google Scholar
  38. Ehrgott M. and Gandibleux X. (2001). Bounds and bound sets for biobjective combinatorial optimization problems. In: Koksalan M. and Zionts S. (eds.),Multiple Criteria Decision Making in the New Millennium, Lecture Notes in Economics and Mathematical Systems 507, 241–253. Springer Verlag.Google Scholar
  39. Ehrgott M. and Gandibleux X. (2004). Bound sets for biobjective combinatorial optimization problems. Technical report, Department of Engineering Science, The University of Auckland.Google Scholar
  40. Ehrgott M., Klamroth K. and Schwehm S. (2004). An MCDM approach to portfolio optimization.European Journal of Operational Research 155, 752–770.CrossRefGoogle Scholar
  41. Ehrgott M. and Ryan D.M. (2002). Constructing robust crew schedules with bicriteria optimization.Journal of Multi-Criteria Decision Analysis 11, 139–150.CrossRefGoogle Scholar
  42. Ehrgott M. and Tenfelde-Podehl D. (2003). Computation of ideal and nadir values and implications for their use in MCDM methods.European Journal of Operational Research 151, 119–131.CrossRefGoogle Scholar
  43. Ehrgott M. and Wiecek M.M. (2004). Multiobjective Programming. In: Figueira J., Greco S. and Ehrgott M. (eds.),Multiple Criteria Decision Analysis: State of the Art Surveys. Kluwer Academic Publishers.Google Scholar
  44. El-Sherbeny N. (2001). Resolution of a vehicle routing problem with a multiobjective simulated annealing method. Ph.D. Dissertation, Université de Mons-Hainaut.Google Scholar
  45. Engrand P. (1997). A multi-objective approach based on simulated annealing and its application to nuclear fuel management. Proceedings of the 5th ASME/SFEN/JSME International Conference on Nuclear Engineering. Icone 5, Nice, France, 416–423.Google Scholar
  46. Engrand P. and Mouney X. (1998). Une méthode originale d’optimisation multi-objectif. Technical Report 98NJ00005, EDF-DER Clamart, France.Google Scholar
  47. Erlebach T., Kellerer H. and Pferschy U. (2001). Approximating multi-objective knapsack problems. In: Dehne F., Sack J.R. and Tamassia R. (eds.)Algorithms and Data Structures. 7th International Workshop, Providence, RI, August 8–10, 2001, Lecture Notes in Computer Science 2125. Springer Verlag, 210–221.Google Scholar
  48. Erlebach T., Kellerer H. and Pferschy U. (2002). Approximating multiobjective knapsack problems.Management Science 48, 1603–1612.CrossRefGoogle Scholar
  49. Fernández E. and Puerto J. (2000). Multiobjective solution of the uncapacitated plant location problem.European Journal of Operational Research, 145, 509–529.CrossRefGoogle Scholar
  50. Fonseca C.M., Fleming P.J., Zitzler E., Deb K. and Thiele L. (2003).Evolutionary Multi-Criterion Optimization. EMO 2003, Second International Conference, Faro, Portugal, April 2003 Proceedings, Lecture Notes in Computer Sciences 2632. Springer Verlag.Google Scholar
  51. Fonseca C.M. and Fleming P.J. (1993). Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Forrest S. (ed.),Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, California, 1933. University of Illinois at Urbana-Champaign. Morgan Kaufman, 416–423.Google Scholar
  52. Fonseca C.M. and Fleming P.J. (1995). An overview of evolutionary algorithms in multiobjective optimization.Evolutionary Computation 3, 1–16.Google Scholar
  53. Fourman M.P. (1985). Compaction of Symbolic Layout using Genetic Algorithms. In: Grefenstette J.J. (ed.),Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms. Lawrence Erlbaum, 141–153.Google Scholar
  54. Fruhwirth B., Burkard R.E. and Rote G. (1989). Approximation of convex curves with application to the bicriterial minimum cost flow problem.European Journal of Operational Research 42, 326–388.CrossRefGoogle Scholar
  55. Gambardella L.M., Taillard E. and Agazzi G. (1999). MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In: Corne D., Dorigo M. and Glover F. (eds.),New Ideas in Optimization. McGraw-Hill, 63–76.Google Scholar
  56. Gandibleux X. and Fréville A. (2000). Tabu search based procedure for solving the 0/1 multiobjective knapsack problem: The two objective case.Journal of Heuristics 6, 361–383.CrossRefGoogle Scholar
  57. Gandibleux X., Mezdaoui N. and Fréville A. (1997). A tabu search procedure to solve multiobjective combinatorial optimization problems. In: Caballero R., Ruiz F. and Steuer R. (eds.),Advances in Multiple Objective and Goal Programming, Lecture Notes in Economics and Mathematical Systems 455. Springer Verlag, 291–300.Google Scholar
  58. Gandibleux X., Morita H. and Katoh N. (1998). A genetic algorithm for 0–1 multiobjective knapsack problem. Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis (NACA98), July 28–31, 1998, Niigata, Japan.Google Scholar
  59. Gandibleux X., Morita H. and Katoh N. (2001). The supported solutions used as a genetic information in a population heuristic. In: Zitzler E., Deb K., Thiele L., Coello Coello C.A. and Corne D. (eds.),First International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science 1993. Springer Verlag, 429–442.Google Scholar
  60. Gandibleux X., Morita H. and Katoh N. (2004). A population-based metaheuristic for solving assignment problems with two objectives.Journal of Mathematical Modelling and Algorithms (to appear).Google Scholar
  61. Gandibleux X., Vancoppenolle D. and Tuyttens D. (1998). A first making use of GRASP for solving MOCO problems. Technical report, University of Valenciennes, France, 1998.Google Scholar
  62. Geiger M. (2001). Genetic algorithms for multiple objective vehicle routing. Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 349–353.Google Scholar
  63. Gen M. and Li Y.Z. (1998a). Solving multi-objective transportation problems by spanning tree-based genetic algorithm. In: Parmee I.C. (ed.),Adaptive Computing in Design and Manufacture: The Integration of Evolutionary and Adaptive Computing Technologies with Product/System Design and Realisation. Springer Verlag, 95–108.Google Scholar
  64. Gen M. and Li Y.Z. (1998b). Spanning tree based genetic algorithm for bicriteria transportation problem.Computers and Industrial Engineering 35, 531–534.CrossRefGoogle Scholar
  65. Glover F. and Laguna M. (1997).Tabu Search. Kluwer Academic Publishers.Google Scholar
  66. Godart J.M. (2001). Problèmes d’optimisation combinatoire à caractère économique dans le secteur du tourisme (organisation de voyages). Ph.D. Dissertation, Université de Mons-Hainaut.Google Scholar
  67. Goldberg D.E. (1989).Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Co.Google Scholar
  68. Gravel M., Price W.L. and Gagné C. (2002). Scheduling continuous casting of aluminium using a multiple objective ant colony optimization metaheuristic.European Journal of Operational Research, 143, 218–229.CrossRefGoogle Scholar
  69. Grefenstette J.J. (1984). GENESIS: A system for using genetic search procedures. Proceedings of the 1984 Conference on Intelligent Systems and Machines, 161–165.Google Scholar
  70. Habenicht W. (1983). Quad trees — A datastructure for discrete vector optimization problems. In: Hansen P. (ed.),Essays and Surveys on Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems 209. Springer Verlag, 136–145.Google Scholar
  71. Hajela P. and Lin C.Y. (1992). Genetic search strategies in multicriterion optimal design.Structural Optimization 4, 99–107.CrossRefGoogle Scholar
  72. Hamacher H.W. and Ruhe G. (1994). On spanning tree problems with multiple objectives.Annals of Operations Research 52, 209–230.CrossRefGoogle Scholar
  73. Hansen M.P. (1998). Metaheuristics for multiple objective combinatorial optimization. Ph.D. Dissertation, Technical University of Denmark, Report IMM-PHD-1998-45.Google Scholar
  74. Hansen M.P. (2000). Tabu search for multiobjective combinatorial optimization: TAMOCO.Control and Cybernetics 29, 799–818.Google Scholar
  75. Hansen P. (1979). Bicriterion path problems. In: Fandel G. and Gal T. (eds.),Multiple Criteria Decision Making Theory and Application, Lecture Notes in Economics and Mathematical Systems 177. Springer Verlag, 109–127.Google Scholar
  76. Hapke M., Jaszkiewicz A. and Slowinski R. (1996). Interactive analysis of multiple-criteria project scheduling problems. Proceedings of the The Fifth International Workshop on Project Management and Scheduling — EURO PMS’96, Poznan, Poland, 107–110.Google Scholar
  77. Hapke M., Jaszkiewicz A. and Slowinski R. (1997). Fuzzy project scheduling with multiple criteria. Proceedings of Sixth IEEE International Conference on Fuzzy Systems, FUZZ-IEEE’97, July 1–5, Barcelona, Spain, 1277–1282.Google Scholar
  78. Hapke M., Jaszkiewicz A. and Slowinski R. (1998a). Fuzzy multi-mode resource-constrained project scheduling with multiple objectives. In: Weglarz J. (ed.)Recent Advances in Project Scheduling. Kluwer Academic Publishers, 355–382.Google Scholar
  79. Hapke M., Jaszkiewicz A. and Slowinski R. (1998b). Interactive analysis of multiple-criteria project scheduling problems.European Journal of Operational Research 107, 315–324.CrossRefGoogle Scholar
  80. Hapke M., Jaszkiewicz A. and Slowinski R. (2000a). Pareto simulated annealing for fuzzy multi-objective combinatorial optimization.Journal of Heuristics 6, 329–354.CrossRefGoogle Scholar
  81. Hapke M., Kominek P., Jaszkiewicz A. and Slowinski R. (2000b). Integrated tools for software project scheduling under uncertainty. In: Brucker P., Heitmann S., Hurink J. and Knust S. (eds.),Proceedings of the 7th International Workhop on Project Management and Scheduling PMS’2000, Osnabrück, Germany, April 17–19, 149–151.Google Scholar
  82. Hertz A., Jaumard B., Ribeiro C. and Formosinho Filho W. 1994). A multicriteria tabu search approach to cell formation problems in group technology with multiple objectives.RAIRO — Recherche Opérationnelle 28, 303–328.Google Scholar
  83. Horn J., Nafpliotis N. and Goldberg D.E. (1994). A niched Pareto genetic algorithm for multiobjective optimization. Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, Orlando, FL, 29 June – 1 July 1994, volume 1, 82–87.Google Scholar
  84. Iredi S., Merkle D. and Middendorf M. (2001). Bi-criterion optimization with multi colony ant algorithms. In: Zitzler E., Deb K., Thiele L., Coello Coello C.A. and Corne D. (eds.),First International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science 1993. Springer Verlag, 359–372.Google Scholar
  85. Jaszkiewicz A. (1997). A metaheuristic approach to multiple objective nurse scheduling.Foundations of Computing and Decision Sciences Journal 22, 169–184.Google Scholar
  86. Jaszkiewicz A. (1998). Genetic local search for multiple objective combinatorial optimization. Working paper RA-014/98, Institute of Computing Science, Poznan University of Technology, Poland.Google Scholar
  87. Jaszkiewicz A. (2001a). Comparison of local search-based metaheuristics on the multiple objective knapsack problem.Foundations of Computing and Decision Sciences Journal 26, 99–120.Google Scholar
  88. Jaszkiewicz A. (2001b). Multiple objective genetic local search algorithm. In: Köksalan M. and Zionts S. (eds.)Multiple Criteria Decision Making in the New Millennium, Lecture Notes in Economics and Mathematical Systems 507, 231–240.Google Scholar
  89. Jaszkiewicz A. (2001c). Multiple objective metaheuristic algorithms for combinatorial optimization. Ph.D. Dissertation, Poznan University of Technology.Google Scholar
  90. Jaszkiewicz A. and Ferhat A.B. (1999). Solving multiple criteria choice problems by interactive trichotomy segmentation.European Journal of Operational Research 113, 271–280.CrossRefGoogle Scholar
  91. Jones D., Mirrazavi S.K. and Tamiz M. (2002). Multi-objective meta-heuristics: An overview of the current state-of-the-art.European Journal of Operational Research 137, 1–9.CrossRefGoogle Scholar
  92. Kim B., Gel E.S., Carlyle W.M. and Fowler J.W. (2001). A new technique to compare algorithms for bi-criteria combinatorial optimization problems. In: Köksalan M. and Zionts S. (eds.),Multiple Criteria Decision Making in the New Millenium, Lecture Notes in Economics and Mathematical Systems 507. Springer Verlag, 113–123.Google Scholar
  93. Knowles J.D. and Corne D.W. (1999). The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimisation. Proceedings of the 1999 Congress on Evolutionary Computation, Washington, D.C., 98–105.Google Scholar
  94. Köksalan M. (1999). A heuristic approach to bicriteria scheduling.Naval Research Logistics 46, 777–789.CrossRefGoogle Scholar
  95. Koktener E. and Köksalan M. (2000). A simulated annealing approach to bicriteria scheduling problems on a single machine.Journal of Heuristics 6, 311–327.CrossRefGoogle Scholar
  96. Küfer K.H., Scherrer A., Monz M., Alonso F., Trinkaus H., Bortfeld T. and Thieke C. (2003). Intensity-modulated radiotherapy — A large scale multi-criteria programming problem.OR Spectrum 25, 223–249.CrossRefGoogle Scholar
  97. Kursawe F. (1992). Evolution strategies for vector optimization. Proceedings of the 10th International Conference on Multiple Criteria Decision Making, Taipei-Taiwan, 187–193.Google Scholar
  98. Laumanns M., Zitzler E. and Thiele L. (2001). On the effect of archiving, elitism, and density based selection in evolutionary multi-objective optimization. Proceedings of the Evolutionary Multi-Criteria Optimization. First International Conference, EMO 2001. Zürich, Switzerland, March 7–9, 2001, Lecture Notes in Computer Science 1993. Springer Verlag, 181–196.Google Scholar
  99. Lawler E.L., Lenstra J.K., Rinooy Kan A.G. and Shmooys D.B. (1985).The traveling salesman problem: A guided tour of combinatorial optimization. Wiley Interscience Series in Pure and Applied Mathematics. John Wiley.Google Scholar
  100. Lee H. and Pulat P.S. (1993). Bicriteria network flow problems: Integer case.European Journal of Operational Research 66, 148–157.CrossRefGoogle Scholar
  101. Liepins G.E., Hilliard M.R., Richardson J. and Palmer M. (1990). Genetic algorithms application to set covering and travelling salesman problems. In: Brown D.E. and White C.C. (eds.),Operations Research and Artificial Intelligence: The Integration of Problem-solving Strategies. Kluwer Academic Publishers, 29–57.Google Scholar
  102. Loukil Moalla T., Teghem J. and Fortemps P. (2000a). Solving multiobjective scheduling problems with tabu search. Workshop on Production Planning and Control, 2–4 October 2000, Facultés Universitaires Catholiques de Mons, Mons, Belgium.Google Scholar
  103. Loukil Moalla T., Teghem J. and Tuyttens D. (2000b). Solving multiobjective scheduling problems with the MOSA method. Workshop on Production Planning and Control, 2–4 October 2000, Facultés Universitaires Catholiques de Mons, Mons, Belgium.Google Scholar
  104. Lučić P. and Teodorović D. (1999). Simulated annealing for the multi-objective aircrew rostering problem.Transportation Research A: Policy and Practice 33, 19–45.CrossRefGoogle Scholar
  105. Malakooti B., Wang J. and Tandler E.C. (1990). A sensor-based accelerated approach for multi-attribute machinability and tool life evaluation.International Journal of Production Research 28, 23–73.Google Scholar
  106. Marett R. and Wright M. (1996). A comparison of neighborhood search techniques for multi-objective combinatorial problems.Computers and Operations Research 23, 465–483.CrossRefGoogle Scholar
  107. Mariano C.E. and Morales E. (1999a). MOAQ and ant-Q algorithm for multiple objective optimization problems. In: Banzhaf W., Daida J., Eiben A.E., Garzon M.H., Honavar V., Jakiela M. and Smith R.E. (eds.),Proceeding of the Genetic and Evolutionary Computation Conference, Orlando, Florida, USA, 13–17 July 1999, volume 1, 894–901.Google Scholar
  108. Mariano C.E. and Morales E. (1999b). A multiple objective ant-q algorithm for the design of water distribution irrigation networks. Technical report, Instituto Mexicano de Tecnología del Agua, México.Google Scholar
  109. McMullen P.R. (2001). An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives.Artificial Intelligence in Engineering 15, 309–317.CrossRefGoogle Scholar
  110. McMullen P.R. and Frazier G.V. (1999). Using simulated annealing to solve a multiobjective assembly line balancing problem with parallel workstations.International Journal of Production Research 36, 2717–2741.Google Scholar
  111. Miettinen K. (1999).Nonlinear Multiobjective Optimization. International Series in Operations Research and Management Science 12. Kluwer Academic Publishers.Google Scholar
  112. Morita H., Gandibleux X. and Katoh N. (2001). Experimental feedback on biobjective permutation scheduling problems solved with a population heuristic.Foundations of Computing and Decision Sciences Journal 26, 23–50.Google Scholar
  113. Murata T. and Ishibuchi H. (1995). MOGA: Multi-objective genetic algorithms. Proceedings of the 2nd IEEE International Conference on Evolutionary Computing, Perth, Australia, 289–294.Google Scholar
  114. Nam D. and Park C.H. (2000). Multiobjective simulated annealing: A comparative study to evolutionary algorithms.International Journal of Fuzzy Systems 2, 87–97.Google Scholar
  115. Osman I. and Laporte G. (1996). Metaheuristics: A bibliography.Annals of Operations Research 63, 513–623.CrossRefGoogle Scholar
  116. Osyczka A. (2001).Evolutionary Algorithms for Single and Multicriteria Design Optimization, Studies in Fuzziness and Soft Computing 79. Physica Verlag.Google Scholar
  117. Pamuk S. and Köksalan M. (2001). An interactive genetic algorithm applied to the multiobjective knapsack problem. In: Köksalan M. and Zionts S. (eds.),Multiple Criteria Decision Making in the New Millennium, Lecture Notes in Economics and Mathematical Systems 507. Springer Verlag, 265–272.Google Scholar
  118. Papadimitriou C.H. and Yannakakis M. (2000). On the approximability of trade-offs and optimal access to web sources. Proceedings of the 41st Annual Symposium on the Foundation of Computer Science FOCS00, 86–92, Redondo Beach, CA (USA).Google Scholar
  119. Paquete L. and Fonseca C.M. (2001). A study of examination timetabling with multiobjective evolutionary algorithms. In: Sousa J.P. de (ed.),MIC’2001 Proceedings 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 149–153.Google Scholar
  120. Parks G. and Suppapitnarm A. (1999). Multiobjective optimization of PWR reload core designs using simulated annealing. Proceedings of the International Conference on Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications. Madrid, Spain, September 1999, volume 2, 1435–1444.Google Scholar
  121. Pires D., Henggeler Antunes C. and Gomes Martins A. (2001). A tabu search multiobjective approach to capacitor allocation in radial distribution systems. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 169–174.Google Scholar
  122. Rahoual M., Kitoun B., Mabed M., Bachelet V., and Benameur F. (2001). Multi-criteria genetic algorithms for the vehicle routing problem with time windows. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 2, 527–532.Google Scholar
  123. Ramos R.M., Alonso S., Sicilia J. and González C. (1998). The problem of the optimal biobjective spanning tree.European Journal of Operational Research 111, 617–628.CrossRefGoogle Scholar
  124. Randriamasy S., Gandibleux X., Figueira J., and Thomin Ph. (2002). Fiche brevet no 03291744.5-2416 intitulée “Dispositif et procédé de détermination de chemins de routage dans un réseau de communications, en présence d’attributs de sélection”. Fiche déposée le 15 Juillet 2002.Google Scholar
  125. Reeves C. (1995).Modern Heuristic Techniques for Combinatorial Problems. McGrawHill.Google Scholar
  126. Ribeiro R. and Lourenço H. (2001). A multi-objective model for a multi-period distribution management problem. In: Sousa J.P. de (ed.),MIC’2001 Proceedings of the 4th Metaheuristics International Conference, Porto, July 16–20, 2001 1, 97–101.Google Scholar
  127. Rosenblatt M.J. and Sinuany-Stern Z. (1989). Generating the discrete efficient frontier to the capital budgeting problem.Operations Research 37, 384–394.Google Scholar
  128. Ruhe G. and Fruhwirth B. (1990). ε — optimality for bicriteria programs and its application to minimum cost flows.Computing 44, 21–34.CrossRefGoogle Scholar
  129. Safer H.M. (1992). Fast Approximation Schemes for Multi-Criteria Combinatorial Optimization. Ph.D. Dissertation, Sloan School of Management, MIT.Google Scholar
  130. Safer H.M. and Orlin J.B. (1995a). Fast approximation schemes for multi-criteria combinatorial optimization. Working paper 3756-95, Sloan School of Management, MIT, Cambridge, MA, 1995.Google Scholar
  131. Safer H.M. and Orlin J.B. (1995b). Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems. Working paper 3757-95, Sloan School of Management, MIT, Cambridge, MA, 1995.Google Scholar
  132. Sawaragi Y., Nakayama H. and Tanino T. (1995).Theory of Multiobjective Optimization. Academic Press.Google Scholar
  133. Sayin S. (2000). Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming.Mathematical Programming 87, 543–560.CrossRefGoogle Scholar
  134. Schaffer J.D. (1984). Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. Ph.D. Dissertation, Vanderbilt University.Google Scholar
  135. Schaffer J.D. (1985). Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette J.J. (ed.),Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms. Lawrence Erlbaum, 93–100.Google Scholar
  136. Serafini P. (1986). Some considerations about computational complexity for multi objective combinatorial problems. In: Jahn J. and Krabs W. (eds.),Recent advances and historical development of vector optimization, Lecture Notes in Economics and Mathematical Systems, 294. Springer Verlag, 222–232.Google Scholar
  137. Serafini P. (1992). Simulated annealing for multiobjective optimization problems. Proceedings of the 10th International Conference on Multiple Criteria Decision Making, Taipei-Taiwan, 87–96.Google Scholar
  138. Shelokar P.S., Adhikari S., Vakil R., Jayaraman V.K. and Kulkarni B.D. (2000). Multiobjective ant algorithm: Combination of strength Pareto fitness assignment and thermodynamic clustering.Foundations of Computing and Decision Sciences 25, 213–230.Google Scholar
  139. Shelokar P.S., Jarayaman V.K. and Kulkarni B.D. (2002). Ant algorithm for single and multiobjective reliability optimization problems.Quality and Reliability Engineering International 18, 497–514.CrossRefGoogle Scholar
  140. Shelokar P.S., Jayarama V.K. and Kulkarni B.D. (2003). Multiobjective optimization of reactor-regenerator system using ant algorithm.Petroleum Science and Technology 21, 1167–1184.CrossRefGoogle Scholar
  141. Sigal I.K. (1994). Algorithms for solving the two-criterion large-scale travelling salesman problem.Computational Mathematics and Mathematical Physics 34, 33–43.Google Scholar
  142. Srinivas N. and Deb K. (1994). Multiobjective optimization using non-dominated sorting in genetic algorithms.Evolutionary Computation 2, 221–248.Google Scholar
  143. Steuer R., Silverman J. and Whisman A. (1993). A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure.Management Science 39, 1255–1260.Google Scholar
  144. Sun M. (1997). Applying tabu search to multiple objective combinatorial optimization problems. Proceedings of the 1997 DSI Annual Meeting, San Diego, California, volume 2, 945–947.Google Scholar
  145. Sun M., Stam A. and Steuer R. (1996). Solving multiple objective programming problems using feed-forward artificial neural networks: The interactive FFANN procedure.Management Science 42, 835–849.Google Scholar
  146. Sun M., Stam A. and Steuer R. (2000). Interactive multiple objective programming using Tchebycheff programs and artificial neural networks.Computers and Operations Research 27, 601–620.CrossRefGoogle Scholar
  147. Sun M. and Steuer R. (1996). Quad-trees and linear lists for identifying nondom-inated criterion vectors.INFORMS Journal on Computing 8, 367–375.CrossRefGoogle Scholar
  148. Suppapitnarm A. and Parks G. (1999). Simulated annealing: An alternative approach to true multiobjective optimization. In: Wu A.S. (ed.),Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’99). Orlando, Florida, 406–407.Google Scholar
  149. Suppapitnarm A., Seffen K., Parks G. and Clarkson P. (2000). A simulated annealing algorithm for multiobjective optimization.Engineering Optimization 33, 59–85.Google Scholar
  150. Sysoev V. and Dolgui A. (1999). A Pareto optimization approach for manufacturing system design. Proceedings of International Conference on Industrial Engineering and Production Management (IEPM’99). July 1–15 1999, Glasgow, Scotland, volume 2, 116–125.Google Scholar
  151. Tamaki H., Mori M., Araki M., Mishima Y. and Ogai H. (1994). Multi-criteria optimization by genetic algorithms: A case of scheduling in hot rolling process. Proceedings of the 3rd Conference of the Association of Asian-Pacific Operational Research Societies within IFORS (APORS94), 1994.Google Scholar
  152. Teghem J., Tuyttens D. and Ulungu E.L. (2000). An interactive heuristic method for multi-objective combinatorial optimization.Computers and Operations Research 27, 621–634.CrossRefGoogle Scholar
  153. Tenfelde-Podehl D. (2002). Facilities Layout Problems: Polyhedral Structure, Multiple Objectives and Robustness. Ph.D. Dissertation, Universität Kaiserslautern.Google Scholar
  154. Thompson M. (2001). Application of multi objective evolutionary algorithms to analogue filter tuning. In: Zitzler E., Deb K., Thiele L., Coello Coello C.A. and Corne D. (eds.),First International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science 1993. Springer Verlag, 546–559.Google Scholar
  155. T’Kindt V., Monmarché N., Tercinet F. and Laügt D. (2002). An ant colony optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem.European Journal of Operational Research 142, 250–257.CrossRefGoogle Scholar
  156. Todd D.S. and Sen P. (1997). A multiple criteria genetic algorithm for containership loading. In: Bäck T. (ed.),Proceedings of the Seventh International Conference on Genetic Algorithms (ICGA97).Google Scholar
  157. Tuyttens D., Teghem J., Fortemps P. and Van Nieuwenhuyse K. (2000). Performance of the MOSA method for the bicriteria assignment problem.Journal of Heuristics 6, 295–310.CrossRefGoogle Scholar
  158. Ulungu E.L. and Teghem J. (1992). Heuristic for multi-objective combinatorial optimization problems with simulated annealing. Presented at the EURO XII Conference, Helsinki.Google Scholar
  159. Ulungu E.L. (1993). Optimisation combinatoire multicritère: Détermination de l’ensemble des solutions efficaces et méthodes interactives. Ph.D. Dissertation, Université de Mons-Hainaut.Google Scholar
  160. Ulungu E.L. and Teghem J. (1994). The two-phases method: An efficient procedure to solve bi-objective combinatorial optimization problems.Foundations of Computing and Decision Sciences 20, 149–165.Google Scholar
  161. Ulungu E.L., Teghem J. and Fortemps P.H. (1995). Heuristics for multi-objective combinatorial optimisation problem by simulated annealing. In: Wei Q., Gu J., Chen G. and Wang S. (eds.),MCDM: Theory and Applications. SCI-TECH Information Services, 228–238.Google Scholar
  162. Ulungu E.L., Teghem J., Fortemps P.H. and Tuyttens D. (1999). MOSA method: A tool for solving multiobjective combinatorial optimization problems.Journal of Multi-Criteria Decision Analysis 8, 221–236.CrossRefGoogle Scholar
  163. Ulungu E.L., Teghem J. and Ost C. (1998). Efficiency of interactive multiobjective simulated annealing through a case study.Journal of the Operational Research Society 49, 1044–1050.CrossRefGoogle Scholar
  164. Viana A. and Sousa P.J. de (2000). Using metaheuristics in multiobjective ressource constrained project scheduling.European Journal of Operational Research 120, 359–374.CrossRefGoogle Scholar
  165. Visée M., Teghem J., Pirlot M. and Ulungu E.L. (1998). Two-phases method and branch and bound procedures to solve the bi-obective knapsack problem.Journal of Global Optimization 12, 139–155.CrossRefGoogle Scholar
  166. Warburton A. (1987). Aproximation of Pareto optima in multiple-objective shortestpath problems.Operations Research 35, 70–79.Google Scholar
  167. White D.J. (1986). Epsilon efficiency.Journal of Optimization Theory and Applications 49, 319–337.CrossRefGoogle Scholar
  168. Zhou G. and Gen M. (1999). Genetic algorithm approach on multi-criteria minimum spanning tree problem.European Journal of Operational Research 114, 141–152.CrossRefGoogle Scholar
  169. Zitzler E. (1999). Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Ph.D. Dissertation, Swiss Federal Institute of Technology.Google Scholar
  170. Zitzler E., Deb K., Thiele L., Coello C. and Corne D. (2001).Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Sciences, 1993. Springer Verlag.Google Scholar
  171. Zitzler E. and Thiele L. (1998). 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.Google Scholar
  172. Zitzler E. and Thiele L. (1999). Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach.IEEE Transactions on Evolutionary Computation 3, 257–271.CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2004

Authors and Affiliations

  • Matthias Ehrgott
    • 1
  • Xavier Gandibleux
    • 2
  1. 1.Department of Engineering ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.LAMIH — UMR CNRS 8530University of Valenciennes, Campus “Le Mont Houy”Valenciennes cedex 9France

Personalised recommendations