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Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored

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Abstract

This paper provides a short review of some of the main topics in which the current research in evolutionary multi-objective optimization is being focused. The topics discussed include new algorithms, efficiency, relaxed forms of dominance, scalability, and alternative metaheuristics. This discussion motivates some further topics which, from the author’s perspective, constitute good potential areas for future research, namely, constraint-handling techniques, incorporation of user’s preferences and parameter control. This information is expected to be useful for those interested in pursuing research in this area.

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References

  1. Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning. Reading: Addison-Wesley Publishing Company, 1989

    MATH  Google Scholar 

  2. Eiben A E, Smith J E. Introduction to Evolutionary Computing. Berlin: Springer, 2003

    MATH  Google Scholar 

  3. Coello Coello C A, Lamont G B, Van Veldhuizen D A. 2nd ed. Evolutionary Algorithms for Solving Multi-Objective Problems. New York: Springer, 2007

    MATH  Google Scholar 

  4. Deb K. Multi-Objective Optimization using Evolutionary Algorithms. Chichester: John Wiley & Sons, 2001

    MATH  Google Scholar 

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

    Article  Google Scholar 

  6. Miettinen K M. Nonlinear Multiobjective Optimization. Boston: Kluwer Academic Publishers, 1999

    MATH  Google Scholar 

  7. Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithms. PhD thesis. Nashville: Vanderbilt University, 1984

    Google Scholar 

  8. Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the First International Conference on Genetic Algorithms and their Applications, 1985, 93–100

  9. Coello Coello C A. Evolutionary multiobjective optimization: a historical view of the field. IEEE Computational Intelligence Magazine, 2006, 1(1): 28–36

    Article  MathSciNet  Google Scholar 

  10. Fonseca C M, Fleming P J. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Forrest S, ed. Proceedings of the Fifth International Conference on Genetic Algorithms. San Fransisco: Morgan Kaufmann Publishers, 1993, 416–423

    Google Scholar 

  11. Horn J, Nafpliotis N, Goldberg D E. A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence. Piscataway: IEEE Service Center, 1994, 1: 82–87

    Chapter  Google Scholar 

  12. Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 1994, 2(3): 221–248

    Article  Google Scholar 

  13. Husbands P. Distributed coevolutionary genetic algorithms for multicriteria and multi-constraint optimisation. In: Fogarty T C, ed. Evolutionary Computing. Springer-Verlag, LNCS, 1994, 865: 150–165

  14. Osyczka A, Kundu S. A genetic algorithm approach to multicriteria network optimization problems. In: Proceedings of the 20th International Conference on Computers and Industrial Engineering, 1996, 329–332

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

    Article  Google Scholar 

  16. Knowles J D, Corne D W. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation, 2000, 8(2): 149–172

    Article  Google Scholar 

  17. Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength Pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux J, Papailou P, Fogarty T, eds. Proceedings of EUROGEN 2001-Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, 2002, 95–100

  18. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182–197

    Article  Google Scholar 

  19. Babbar M, Lakshmikantha A, Goldberg D E. A modified NSGA-II to solve noisy multiobjective problems. In: Foster J, ed. Proceedings of 2003 Genetic and Evolutionary Computation Conference. Late-Breaking Papers. Chicago: AAAI, 2003, 21–27

    Google Scholar 

  20. Jozefowiez N, Semet F, Talbi E G. Enhancements of NSGA II and its application to the vehicle routing problem with route balancing. In: Talbi E G, Liardet P, Collet P, Lutton E, Schoenauer M, eds. Proceedings of Artificial Evolution, 7th International Conference, Evolution Artificielle, EA 2005. Lille: Springer, LNCS, 2005, 3871: 131–142

    Google Scholar 

  21. Nojima Y, Narukawa K, Kaige S, Ishibuchi H. Effects of removing overlapping solutions on the performance of the NSGA-II algorithm. In: Coello Coello C A, Hernández-Aguirre A, Zitzler E, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Third International Conference (EMO 2005). Guanajuato: Springer, LNCS, 2005, 3410: 341–354

    Google Scholar 

  22. Köppen M, Yoshida K. Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Crterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 727–741

    Chapter  Google Scholar 

  23. Goldberg D E, Richardson J. Genetic algorithm with sharing for multimodal function optimization. In: Grefenstette J J, ed. Proceedings of Genetic Algorithms and Their Applications, the Second International Conference on Genetic Algorithms. Hillsdale: Lawrence Erlbaum, 1987, 41–49

    Google Scholar 

  24. Deb K, Goldberg D E. An investigation of niche and species formation in genetic function optimization. In: Schaffer J D, ed. Proceedings of the Third International Conference on Genetic Algorithms. San Mateo: Morgan Kaufmann Publishers, 1989, 42–50

    Google Scholar 

  25. Knowles J, Corne D. Properties of and adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation, 2003, 7(2): 100–116

    Article  Google Scholar 

  26. Cui X X, Li M, Fang T J. Study of population diversity of multiobjective evolutionary algorithm based on immune and entropy principles. In: Proceedings of the Congress on Evolutionary Computation 2001 (CEC’2001). Piscataway: IEEE Service Center, 2001, 2: 1316–1321

    Google Scholar 

  27. Farhang-Mehr A, Azarm S. Diversity assessment of Pareto optimal solution sets: an entropy approach. In: Proceedings of Congress on Evolutionary Computation (CEC’2002). Piscataway: IEEE Service Center, 2002, 1: 723–728

    Google Scholar 

  28. Farhang-Mehr A, Azarm S. Entropy-based multi-objective genetic algorithm for design optimization. Structural and Multidisciplinary Optimization, 2002, 24(25): 351–361

    Article  Google Scholar 

  29. Zitzler E, Künzli S. Indicator-based selection in multiobjective search. In: Yao X, et al, eds. Parallel Problem: Solving from Nature — PPSN VIII. Birmingham: Springer-Verlag, LNCS, 2004, 3242: 832–842

    Google Scholar 

  30. Zitzler E, Thiele L, Laumanns M, Fonseca C M, Da Fonseca V G. Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation, 2003, 7(2): 117–132

    Article  Google Scholar 

  31. Zitzler E, Thiele L, Bader J. SPAM: set preference alogrithm for multiobjective optimization. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N, eds. Parallel Problem Solving from Nature-PPSN X. Dortmund: Springer, LNCS, 2008, 5199: 847–858

    Chapter  Google Scholar 

  32. Emmerich M, Beume N, Naujoks B. An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello C A, Hernández-Aguirre A, Zitzler E, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Third International Conference (EMO 2005). Guanajuato: Springer, LNCS, 2005, 3410: 62–76

    Google Scholar 

  33. Beume N, Naujoks B, Emmerich M. SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 2007, 181(3): 1653–1669

    Article  MATH  Google Scholar 

  34. Zitzler E, Thiele L. Multiobjective optimization using evolutionary algorithms—a comparative study. In: Eiben A E, ed. Parallel Problem Solving from Nature V. Amsterdam: Springer-Verlag, 1998, 292–301

    Chapter  Google Scholar 

  35. Zitzler E. Evolutionary algorithms for multiobjective optimization: Methods and application. PhD thesis. Zurich: Swiss Federal Institute of Technology (ETH), 1999

    Google Scholar 

  36. Igel C, Hansen N, Roth S. Covariance matrix adaptation for multiobjective optimization. Evolutionary Computation, 2007, 15(1): 1–28

    Article  Google Scholar 

  37. Igel C, Suttorp T, Hansen N. Steady-state selection and efficient covariance matrix update in the multi-objective CM-ES. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 171–185

    Chapter  Google Scholar 

  38. Sefrioui M, Periaux J. Nash genetic algorithms: examples and applications. In: Proceeding of 2000 Congress on Evolutionary Computation. San Diego: IEEE Service Center, 2000, 1: 509–516

    Chapter  Google Scholar 

  39. Landa-Becerra R, Coello Coello C A. Solving hard multiobjective optimization problems using ε-constraint with cultured differential evolution. In: Runarsson T P, Beyer H G, Burke E, Merelo-Gurervós J J, Whitley D L, Yao X, eds. Proceedings of 9th International Conference on Parallel Problem Solving from Nature-PPSN IX. Reykjavk: Springer, LNCS, 2006, 4193: 543–552

    Chapter  Google Scholar 

  40. Nebro A J, Durillo J J, Luna F, Dorronsoro B, Alba E. A cellular genetic algorithm for multiobjective optimization. In: Pelta D A, Krasnogor N, eds. Proceedings of the Workshop on Nature Inspired Cooperative Strategies for Optimization (NICSO 2006), 2006, 25–36

  41. Nebro A J, Durillo J J, Luna F, Dorronsoro B, Alba E. Design issues in a multiobjective cellular genetic algorithm. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 126–140

    Chapter  Google Scholar 

  42. Coello Coello C A, Toscano-Pulido G. Multiobjective optimization using a micro-genetic algorithm. In: Spector L, Good-man E D, Wu A, Langdon W B, Voigt H M, Gen M, Sen S, Dorigo M, Pezeshk S, Garzon M H, Burke E, eds. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2001). San Francisco: Morgan Kaufmann Publishers, 2001, 274–282

    Google Scholar 

  43. Toscano-Pulido G, Coello Coello C A. The micro genetic algorithm 2: towards online adaptation in evolutionary multiobjective optimization. In: Fonseca C M, Fleming P J, Zitzler E, Deb K, Thiele L, eds. Proceedings of Second International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Faro: Springer, LNCS, 2003, 2632: 252–266

    Chapter  Google Scholar 

  44. Jensen M T. Reducing the run-time complexity of multionbjective EAs: the NSGA-II and other algorithms. IEEE Transactions on Evolutionary Computation, 2003, 7(5): 503–515

    Article  Google Scholar 

  45. Kung H T, Luccio F, Preparata F P. On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery, 1975, 22(4): 469–476

    MATH  MathSciNet  Google Scholar 

  46. Rohling G. Multiple objective evolutionary algorithms for independent, computationally expensive objective evaluations. PhD thesis. Atlanta: Georgia Institute of Technology, 2004

    Google Scholar 

  47. Yukish MA. Algorithms to identify Pareto points in multi-dimensional data sets. PhD thesis. Philadelphia: Pennsylvania State University, 2004

    Google Scholar 

  48. Krishnakumar K. Micro-genetic algorithms for stationary and nonstationary function optimization. In: Proceedings of SPIE: Intelligent Control and Adaptive Systems, 1989, 1196: 289–296

    Google Scholar 

  49. Won K S, Ray T. Performance of Kriging and Cokriging based surrogate models within the unified framework for surrogate assisted optimization. In: Proceedings of 2004 Congress on Evolutionary Computation (CEC’2004). Portland: IEEE Service Center, 2004, 2: 1577–1585

    Google Scholar 

  50. Karakasis M K, Giannakoglou K C. Metamodel-assisted multiobjective evolutionary optimization. In: Schilling R, Haase W, Periaux J, Baier H, Bugeda G, eds. Proceedings of EUROGEN 2005-Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, 2005

  51. Voutchkov I, Kene A J. Multiobjective optimization using surrogates. In: Parmee I C, ed. Proceedings of the Seventh International Conference on Adaptive Computing in Design and Manufacture 2006. Bristol: The institute for People-centred Computation, 2006, 167–175

    Google Scholar 

  52. Knowles J. ParEGO: A hybrid algorithm with on-line landscape approximation for exersive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, 2006, 10(1): 50–66

    Article  Google Scholar 

  53. Ray T, Smith W. A surrogate assisted parallel multiobjective evlutionary algorithm for robust engineering design. Engineering Optimization, 2006, 38(8): 997–1011

    Article  Google Scholar 

  54. Reynolds R G, Michalewiez Z, Cavaretta M. Using cultural algorithms for constraint handing in GENOCOP. In: McDonnell J R, Reynolds R G, Fogel D B, eds. Proceedings of the Fourth Annual Conference on Evolutionary Programming. Cambridge: MIT Press, 1995, 298–305

    Google Scholar 

  55. Coello Coello C A, Landa-Becerra R. Evolutionary multionbjective optimization using a cultural algorithm. In: Proceedings of 2003 IEEE Swarm Intelligence Symposium. Indianapolis: IEEE Service Center, 2003

    Google Scholar 

  56. Jin Y C. A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing, 2005, 9(1): 3–12

    Article  Google Scholar 

  57. Smith R E, Dike B A, Stegmann S A. Fitness inheritance in genetic algorithms. In: Proceedings of the 1995 ACM Symposium on Applied Computing. Nashville: ACM Press, 1995, 345–350

    Chapter  Google Scholar 

  58. Bui L T, Abbass H A, Essam D. Fitness inheritance for noisy evolutionary multi-objective optimization. In: Beyer H G, et al, eds. Proceedings of 2005 Genetic and Evolutionary Computation Conference (GECCO’2005). New York: ACM Press, 2005, 1: 779–785

    Chapter  Google Scholar 

  59. Reyes-Sierra M, Coello Coeello C A. A study of fitness inheritance and approximation techniques for multi-objective particle swarm optimization. In: Proceedings of 2005 IEEE Congress on Evolutionary Computation (CEC’2005). Edinburgh: IEEE Service Center, 2005, 1: 65–72

    Chapter  Google Scholar 

  60. Landa-Becerra R, Santana-Quintero L V, Coello Coello C A. Knowledge incorporation in multi-objective evolutionary algorithms. In: Ghosh A, Dehuri S, Ghosh S, eds. Multi-objective Evolutionary Algorithms for Knowledge Discovery from Data Bases. Berlin: Springer, 2008, 23–46

    Chapter  Google Scholar 

  61. Hernández-Díaz A G, Santana-Quintero L V, Coello Coello C A, Caballero R, Molin A J. A new proposal for multi-objective optimization using differential evolution and rough sets theory. In: Keijzer M, et al, eds. Proceedings of 2006 Genetic and Evolutionary Computation Conference (GECCO’2006). Seattle: ACM Press, 2006, 1: 675–682

    Chapter  Google Scholar 

  62. Santana-Quintero L V, Ramírez N, Coello Coello C A. A multiobjective particle swarm optimizer hybridized with scatter search. In: Gelbukh A, Reyes-Garcia C A, eds. Proceedings of MICAI 2006: Advances in Artificial Intelligence, 5th Mexican International Conference on Artificial Intelligence. Apizaco: Springer, 2006, LNAI, 4293: 294–304

    Google Scholar 

  63. Wanner E F, Guimaráe S F G, Takahashi R H C, Fleming P J. Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria. Evolutionary Computation, 2008, 16(2): 185–224

    Article  Google Scholar 

  64. Adra S F, Griffin I, Fleming P J. An informed convergence accelerator for evolutionary multiobjective optimiser. In: Thierens D, ed. Proceedings of 2007 Genetic and Evolutionary Computation Conference (GECCO’2007). London: ACM Press, 2007, 1: 734–740

    Chapter  Google Scholar 

  65. Adra S F. Improving convergence, diversity and pertinency in multiobjective optimisation. PhD thesis. Sheffield: The University of Sheffield, 2007

    Google Scholar 

  66. Kokolo I, Hajime K, Shigenobu K. Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of the Congress on Evolutionary Computation 2001 (CEC’2001). Piscataway: IEEE Service Center, 2001, 2: 957–962

    Google Scholar 

  67. Laumanns M, Thiele L, Deb K, Zitzler E. Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation, 2002, 10(3): 263–282

    Article  Google Scholar 

  68. Villalobos-Arias M A, Toscano Pulido G, Coello Coello C A. A proposal to use stripes to maintain diversity in a multi-objective particle swarm optimizer. In: Proceedings of 2005 IEEE Swarm Intelligence Symposium (SIS’05). IEEE Press, 2005, 22–29

  69. Hernández-Díaz A G, Santana-Quintero L V, Coello Coello C A, Molin A J. Pareto-adaptive ε-dominance. Evolutionary Computation, 2007, 15(4): 493–517

    Article  Google Scholar 

  70. Deb K, Mohan M, Mishra S. Towards a quick computation of wellspread Pareto-optimal solutions. In: Fonseca CM, Fleming P J, Zitzler E, Deb K, Thiele L, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Second International Conference (EMO 2003). Faro: Springer, LNCS, 2003, 2632: 222–236

    Chapter  Google Scholar 

  71. Mostaghim S, Teich J. The role of ε-dominance in multi objective particle swarm optimization methods. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC’2003). Canberra: IEEE Press, 2003, 3: 1764–1771

    Chapter  Google Scholar 

  72. Deb K, Mohan M, Mishra S. Evaluating the ε-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evolutionary Computation, 2005, 13(4): 501–525

    Article  Google Scholar 

  73. Santana-Quintero L V, Coello Coello C A. An algorithm based on differential evolution for multi-objective problems. International Journal of Computational Intelligence Research, 2005, 1(2): 151–169

    Article  MathSciNet  Google Scholar 

  74. Khare V, Yao X, Deb K. Performance scaling of multi-objective evolutionary algorithms. In: Fonseca C M, Fleming P J, Zitzler E, Deb K, Thiele L, eds. Proceedings of Second International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Faro: Springer, LNCS, 2003, 2632: 376–390

    Chapter  Google Scholar 

  75. Hughes E J. Evolutionary many-objective optimisation: many once or one many? In: Proceedings of 2005 IEEE Congress on Evolutionary Computation (CEC’2005). Edinburgh: IEEE Service Center, 2005, 1: 222–227

    Chapter  Google Scholar 

  76. Wagner T, Beume N, Naujoks B. Pareto-, aggregation-, and indicatorbased methods in many-objective optimization. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 742–756

    Chapter  Google Scholar 

  77. Farina M, Amato P. On the optimal solution definition for manycriteria optimization problems. In: Proceedings of the NAFIPSFLINT International Conference’ 2002, Piscataway: IEEE Service Center, 2002, 233–238

    Google Scholar 

  78. Knowles J, Corne D. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 757–771

    Chapter  Google Scholar 

  79. Purshouse R C. On the evolutionary optimisation of many objectives. PhD thesis. Sheffield: The University of Sheffield, 2003

    Google Scholar 

  80. Purshouse R C, Fleming P J. On the evolutionary optimization of many conflicting objectives. IEEE Transactions on Evolutionary Algorithms, 2007, 11(6): 770–784

    Article  Google Scholar 

  81. Di Pierro F. Many-objective evolutionary algorithms and applications to water resources engineering. PhD thesis. Exeter: University of Exeter, 2006

    Google Scholar 

  82. Di Pierro F, Khu S T, Savić D A. An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Transactions on Evolutionary Computation, 2007, 11(1): 17–45

    Article  Google Scholar 

  83. Farina M, Amato P. A fuzzy definition of “optimality” for manycriteria optimization problems. IEEE Transactions on Systems, Man, and Cybernetics Part A—Systems and Humans, 2004, 34(3): 315–32

    Article  Google Scholar 

  84. Sülflow A, Drechsler N, Drechsler R. Robust multi-objective optimization in high dimensional spaces. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 715–726

    Chapter  Google Scholar 

  85. Saxena D K, Deb K. Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: employing correntropy and a novel maximum variance unfolding. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 772–787

    Chapter  Google Scholar 

  86. Brockhoff D, Zitzler E. Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. In: Runarsson T P, Beyer H G, Burke E, Merelo-Guervós J J, Whitley L D, Yao X, eds. Proceedings of Parallel Problem Solving from Nature — PPSN IX, 9th International Conference. Reykjavik: Springer, LNCS, 2006, 4193: 533–542

    Chapter  Google Scholar 

  87. Jaimes A L, Coello Coello C A, Chakraborty D. Objective reduction using a feature selection technique. In: Proceedings of 2008 Genetic and Evolutionary Computation Conference (GECCO’2008). Atlanta: ACM Press, 2008, 674–680

    Google Scholar 

  88. Durillo J J, Nebro A J, Coello Coello C A, Luna F, Alba E. A comparative study of the effect of parameter scalability in multi-objective metaheuristics. In: Proceedings of 2008 Congress on Evolutionary Computation (CEC’2008). Hong Kong: IEEE Service Center, 2008, 1893–1900

    Google Scholar 

  89. Nebro A J, Luna F, Alba E, Dorronsoro B, Durillo J J, Beha M A. AbYSS: adapting scatter search to multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2008, 12(4): 439–457

    Article  Google Scholar 

  90. Corne D, Dorigo M, Glover F, eds. New Ideas in Optimization. London: McGraw-Hill, 1999

    Google Scholar 

  91. De Castro L N, Timmis J. An Introduction to Artificial Immune Systems: A New Computational Intelligence Paradigm. London: Springer, 2002

    Google Scholar 

  92. Dasgupta D, ed. Artificial Immune Systems and Their Applications. Berlin: Springer-Verlag, 1999

    MATH  Google Scholar 

  93. De Castro L N, Von Zuben F J. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, 2002, 6(3): 239–251

    Article  Google Scholar 

  94. Luh G C, Chued C H, Liu W W. MOIA: multi-objective immune algorithm. Engineering Optimization, 2003, 35(2): 143–164

    Article  MathSciNet  Google Scholar 

  95. Luh G C, Chued C H. Multi-objective optimal design of truss structure with immune algorithm. Computers and Structures, 2004, 82: 829–844

    Article  MathSciNet  Google Scholar 

  96. Coello Coello C A, Cruz-Cortés N. Solving multionbjective optimization problems using an artificial immune system. Genetic Programming and Evolvable Machines, 2005, 6(2): 163–190

    Article  Google Scholar 

  97. Freschi F, Repetto M. VIS: an artificial immune network for multiobjective optimization. Engineering Optimization, 2006, 38(8): 975–996

    Article  Google Scholar 

  98. Campelo F, Guimaráes F G, Igarashi H. Overview of artificial immune systems for multi-objective optimization. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 937–951

    Chapter  Google Scholar 

  99. Tavakkoli-Moghaddam R, Rahimi-Vahed A, Mirzaei A H. A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: weighted mean completion time and weighted mean tardiness. Information Sciences, 2007, 177(22): 5072–5090

    Article  MATH  MathSciNet  Google Scholar 

  100. Tavakkoli-Moghaddam R, Rahimi-Vahed A, Mirzaei A H. Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm. International Journal of Advanced Manufacturing Technology, 2008, 36(9–10): 969–981

    Google Scholar 

  101. Zhang X R, Lu B, Gou S, Jiao L. Immune multiobjective optimization algorithm using unsupervised feature selection. In Rothlauf F, et al, eds. Applications of Evolutionary Computing. EvoWorkshops 2006: EvoBIO, EvoCOMNET, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, and EvoSTOC. Budapest: Springers, LNCS, 2006, 3907: 484–494

    Google Scholar 

  102. Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies. In: Varela F J, Bourgine P, eds. Proceedings of the First European Conference on Artificial Life. Cambridge: MIT Press, 1992, 134–142

    Google Scholar 

  103. Dorigo M, Di Caro G. The ant colony optimization meta-heuristic. In: Corne D, Dorigo M, Glover F, eds. New Ideas in Optimization. London: McGraw-Hill, 1999, 11–32

    Google Scholar 

  104. Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence: From Natural to Artificial Systems. New York: Oxford University Press, 1999

    MATH  Google Scholar 

  105. Dorigo M, Stützle T. Ant Colony Optimization. Cambridge: The MIT Press, 2004

    MATH  Google Scholar 

  106. Mariano-Romero C E, Morales-Manzanares E. MOAQ an ant-Q algorithm for multiple objective optimization problems. In: Banzhaf W, Daida J, Eiben A E, Garzon M H, Honavar V, Jakiela M, Smith R E, eds. Proceedings of Genetic and Evolutionary Computing Conference (GECCO 99). San Francisco: Morgan Kaufmann, 1999, 1: 894–901

    Google Scholar 

  107. Iredi S, Merkle D, Middendorf M. Bi-criterion optimization with multi colony ant algorithms. In: Zitzler E, Deb K, Thiele L, Coello Coello C A, Corne D, eds. Proceedings of First International Conference on Evolutionary Multi-Criterion Optimization. Berlin: Springer-Verlag, LNCS, 2001, 1993: 359–372

    Google Scholar 

  108. Barán B, Schaerer M. A multiobjective ant colony system for vehicle routing problem with time windows. In: Proceedings of the 21st IASTED International Conference on Applied Informatics. Innsbruck: IASTED, 2003, 97–102

    Google Scholar 

  109. Guntsch M, Middendorf M. Solving multi-criteria optimization problems with population-based ACO. In: Fonseca C M, Fleming P J, Zitzler E, Deb K, Thiele L, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Second International Conference (EMO 2003). Faro: Springer, LNCS, 2003, 2632: 464–478

    Chapter  Google Scholar 

  110. Doerner K, Gutjahr W J, Hartl R F, Strauss C, Stummer C. Pareto ant colony optimization: a metaheuristic approach to multiobjective portfolio selection. Annals of Operations Research, 2004, 131(1–4): 79–99

    Article  MATH  MathSciNet  Google Scholar 

  111. Doerner K F, Gutjahr W J, Hartl R F, Strauss C, Stummer C. Pareto ant colony optimization with ILP preprocessing in multiobjective portfolio selection. European Journal of Operational Research, 2006, 171(3): 830–841

    Article  MATH  MathSciNet  Google Scholar 

  112. García-Martínez C, Cordón O, Herrera F. A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. European Journal of Operational Research, 2007, 180(1): 116–148

    Article  MATH  Google Scholar 

  113. Ehrgott M, Gandibleu X X. Multiobjective combinatorial optimization—theory, methodology, and applications. In: Ehrgott E, Gandibleux X, eds. Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Boston: Kluwer Academic Publishers, 2002, 369–444

    Google Scholar 

  114. Gandibleu X X, Ehrgott M. 1984–2004 — 20 years of multiobjective metaheuristics. But what about the solution of combinatorial problems with multiple objectives? In: Coello Coello C A, Hernández-Aguirre A, Zitzler E, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Third International Conference (EMO 2005). Guanajuato: Springer, LNCS, 2005, 3410: 33–46

    Google Scholar 

  115. Kennedy J, Eberhart R C. Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks. Piscataway: IEEE Service Center, 1995, 1942–1948

    Chapter  Google Scholar 

  116. Kennedy J, Eberhart R C. Swarm Intelligence. San Francisco: Morgan Kaufmann Publishers, 2001

    Google Scholar 

  117. Eberhart R C, Shi Y. Comparison between genetic algorithms and particle swarm optimization. In: Porto V W, Saravanan N, Waagen D, Eibe A E, eds. Proceedings of the Seventh Annual Conference on Evolutionary Programming. Berlin: Springer-Verlag, 1998, 611–619

    Google Scholar 

  118. Kennedy J, Eberhart R C. A discrete binary version of the particle swarm algorithm. In: Proceedings of the 1997 IEEE Conference on Systems, Man, and Cybernetics. Piscataway: IEEE Service Center, 1997, 4104–4109

    Google Scholar 

  119. Engelbrecht A P. Computational Intelligence: An Introduction. Chichester: John Wiley & Sons, 2003

    Google Scholar 

  120. Engelbrecht A P. Fundamentals of Computational Swarm Intelligence. West Sussex: John Wiley & Sons, 2005

    Google Scholar 

  121. Mostaghim S, Teich J. Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of 2003 IEEE Swarm Intelligence Symposium. Indianapolis: IEEE Service Center, 2003, 26–33

    Chapter  Google Scholar 

  122. Li X D. A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Cantú-Paz E, et al, eds. Proceedings of Genetic and Evolutionary Computation—GECCO 2003, Part I. Berlin: Springer, LNCS, 2003, 2723: 37–48

    Chapter  Google Scholar 

  123. Coello Coello C A, Toscano-Pulido G, Salazar Lechuga M. Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 256–279

    Article  Google Scholar 

  124. Srinivasan D, Seow T H. Particle swarm inspired evolutionary algorithm (PS-EA) for multi-criteria optimization problems. In: Abraham A, Jain L, Goldberg R, eds. Evolutionary Multiobjective Optimization: Theoretical Advances And Applications. London: Springer-Verlag, 2005, 147–165

    Chapter  Google Scholar 

  125. Alvarez-Benitez J E, Everson R M, Fieldsend J E. A MOPSO algorithm based exclusively on Pareto dominance concepts. In: Coello Coello C A, Hernánde-Aguirre A, Zitzler E, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Third International Conference (EMO 2005). Guanajuato: Springer, LNCS, 2005, 3410: 459–473

    Google Scholar 

  126. Reyes-Sierra M, Coello Coello C A. Improving PSO-based multiobjective optimization using crowding, mutation and ε-dominance. In: Coello Coello C A, Aguirre A H, Zitzler E, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Third International Conference (EMO 2005). Guanajuato: Springer, LNCS, 2005, 3410: 505–519

    Google Scholar 

  127. Reyes-Sierra M, Coello Coello C A. Multi-objective particle swarm optimizers: a survey of the state-of-the-art. International Journal of Computational Intelligence Research, 2006, 2(3): 287–308

    MathSciNet  Google Scholar 

  128. Branke J, Mostaghim S. About selecting the personal best in multiobjective particle swarm optimization. In: Runarsson T P, Beyer H G, Burke E, Merelo-Guervós J J, Whitley L D, Yao X, eds. Proceedings of Parallel Problem Solving from Nature — PPSN IX, 9th International Conference. Reykjavik: Springer, LNCS, 2006, 4193: 523–532

    Chapter  Google Scholar 

  129. Toscano-Pulido G, Coello Coello C A, Santana-Quintero L V. EMOPSO: a multi-objective particle swarm optimizer with emphasis on efficiency. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Springer, LNCS, 2007, 4403: 272–285

  130. Glover F. Heuristics for integer programming using surrogate constraints. Decision Sciences, 1977, 8: 156–166

    Article  Google Scholar 

  131. Glover F. Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discrete Applied Mathematics, 1994, 49: 231–255

    Article  MATH  MathSciNet  Google Scholar 

  132. Laguna M, Martí R. Scatter Search: Methodology and Implementations in C. Bostion: Kluwer Academic Publishers, 2003

    Google Scholar 

  133. Marti R. Scatter search-wellsprings and challenges. European Journal of Operational Research, 2006, 169: 351–358

    Article  MATH  MathSciNet  Google Scholar 

  134. Romero-Zaliz R, Zwir I, Ruspini E. Generalized analysis of promoters: a method for DNA sequence description. In: Coello Coello C A, Lamont G B, eds. Applications of Multi-Objective Evolutionary Algorithms. World Scientific, 2004, 427–449

  135. Vasconcelos J A, Maciel J H R D, Parreiras R O. Scatter search techniques applied to electromagnetic problems. IEEE Transactions on Magnetics, 2005, 41(5): 1804–1807

    Article  Google Scholar 

  136. Beausoleil R P. “MOSS” multiobjective scatter search applied to nonlinear multiple criteria optimization. European Journal of Operational Research, 2006, 169(2): 426–44

    Article  MATH  MathSciNet  Google Scholar 

  137. Knowles J, Corne D. Memetic algorithms for multiobjective optimization: issues, methods and prospects. In: Hart W E, Krasnogor N, Smith J E, eds. Recent Advances in Memetic Algorithms. Heidelberg: Springer, Studies in Fuzziness and Soft Computing, 2005, 166: 313–352

    Chapter  Google Scholar 

  138. Surry P D, Radcliffe N J. The COMOGA method: constrained optimisation by multiobjective genetic algorithms. Control and Cybernetics, 1997, 26(3): 391–412

    MathSciNet  Google Scholar 

  139. Hernández-Aguirre A, Botello-Rionda S, Lizárraga-Lizárraga G, Coello Coello C A. IS-PAES: multiobjective optimization with efficient constraint handling. In: Burczyński T, Osyczka A, eds. IUTAM Symposium on Evolutionary Methods in Mechanics. Drodrecht/ Boston/London: Kluwer Academic Publishers, 2004, 111–120

    Chapter  Google Scholar 

  140. Wang Y, Cai Z X. A constrained optimization evolutionary algorithm based on multiobjective optimization techniques. In: Proceeding of 2005 IEEE Congress on Evolutionary Computation (CEC’2005). Edinbugh: IEEE Service Center, 2005, 2: 1081–1087

    Chapter  Google Scholar 

  141. Wang J C, Terpenny J P. Interactive preference incorporation in evolutionary engineering design. In: Jin Y C, ed. Knowledge Incorporation in Evolutionary Computation. Berlin: Springer, 2005, 525–543

    Google Scholar 

  142. Mezura-Montes E, Coello Coello C A. Constrained optimization via multiobjective evolutionary algorithms. In: Knowles J, Corne D, Deb K, eds. Multi-Objective Problem Solving from Nature: From Concepts to Applications. Berlin: Springer, 2008, 53–75

    Chapter  Google Scholar 

  143. Gupta H, Deb K. Handling constraints in robust multi-objective optimization, In: Proceedings of 2005 IEEE Congress on Evolutionary Computation (CEC’2005). Edinburgh: IEEE Service Center, 2005, 1: 25–32

    Chapter  Google Scholar 

  144. Oyama A, Shimoyama K, Fujii K. New constraint-handling method for multi-objective and multi-constraint evolutionary optimization. Transactions of the Japan Society for Aeronautical and Space Sciences, 2007, 50(167): 56–62

    Article  Google Scholar 

  145. Woldesembet Y G, Tessema B G, Yen G G. Constraint handling in multi-objective evolutionary optimization. In: Proceedings of 2007 IEEE Congress on Evolutionary Computation (CEC’2007). Singapore: IEEE Press, 2007, 3077–3084

    Chapter  Google Scholar 

  146. Harada K, Sakum A J, Ono I, Kobayashi S. Constraint-handling method for multi-objective function optimization: Pareto descent repair operator. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T, eds. Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference (EMO 2007). Matshushima: Springer, LNCS, 2007, 4403: 156–170

    Chapter  Google Scholar 

  147. Coello Coello C A. Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 2002, 191(11–12): 1245–1287

    Article  MATH  MathSciNet  Google Scholar 

  148. Cvetković D, Parmee I C. Preferences and their application in evolutionary multiobjective optimisation. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 42–57

    Article  Google Scholar 

  149. Jin Y C, Sendhoff B. Incorporation of fuzzy preferences into evolutionary multiobjective optimization. In: Langdon W B, Cantú-Paz E, Mathias K, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter M A, Schultz A C, Miller J F, Burke E, Jonoska N, eds. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2002). San Francisco: Morgan Kaufmann Publishers, 2002, 683

    Google Scholar 

  150. Brank E J, Deb K. Integrating user preferences into evolutionary multiobjective optimization. In: Jin Y C, ed. Knowledge Incorporation in Evolutionary Computation. Berlin: Springer, 2005, 461–477

    Google Scholar 

  151. FigueirA J, Mousseau V, Roy B, eds. Multiple Criteria Decision Analysis: State of the Art Surveys. New York: Springer, 2005

    MATH  Google Scholar 

  152. Eiben A E, Hinterding R, Michalewicz Z. Parameter control in evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 1999, 3(2): 124–141

    Article  Google Scholar 

  153. Eiben A E, Michalewicz Z, Schoenauer M, Smith J E. Parameter control in evolutionary algorithms. In: Lobo F G, Lima C F, Michalewicz Z, eds. Parameter Setting in Evolutionary Algorithms. Berlin: Springer-Verlag, 2007, 19–46

    Chapter  Google Scholar 

  154. Meyer-Nieberg S, Beyer H G. Self-adaptation in evolutionary algorithms. In: Lobo F G, Lima C F, Michalewicz Z, eds. Parameter Setting in Evolutionary Algorithms. Berlin: Springer-Verlag, 2007, 47–75

    Chapter  Google Scholar 

  155. Laumanns M, Rudolph G, Schwefel H P. Mutation control and convergence in evolutionary multi-objective optimization. In: Proceedings of the 7th International Mendel Conference on Soft Computing (MENDEL 2001). Brno: Brno University of Technology, 2001

    Google Scholar 

  156. Tan K C, Lee T H, Khor E F. Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2001, 5(6): 565–588

    Article  Google Scholar 

  157. Büche D, Guidati G, Stoll P, Kourmoursakos P. Self-organizing maps for Pareto optimization of airfoils. In: Merelo Guervós J J, Adamidis P, Beyer H G, Fernández-Villacanas J L, Schwefel H P, eds. Parallel Problem Solving from Nature-PPSN VII. Granada: Springer-Verlag, LNCS, 2002, 2439: 122–131

    Chapter  Google Scholar 

  158. Abbass H A. The self-adaptive Pareto differential evolution algorithm. In: Proceedings of Congress on Evolutionary Computation (CEC’2002). Piscataway: IEEE Service Center, 2002, 831–836

    Google Scholar 

  159. Zhu Z Y, Leung K S. Asynchronous self-Adjustable island genetic algorithm for multi-objective optimization problems. In: Proceedings of Congress on Evolutionary Computation (CEC’2002). Piscataway: IEEE Service Center, 2002, 1: 837–842

    Google Scholar 

  160. Deb K. Evolutionary multi-objective optimization without additional parameters. In: Lobo F G, Lima C F, Michalewicz Z, eds. Parameter Setting in Evolutionary Algorithms. Berlin: Springer-Verlag, 2007, 241–257

    Chapter  Google Scholar 

  161. De Jong K. Parameter setting in EAs: a 30 year perspective. In: Lobo F G, Lima G F, Michalewicz Z, eds. Parameter Setting in Evolutionary Algorithms. Berlin: Springer-Verlag, 2007, 1–18

    Chapter  Google Scholar 

  162. Toscano-Pulido G. On the use of self-adaptation and elitism for multiobjective particle swarm optimization. PhD thesis. Mexico City: CINVESTAV-IPN, 2005

    Google Scholar 

  163. Laumanns M, Thiele L, Zitzler E. Running time analysis of multiobjective evolutionary algorithms on Pseudo-Boolean functions. IEEE Transactions on Evolutionary Computation, 2004, 8(2): 170–182

    Article  Google Scholar 

  164. Laumanns M, Thiele L, Zitzler E. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing, 2004, 3(1): 37–51

    Article  MATH  MathSciNet  Google Scholar 

  165. Mostaghim S, Teich J, Tyagi A. Comparison of data structures for storing Pareto-sets in MOEAs. In: Proceedings of Congress on Evolutionary Computation (CEC’2002). Piscataway: IEEE Service Center, 2002, 1: 843–848

    Google Scholar 

  166. Habenicht W. Quad trees: a data structure for discrete vector optimization problems. Lecture Notes in Economics and Mathematical Systems, 1982, 209: 136–145

    Google Scholar 

  167. Fieldsend J E, Everson R M, Singh S. Using unconstrained elite archives for multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2003, 7(3): 305–323

    Article  Google Scholar 

  168. Schütze O. A new data structure for the nondominance problem in multi-objective optimization. In: Fonseca C M, Fleming P J, Zitzler E, Deb K, Thiele L, eds. Proceedings of Evolutionary Multi-Criterion Optimization, Second International Conference (EMO 2003). Springer, LNCS, 2003, 2632: 509–518

  169. Laumanns M, Thiele L, Deb K, Zitzler E. On the convergence and diversity-preservation properties of multi-objective evolutionary algorithms. Technical Report 108, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH). Zurich, 2001

    Google Scholar 

  170. Villalobos-Arias M, Coello Coello C A, Hernández-Lerma O. Asymptotic convergence of metaheuristics for multiobjective optimization problems. Soft Computing, 2006, 10(11): 1001–1005

    Article  MATH  Google Scholar 

  171. Schuetze O, Laumanns M, Tantar E, Coello Coello C A, Talbi E G. Convergence of stochastic search algorithms to gap-free Pareto front approximations. In: Thierens D, ed. Proceedings of 2007 Genetic and Evolutionary Computation Conference (GECCO’2007). London: ACM Press, 2007, 1: 892–899

    Chapter  Google Scholar 

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  1. Evolutionary Computation Group, Departamento de Computcaión, Ginvestav-IPN, México D. F., 07300, México

    Carlos A. Coello Coello

  2. UMI-LAFMIA 3175 CNRS, México D. F., 07300, México

    Carlos A. Coello Coello

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Coello Coello, C.A. Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored. Front. Comput. Sci. China 3, 18–30 (2009). https://doi.org/10.1007/s11704-009-0005-7

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