Evolutionary multi-objective optimization:some current research trends and topics that remain to be explored
Evolutionary multi-objective optimization:some current research trends and topics that remain to be explored
Carlos A. COELLO COELLO1,2()
1. Evolutionary Computation Group, Departamento de Computcaión, Ginvestav-IPN, México D. F. 07300, México; 2. UMI-LAFMIA 3175 CNRS, México D. F. 07300, México
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.
Corresponding Author(s):
COELLO COELLO Carlos A.,Email:ccoello@cs.cinvestav.mx
引用本文:
. Evolutionary multi-objective optimization:some current research trends and topics that remain to be explored[J]. Frontiers of Computer Science in China, 2009, 3(1): 18-30.
Carlos A. COELLO COELLO. Evolutionary multi-objective optimization:some current research trends and topics that remain to be explored. Front Comput Sci Chin, 2009, 3(1): 18-30.
Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning. Reading: Addison-Wesley Publishing Company, 1989
2
Eiben A E, Smith J E. Introduction to Evolutionary Computing. Berlin: Springer, 2003
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
4
Deb K. Multi-Objective Optimization using Evolutionary Algorithms. Chichester: John Wiley & Sons, 2001
5
Coello Coello C A. An updated survey of GA-based multiobjective optimization techniques. ACM Computing Surveys , 2000, 32(2): 109-143 doi: 10.1145/358923.358929
6
Miettinen K M. Nonlinear Multiobjective Optimization. Boston: Kluwer Academic Publishers, 1999
7
Schaffer J D. Multiple objective optimization with vector evaluated genetic algorithms. . Nashville: Vanderbilt University, 1984
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 doi: 10.1109/MCI.2006.1597059
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
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
12
Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation , 1994, 2(3): 221-248 doi: 10.1162/evco.1994.2.3.221
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 doi: 10.1109/4235.797969
16
Knowles J D, Corne D W. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation , 2000, 8(2): 149-172 doi: 10.1162/106365600568167
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 doi: 10.1109/4235.996017
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
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
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
22
K?oppen 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
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
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
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 doi: 10.1109/TEVC.2003.810755
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
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
28
Farhang-Mehr A, Azarm S. Entropy-based multi-objective genetic algorithm for design optimization. Structural and Multidisciplinary Optimization , 2002, 24(25): 351-361 doi: 10.1007/s00158-002-0247-6
29
Zitzler E, Künzli S. Indicator-based selection in multiobjective search. In: Yao X, , eds. Parallel Problem: Solving from Nature – PPSN VIII . Birmingham: Springer-Verlag, LNCS, 2004, 3242: 832-842
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 doi: 10.1109/TEVC.2003.810758
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
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
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 doi: 10.1016/j.ejor.2006.08.008
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 doi: 10.1007/BFb0056872
35
Zitzler E. Evolutionary algorithms for multiobjective optimization: Methods and application. . Zurich: Swiss Federal Institute of Technology (ETH), 1999
36
Igel C, Hansen N, Roth S. Covariance matrix adaptation for multiobjective optimization. Evolutionary Computation , 2007, 15(1): 1-28 doi: 10.1162/evco.2007.15.1.1
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
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
39
Landa-Becerra R, Coello Coello C A. Solving hard multiobjective optimization problems using ?-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
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
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
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
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 doi: 10.1109/TEVC.2003.817234
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
46
Rohling G. Multiple objective evolutionary algorithms for independent, computationally expensive objective evaluations. . Atlanta: Georgia Institute of Technology, 2004
47
Yukish MA. Algorithms to identify Pareto points inmulti-dimensional data sets. . Philadelphia: Pennsylvania State University, 2004
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
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
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
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 doi: 10.1109/TEVC.2005.851274
53
Ray T, Smith W. A surrogate assisted parallel multiobjective evolutionary algorithm for robust engineering design. Engineering Optimization , 2006, 38(8): 997-1011 doi: 10.1080/03052150600882538
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
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
56
Jin Y C. A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing , 2005, 9(1): 3-12 doi: 10.1007/s00500-003-0328-5
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
58
Bui L T, Abbass H A, Essam D. Fitness inheritance for noisy evolutionary multi-objective optimization. In: Beyer H G, , eds. Proceedings of 2005 Genetic and Evolutionary Computation Conference (GECCO’2005) . New York: ACM Press, 2005, 1: 779-785
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
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 doi: 10.1007/978-3-540-77467-9_2
61
Hernández-Díaz A G, Santana-Quintero L V, Coello Coello C A, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough sets theory. In: Keijzer M, , eds. Proceedings of 2006 Genetic and Evolutionary Computation Conference (GECCO’2006) . Seattle: ACM Press, 2006, 1: 675-682
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
63
Wanner E F, Guimaráes 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 doi: 10.1162/evco.2008.16.2.185
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
65
Adra S F. Improving convergence, diversity and pertinency in multiobjective optimisation. . Sheffield: The University of Sheffield, 2007
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
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 doi: 10.1162/106365602760234108
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, Molina J. Pareto-adaptive ?-dominance. Evolutionary Computation , 2007, 15(4): 493-517 doi: 10.1162/evco.2007.15.4.493
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
71
Mostaghim S, Teich J. The role of ?-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
72
Deb K, Mohan M, Mishra S. Evaluating the ?-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evolutionary Computation , 2005, 13(4): 501-525 doi: 10.1162/106365605774666895
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
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
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
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
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
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
79
Purshouse R C. On the evolutionary optimisation of many objectives. . Sheffield: The University of Sheffield, 2003
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 doi: 10.1109/TEVC.2007.910138
81
Di Pierro F. Many-objective evolutionary algorithms and applications to water resources engineering. . Exeter: University of Exeter, 2006
82
Di Pierro F, Khu S T, Savi? D A. An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Transactions on Evolutionary Computation , 2007, 11(1): 17-45 doi: 10.1109/TEVC.2006.876362
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): 315-326 doi: 10.1109/TSMCA.2004.824873
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
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
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
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
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
89
Nebro A J, Luna F, Alba E, Dorronsoro B, Durillo J J, Beham A. AbYSS: adapting scatter search to multiobjective optimization. IEEE Transactions on Evolutionary Computation , 2008, 12(4): 439-457 doi: 10.1109/TEVC.2007.913109
90
Corne D, Dorigo M, Glover F, eds. New Ideas in Optimization. London: McGraw-Hill, 1999
91
De Castro L N, Timmis J. An Introduction to Artificial Immune Systems: A New Computational Intelligence Paradigm. London: Springer, 2002
92
Dasgupta D, ed. Artificial Immune Systems and Their Applications. Berlin: Springer-Verlag, 1999
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 doi: 10.1109/TEVC.2002.1011539
94
Luh G C, Chued C H, Liu W W. MOIA: multi-objective immune algorithm. Engineering Optimization , 2003, 35(2): 143-164 doi: 10.1080/0305215031000091578
95
Luh G C, Chued C H. Multi-objective optimal design of truss structure with immune algorithm. Computers and Structures , 2004, 82: 829-844 doi: 10.1016/j.compstruc.2004.03.003
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 doi: 10.1007/s10710-005-6164-x
97
Freschi F, Repetto M. VIS: an artificial immune network for multiobjective optimization. Engineering Optimization , 2006, 38(8): 975-996 doi: 10.1080/03052150600880706
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
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 doi: 10.1016/j.ins.2007.06.001
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 doi: 10.1007/s00170-006-0906-7
101
Zhang X R, Lu B, Gou S, Jiao L. Immune multiobjective optimization algorithm using unsupervised feature selection. In Rothlauf F, , eds. Applications of Evolutionary Computing . EvoWorkshops 2006: EvoBIO, EvoCOMNET, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, and EvoSTOC. Budapest: Springers, LNCS, 2006, 3907: 484-494
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
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
104
Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence: From Natural to Artificial Systems. New York: Oxford University Press, 1999
105
Dorigo M, Stützle T. Ant Colony Optimization. Cambridge: The MIT Press, 2004
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
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
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
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
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 doi: 10.1023/B:ANOR.0000039513.99038.c6
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 doi: 10.1016/j.ejor.2004.09.009
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 doi: 10.1016/j.ejor.2006.03.041
113
Ehrgott M, Gandibleux 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
114
Gandibleux 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
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
116
Kennedy J, Eberhart R C. Swarm Intelligence. San Francisco: Morgan Kaufmann Publishers, 2001
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
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
119
Engelbrecht A P. Computational Intelligence: An Introduction. Chichester: John Wiley & Sons, 2003
120
Engelbrecht A P. Fundamentals of Computational Swarm Intelligence. West Sussex: John Wiley & Sons, 2005
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
122
Li X D. A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Cantú-Paz E, , eds. Proceedings of Genetic and Evolutionary Computation—GECCO 2003,Part I. Berlin: Springer, LNCS, 2003, 2723: 37-48
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 doi: 10.1109/TEVC.2004.826067
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 doi: 10.1007/1-84628-137-7_7
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
126
Reyes-Sierra M, Coello Coello C A. Improving PSO-based multiobjective optimization using crowding, mutation and ?-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
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
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
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 doi: 10.1111/j.1540-5915.1977.tb01074.x
131
Glover F. Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discrete Applied Mathematics , 1994, 49: 231-255 doi: 10.1016/0166-218X(94)90211-9
132
Laguna M, Mart′? R. Scatter Search : Methodology and Implementations in C. Bostion: Kluwer Academic Publishers, 2003
133
Martí R. Scatter search–wellsprings and challenges. European Journal of Operational Research , 2006, 169: 351-358 doi: 10.1016/j.ejor.2004.08.003
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 doi: 10.1109/TMAG.2005.846474
136
Beausoleil R P. “MOSS” multiobjective scatter search applied to nonlinear multiple criteria optimization. European Journal of Operational Research , 2006, 169(2): 426-449 doi: 10.1016/j.ejor.2004.08.008
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
138
Surry P D, Radcliffe N J. The COMOGA method: constrained optimization by multiobjective genetic algorithms. Control and Cybernetics , 1997, 26(3): 391-412
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
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
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
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 doi: 10.1007/978-3-540-72964-8_3
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
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 doi: 10.2322/tjsass.50.56
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
146
Harada K, Sakuma 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
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 doi: 10.1016/S0045-7825(01)00323-1
148
Cvetkovi? D, Parmee I C. Preferences and their application in evolutionary multiobjective optimisation. IEEE Transactions on Evolutionary Computation , 2002, 6(1): 42-57 doi: 10.1109/4235.985691
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
150
Branke 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
151
Figueira J, Mousseau V, Roy B, eds. Multiple Criteria Decision Analysis: State of the Art Surveys. New York: Springer, 2005
152
Eiben A E, Hinterding R, Michalewicz Z. Parameter control in evolutionary algorithms. IEEE Transactions on Evolutionary Computation , 1999, 3(2): 124-141 doi: 10.1109/4235.771166
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 doi: 10.1007/978-3-540-69432-8_2
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 doi: 10.1007/978-3-540-69432-8_3
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
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 doi: 10.1109/4235.974840
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
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
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
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 doi: 10.1007/978-3-540-69432-8_12
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 doi: 10.1007/978-3-540-69432-8_1
162
Toscano-Pulido G. On the use of self-adaptation and elitism for multiobjective particle swarm optimization. . Mexico City: CINVESTAV-IPN, 2005
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 doi: 10.1109/TEVC.2004.823470
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 doi: 10.1023/B:NACO.0000023415.22052.55
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
166
Habenicht W. Quad trees: a data structure for discrete vector optimization problems. Lecture Notes in Economics and Mathematical Systems , 1982, 209: 136-145
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 doi: 10.1109/TEVC.2003.810733
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
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 doi: 10.1007/s00500-005-0027-5
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
