Using multi-objective evolutionary algorithms for single-objective optimization

4OR

Volumn 11, Issue 3, 2013, Pages 201-228

  Segura, Carlos ^a   Coello Coello, Carlos A ^a   Miranda, Gara ^b   León, Coromoto ^b  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

Constrained optimization; Diversity preservation; Multi objective optimization; Multiobjectivization; Single objective optimization

Indexed keywords

EID: 84885333357     PISSN: 16194500     EISSN: 16142411     Source Type: Journal    
DOI: 10.1007/s10288-013-0248-x     Document Type: Article

References (114)

1. Abbass HA, Deb K (2003) Searching under multi-evolutionary pressures. In: Proceedings of the fourth conference on evolutionary multi-criterion optimization. Springer, pp 391-404.
2. Angantyr A, Andersson J, Aidanpaa JO (2003) Constrained optimization based on a multiobjective evolutionary algorithm. In: 2003 IEEE congress on evolutionary computation, Canberra, Australia, IEEE Service Center, Piscataway, New Jersey, CEC'03, vol 3, pp 1560-1567.
3. Bäck T, Fogel DB, Michalewicz Z (eds) (1997) Handbook of evolutionary computation. IOP Publishing Ltd., Bristol.
4. Bleuler S, Bader J, Zitzler E (2008) Reducing bloat in GP with multiple objectives, natural computing series. In: Knowles J, Corne D, Deb K, Chair D (eds) Multiobjective problem solving from nature. Springer, Berlin, pp 177-200.
5. Brockhoff D, Friedrich T, Hebbinghaus N, Klein C, Neumann F, Zitzler E (2009) On the effects of adding objectives to plateau functions. IEEE Trans Evol Comput 13(3): 591-603.
6. Bui LT, Abbass HA, Branke J (2005) Multiobjective optimization for dynamic environments. In: 2005 IEEE congress on evolutionary computation, CEC'05, vol 3, pp 2349-2356.
7. Burke EK, Gustafson S, Kendall G (2004) Diversity in genetic programming: an analysis of measures and correlation with fitness. IEEE Trans Evol Comput 8(1): 47-62.
8. Cai Z, Wang Y (2006) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evol Comput 10(6): 658-675.
9. Camponogara E, Talukdar SN (1997) A genetic algorithm for constrained and multiobjective optimization. In: Alander JT (ed) 3rd Nordic workshop on genetic algorithms and their applications (3NWGA). University of Vaasa, Vaasa, pp 49-62.
10. Chowdhury S, Dulikravich G (2010) Improvements to single-objective constrained predator-prey evolutionary optimization algorithm. Struct Multidiscip Optim 41(4): 541-554.
11. Churchill A, Husbands P, Philippides A (2013) Multi-objectivization of the tool selection problem on a budget of evaluations. In: Purshouse R, Fleming P, Fonseca C, Greco S, Shaw J (eds) Evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg, pp 600-614.
12. Coello CA (2000a) Constraint-handling using an evolutionary multiobjective optimization technique. Civ Eng Environ Syst 17: 319-346.
13. Coello CA (2000b) Treating constraints as objectives for single-objective evolutionary optimization. Eng Optim 32(3): 275-308.
14. Coello CA (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11-12): 1245-1287.
15. Coello CA, Lamont GB (2004) Applications of multi-objective evolutionary algorithms. World Scientific, Singapore.
16. Coello CA, Mezura-Montes E (2002) Handling constraints in genetic algorithms using dominance-based tournaments. In: Parmee IC (ed) Adaptive computing in design and manufacture V. Springer, London, pp 273-284.
17. Coello CAC, Lamont GB, van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New York iSBN 978-0-387-33254-3.
18. Corne D, Dorigo M, Glover F, Dasgupta D, Moscato P, Poli R, Price KV (1999) New ideas in optimization. McGraw-Hill, Maidenhead, UK.
19. Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49: 1-23.
20. Črepinšek M, Liu SH, Mernik L (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3), Article number: 35.
21. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester.
22. Deb K, Goldberg DE (1989) An investigation of niche and species formation in genetic function optimization. In: Schaffer JD (ed) Proceedings of the third international conference on genetic algorithms. George Mason University, Morgan Kaufmann Publishers, San Mateo, pp 42-50.
23. Deb K, Sundar J (2006) Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'06, pp 635-642.
24. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2): 182-197.
25. Deb K, Lele S, Datta R (2007) A hybrid evolutionary multi-objective and SQP based procedure for constrained optimization. In: Kang L, Liu Y, Zeng S (eds) Advances in computation and intelligence, Lecture Notes in Computer Science, vol 4683. Springer, Berlin Heidelberg, pp 36-45.
26. Doncieux S, Mouret JB (2010) Behavioral diversity measures for Evolutionary Robotics. In: 2010 IEEE congress on evolutionary computation, CEC'10, pp 1-8.
27. Eiben A, Ruttkay Z (1998) Constraint-satisfaction problems. In: Bäck T, Fogel D, Michalewicz M (eds) Handbook of evolutionary computation. IOP Publishing Ltd./Oxford University Press, Oxford, pp C5. 7: 1-C5. 7: 8.
28. Eiben AE, Smith JE (2008) Introduction to evolutionary computing (natural computing series). Springer, Berlin.
29. Esbensen H (1995) Finding (Near-)optimal steiner trees in large graphs. In: Proceedings of the 6th international conference on genetic algorithms. Morgan Kaufmann, San Francisco, CA, USA, pp 485-491.
30. Eshelman L (1990) The CHC adaptive search algorithm. In: Rawlins G (ed) Foudations of genetic algorithms. Morgan Kaufmann, San Francisco, pp 265-283.
31. Fonseca C, Fleming P (1993) Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proceedings of the 5th international conference on genetic algorithms. Morgan Kaufmann, San Francisco, CA, USA, pp 416-423.
32. Friedrich T, Oliveto PS, Sudholt D, Witt C (2008) Theoretical analysis of diversity mechanisms for global exploration. In: Proceedings of the 10th annual conference on Genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'08, pp 945-952.
33. Garcia-Najera A (2009) Preserving population diversity for the multi-objective vehicle routing problem with time windows. In: Proceedings of the 11th annual conference companion on genetic and evolutionary computation conference: late breaking papers, ACM, New York, NY, USA, GECCO'09, pp 2689-2692.
34. Garza-Fabre M, Toscano-Pulido G, Rodriguez-Tello E (2012) Locality-based multiobjectivization for the HP model of protein structure prediction. In: Proceedings of the fourteenth international conference on genetic and evolutionary computation conference, ACM, New York, NY, USA, GECCO'12, pp 473-480.
35. Glover F, Kochenberger GA (2003) Handbook of metaheuristics (International Series in Operations Research & Management Science). Springer, Berlin.
36. Gong W, Cai Z (2008) A multiobjective differential evolution algorithm for constrained optimization. In: 2008 IEEE congress on evolutionary computation, IEEE Service Center, Hong Kong, CEC'08, pp 181-188.
37. Greiner D, Emperador J, Winter G, Galván B (2007) Improving computational mechanics optimum design using helper objectives: an application in frame bar structures. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T (eds) Evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 4403. Springer, Berlin Heidelberg, pp 575-589.
38. Handl J, Kell DB, Knowles J (2007) Multiobjective optimization in bioinformatics and computational biology. IEEE/ACM Trans Comput Biol Bioinforma 4(2): 279-292.
39. Handl J, Lovell SC, Knowles J (2008a) Investigations into the effect of multiobjectivization in protein structure prediction. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N (eds) Parallel problem solving from nature-PPSN X, Lecture Notes in Computer Science, vol 5199. Springer, Berlin Heidelberg, pp 702-711.
40. Handl J, Lovell SC, Knowles J (2008b) Multiobjectivization by decomposition of scalar cost functions. In: Proceedings of the 10th international conference on parallel problem solving from nature: PPSN X. Springer-Verlag, Berlin, Heidelberg, pp 31-40.
41. Hernández-Aguirre A, Botello-Rionda S, Lizárraga-Lizárraga G, Mezura-Montes E (2004) Handling constraints using multiobjective optimization concepts. Int J Numer Methods Eng 59(15): 1989-2017.
42. Horn J, Nafpliotis N, Goldberg DE (1994) A Niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the first IEEE conference on evolutionary computation. IEEE World Congress on Computational Intelligence, IEEE Service Center, Piscataway, New Jersey, vol 1, pp 82-87.
43. Ishibuchi H, Murata T (1998) A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans Syst Man Cybern Part C-Appl Rev 28(3): 392-403.
44. Ishibuchi H, Nojima Y (2007) Optimization of scalarizing functions through evolutionary multiobjective optimization. In: Proceedings of the 4th international conference on evolutionary multi-criterion optimization, Springer, Berlin, Heidelberg, EMO'07, pp 51-65.
45. Ishibuchi H, Doi T, Nojima Y (2006) Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms. In: Proceedings of the 9th international conference on parallel problem solving from nature, Springer, Berlin, Heidelberg, PPSN'06, pp 493-502.
46. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: 2008 IEEE congress on evolutionary computation, CEC'08, pp 2419-2426.
47. Ishibuchi H, Hitotsuyanagi Y, Nakashima Y, Nojima Y (2010) Multiobjectivization from two objectives to four objectives in evolutionary multi-objective optimization algorithms. In: Nature and biologically inspired computing (NaBIC), 2010 Second World Congress on, pp 502-507.
48. Jähne M, Li X, Branke J (2009) Evolutionary algorithms and multi-objectivization for the travelling salesman problem. In: Proceedings of the 11th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'09, pp 595-602.
49. Jansen T, Wegener I (2005) Real royal road functions-where crossover provably is essential. Discret Appl Math 149(1-3): 111-125.
50. Jensen M (2004) Helper-objectives: using multi-objective evolutionary algorithms for single-objective optimisation. J Math Model Algor 3(4): 323-347.
51. Jia L, Zeng S, Zhou D, Zhou A, Li Z, Jing H (2011) Dynamic multi-objective differential evolution for solving constrained optimization problem. In: 2011 IEEE congress on evolutionary computation, pp 2649-2654.
52. Jiménez F, Gómez-Skarmeta A, Sánchez G (2002) How evolutionary multi-objective optimization can be used for goals and priorities based optimization. In: Primer Congreso Español de Algoritmos Evolutivos y Bioinspirados (AEB'02), Mérida España, pp 460-465.
53. de Jong ED, Watson RA, Pollack JB (2001) Reducing bloat and promoting diversity using multi-objective methods. In: Spector L, Goodman ED, Wu A, Langdon WB, Voigt HM, Gen M, Sen S, Dorigo M, Pezeshk S, Garzon MH, Burke EK (eds) Proceedings of the genetic and evolutionary computation conference GECCO'01. Morgan Kaufmann, San Francisco, pp 11-18 GECCO'01.
54. Khare V, Yao X, Deb K (2003) Performance scaling of multi-objective evolutionary algorithms. In: Proceedings of the second evolutionary multi-criterion optimization conference. Springer, LNCS, vol 2632, pp 376-390.
55. Knowles J, Corne D (2003) Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Trans Evol Comput 7(2): 100-116.
56. Knowles J, Corne D (2007) 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 the fourth international conference on evolutionary multi-crietrion optimization, LNCS, vol 4403. Springer, pp 757-771.
57. Knowles J, Watson RA, Corne D (2001) Reducing local optima in single-objective problems by multi-objectivization. In: Proceedings of the first international conference on evolutionary multi-criterion optimization, Springer, London, UK, EMO '01, pp 269-283.
58. Kukkonen S, Lampinen J (2006) Constrained real-parameter optimization with generalized differential evolution. In: 2006 IEEE congress on evolutionary computation, IEEE, Vancouver, BC, Canada, CEC'06, pp 911-918.
59. Landa Silva J, Burke E (2004) Using diversity to guide the search in multi-objective optimization. In: Coello Coello CA, Lamont GB (eds) Applications of multi-objective evolutionary algorithms. World Scientific, Singapore, pp 727-751.
60. Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput 10(3): 263-282.
61. Lehman J, Stanley KO (2008) Exploiting open-endedness to solve problems through the search for novelty. In: Proceedings of the eleventh international conference on artificial life, MIT Press, Cambridge, MA.
62. Liang JJ, Suganthan PN (2006) Dynamic multi-swarm particle swarm optimizer with a novel constrain-handling mechanism. In: 2006 IEEE congress on evolutionary computation, IEEE, Vancouver, BC, Canada, CEC'06, pp 316-323.
63. Liepins G, Hilliard M, Richardson J, Palmer M (1990) Genetic algorithms applications to set covering and traveling salesman problems. In: Brown D, White I, Chelsea C (eds) Operations research and artificial intelligence: the integration of problem-solving strategies. Springer, The Netherlands, pp 29-57.
64. Lochtefeld DF, Ciarallo FW (2011) Helper-objective optimization strategies for the job-shop scheduling problem. Appl Soft Comput 11(6): 4161-4174.
65. Lochtefeld DF, Ciarallo FW (2012) Multiobjectivization via helper-objectives with the tunable objectives problem. IEEE Trans Evol Comput 16(3): 373-390.
66. Louis SJ, Rawlins G (1993) Pareto optimality, GA-easiness and deception. In: Proceedings of the fifth international conference on genetic algorithms, Morgan Kaufmann, pp 118-123.
67. Mahfoud SW (1992) Crowding and preselection revisited. In: Männer R, Manderick B (eds) Parallel problem solving from nature 2 (PPSN-II). Elsevier, Amsterdam, pp 27-36.
68. Mezura-Montes E (2009) Constraint-handling in evolutionary optimization, 1st edn. Springer, UK.
69. Mezura-Montes E, Coello CA (2005) Use of multiobjective optimization concepts to handle constraints in genetic algorithms. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization: theoretical advances and applications. Springer, London, pp 229-254.
70. Mezura-Montes E, Coello CA (2008) Constrained optimization via multiobjective evolutionary algorithms. In: Knowles J, Corne D, Deb K, Chair D (eds) Multiobjective problem solving from nature, natural computing series. Springer, Berlin, pp 53-75.
71. Mezura-Montes E, Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1(4): 173-194.
72. Mouret JB (2011) Novelty-based multiobjectivization. In: Doncieux S, Bredèche N, Mouret JB (eds) New horizons in evolutionary robotics, studies in computational intelligence, vol 341. Springer, Berlin, pp 139-154.
73. Mouret JB, Doncieux S (2009a) Overcoming the bootstrap problem in evolutionary robotics using behavioral diversity. In: 2009 IEEE congress on evolutionary computation, CEC'09, pp 1161-1168.
74. Mouret JB, Doncieux S (2009b) Using behavioral exploration objectives to solve deceptive problems in neuro-evolution. In: Proceedings of the 11th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'09, pp 627-634.
75. Mouret JB, Doncieux S (2012) Encouraging behavioral diversity in evolutionary robotics: an empirical study. Evol Comput 20(1): 91-133.
76. Nebro AJ, Durillo JJ, Luna F, Dorronsoro B, Alba E (2007) Design issues in a multiobjective cellular genetic algorithm. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T (eds) 4th International conference on evolutionary multi-criterion optimization, EMO 2007, Lecture Notes in Computer Science, vol 4403. Springer, pp 126-140.
77. Neumann F, Wegener I (2006) Minimum spanning trees made easier via multi-objective optimization. Nat Comput 5(3): 305-319.
78. Nguyen QU, Nguyen XH, O'Neill M, Agapitos A (2012) An investigation of fitness sharing with semantic and syntactic distance metrics. In: Moraglio A, Silva S, Krawiec K, Machado P, Cotta C (eds) 15th European conference on genetic programming, EuroGP2012, Lecture Notes in Computer Science, vol 7244. Springer, pp 109-120.
79. Oyama A, Shimoyama K, Fujii K (2005) New constraint-handling method for multi-objective multi-constraint evolutionary optimization and its application to space plane design. In: Schilling R, Haase W, Periaux J, Baier H, Bugeda G (eds) Evolutionary and deterministic methods for design, optimization and control with applications to industrial and societal problems (EUROGEN 2005), Munich, Germany.
80. Parmee IC, Purchase G (1994) The development of a directed genetic search technique for heavily constrained design spaces. In: Parmee IC (ed) Adaptive computing in engineering design and control-'94. University of Plymouth, Plymouth, UK, pp 97-102.
81. Price K, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, Berlin Natural Computing Series.
82. Purshouse R, Fleming P (2007) On the evolutionary optimization of many conflicting objectives. IEEE Trans Evol Comput 11(6): 770-784.
83. Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4): 386-396.
84. Ray T, Kang T, Chye SK (2000) An evolutionary algorithm for constrained optimization. In: Whitley D, Goldberg D, Cantú-Paz E, Spector L, Parmee IC, Beyer HG (eds) Proceedings of the genetic and evolutionary computation conference. Morgan Kaufmann, San Francisco, pp 771-777, GECCO'00.
85. Ray T, Singh HK, Isaacs A, Smith W (2009) Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary computation, Springer. Studies in Computational Intelligence, Volume 198. Berlin, Chap 7, pp 145-165.
86. Reynoso-Meza G, Blasco X, Sanchis J, Martínez M (2010) Multiobjective optimization algorithm for solving constrained single objective problems. In: 2010 IEEE congress on evolutionary computation, IEEE Press, Barcelona, Spain, CEC'10, pp 3418-3424.
87. Runarsson TP, Sarker R (1999) Constrained nonlinear integer programming and evolution strategies. In: Proceedings of the 3rd Australia-Japan joint workshop on intelligent and evolutionary systems, Canberra, Australia, pp 193-200.
88. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Genetic algorithms and their applications: proceedings of the first international conference on genetic algorithms, Lawrence Erlbaum, pp 93-100.
89. Scharnow J, Tinnefeld K, Wegener I (2005) The analysis of evolutionary algorithms on sorting and shortest paths problems. J Math Model Algor 3(4): 349-366.
90. Schoenauer M, Xanthakis S (1993) Constrained GA optimization. In: Forrest S (ed) Proceedings of the fifth international conference on genetic algorithms (ICGA-93). University of Illinois at Urbana-Champaign, Morgan Kauffman, San Mateo, CA, pp 573-580.
91. Segredo E, Segura C, León C (2011) A multiobjectivised memetic algorithm for the frequency assignment problem. In: 2011 IEEE congress on evolutionary computation, CEC'11, pp 1132-1139.
92. Segura C, Segredo E, León C (2011) Parallel Island-based multiobjectivised memetic algorithms for a 2D packing problem. In: Proceedings of the 13th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'11, pp 1611-1618.
93. Segura C, Segredo E, León C (2012a) Analysing the robustness of multiobjectivisation approaches applied to large scale optimisation problems. In: Schütze O, Coello C, Tantar A, Tantar E, Bouvry P, Moral P, Legrand P (eds) Evolve-a bridge between probability, set oriented numerics, and evolutionary computation II, advances in intelligent systems and computing. Springer, Berlin, pp 365-391.
94. Segura C, Segredo E, León C (2012b) Scalability and robustness of parallel hyperheuristics applied to a multiobjectivised frequency assignment problem. Soft Comput 1-17.
95. Segura C, Coello Coello CA, Segredo E, Miranda G, León C (2013) Improving the diversity preservation of multi-objective approaches used for single-objective optimization. In: 2013 IEEE congress on evolutionary computation, IEEE, pp 3198-3205.
96. Simões A, Costa E (2011) Memory-based CHC algorithms for the dynamic traveling salesman problem. In: Proceedings of the 13th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, GECCO'11, pp 1037-1044.
97. Singh H, Ray T, Smith W (2010) Performance of infeasibility empowered memetic algorithm for cec 2010 constrained optimization problems. In: 2010 IEEE congress on evolutionary computation (CEC), pp 1-8.
98. Singh HK, Ray T, Sarker RA (2013) Optimum oil production planning using infeasibility driven evolutionary algorithm. Evol Comput 21(1): 65-82.
99. Snijders P, de Jong ED, de Boer B, Weissing F (2006) Multi-objective diversity maintenance. In: Cattolico M (ed) Proceedings of the 11th annual conference on genetic and evolutionary computation, ACM, GECCO'06, pp 1429-1430.
100. Surry PD, Radcliffe NJ (1997) The COMOGA method: constrained optimisation by multiobjective genetic algorithms. Control Cybern 26(3): 391-412.
101. Toffolo A, Benini E (2003) Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol Comput 11(2): 151-167.
102. Toscano Pulido G, Coello Coello CA (2004) Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of the genetic and evolutionary computation conferenc, GECCO'04, Springer, Lecture Notes in Computer Science, vol 3102. Seattle, Washington, USA, pp 225-237.
103. Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4).
104. Venter G, Haftka R (2010) Constrained particle swarm optimization using a bi-objective formulation. Struct Multidiscip Optim 40(1-6): 65-76.
105. Wang Y, Liu D, Cheung YM (2005) Preference Bi-objective evolutionary algorithm for constrained optimization. In: et al YH (ed) Computational intelligence and security. International Conference, CIS 2005, Lecture Notes in Artificial Intelligence, vol 3801. Springer, Xi'an, China, pp 184-191.
106. Wang Y, Cai Z, Guo G, Zhou Y (2007a) Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Trans Syst Man Cybern Part B-Cybern 37(3): 560-575.
107. Wang Y, Liu H, Cai Z, Zhou Y (2007b) An orthogonal design based constrained evolutionary optimization algorithm. Eng Optim 39(6): 715-736.
108. Wang Y, Cai Z, Zhou Y, Zeng W (2008) An adaptive tradeoff model for constrained evolutionary optimization. IEEE Trans Evol Comput 12(1): 80-92.
109. Wang YN, Wu LH, Yuan XF (2010) Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Comput 14(3): 193-209.
110. Watanabe S, Sakakibara K (2005) Multi-objective approaches in a single-objective optimization environment. In: 2005 IEEE congress on evolutionary computation, CEC'05, vol 2, pp 1714-1721.
111. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1): 67-82.
112. Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1(1): 32-49.
113. Zhou Y, Li Y, He J, Kang L (2003) Multi-objective and MGG evolutionary algorithm for constrained optimization. In: 2003 IEEE congress on evolutionary computation, Canberra, Australia, IEEE Service Center, Piscataway, New Jersey, CEC'03, vol 1, pp 1-5.
114. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2): 173-195.