Soft Computing

, Volume 21, Issue 9, pp 2407–2419 | Cite as

Ensemble of many-objective evolutionary algorithms for many-objective problems

  • Yalan Zhou
  • Jiahai Wang
  • Jian Chen
  • Shangce Gao
  • Luyao Teng
Methodologies and Application

Abstract

The performance of most existing multiobjective evolutionary algorithms deteriorates severely in the face of many-objective problems. Many-objective optimization has been gaining increasing attention, and many new many-objective evolutionary algorithms (MaOEA) have recently been proposed. On the one hand, solution sets with totally different characteristics are obtained by different MaOEAs, since different MaOEAs have different convergence-diversity tradeoff relations. This may suggest the potential usefulness of ensemble approaches of different MaOEAs. On the other hand, the performance of MaOEAs may vary greatly from one problem to another, so that choosing the most appropriate MaOEA is often a non-trivial task. Hence, an MaOEA that performs generally well on a set of problems is often desirable. This study proposes an ensemble of MaOEAs (EMaOEA) for many-objective problems. When solving a single problem, EMaOEA invests its computational budget to its constituent MaOEAs, runs them in parallel and maintains interactions between them by a simple information sharing scheme. Experimental results on 80 benchmark problems have shown that, by integrating the advantages of different MaOEAs into one framework, EMaOEA not only provides practitioners a unified framework for solving their problem set, but also may lead to better performance than a single MaOEA.

Keywords

Many-objective evolutionary algorithm Ensemble Algorithm portfolios Many-objective optimization 

References

  1. Adra S, Fleming P (2011) Diversity management in evolutionary many-objective optimization. IEEE Trans Evol Comput 15(2):183–195CrossRefGoogle Scholar
  2. Alcala-Fdez J, Sanchez L, Garcia S (2008) KEEL: a software tool to assess evolutionary algorithms to data mining problems. Soft Comput 13(3):307–318CrossRefGoogle Scholar
  3. Asafuddoula M, Ray T, Sarker R (2015) A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans Evol Comput 19(3):445–460CrossRefGoogle Scholar
  4. Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76CrossRefGoogle Scholar
  5. Bandyopadhyay S, Mukherjee A (2015) An algorithm for many-objective optimization with reduced objective computations: a study in differential evolution. IEEE Trans Evol Comput 19(3):400–413CrossRefGoogle Scholar
  6. Brockhoff D, Zitzler E (2009) Objective reduction in evolutionary multiobjective optimization: theory and applications. Evol Comput 17(2):135–166CrossRefGoogle Scholar
  7. Cheng J, Yen GG, Zhang G (2015) A many-objective evolutionary algorithm with enhanced mating and environmental selections. IEEE Trans Evol Comput 19(4):592–605CrossRefGoogle Scholar
  8. Cheshmehgaz H, Haron H, Sharifi A (2013) The review of multiple evolutionary searches and multi-objective evolutionary algorithms. Artif Intell Rev 43(3):311–343CrossRefGoogle Scholar
  9. Chikumbo O, Goodman ED, Deb K (2012) Approximating a multidimensional pareto front for a land use management problem: a modified MOEA with an epigenetic silencing metaphor. In: Proceedings of the 2012 IEEE Congress on Evolutionary Computation, pp 1–9Google Scholar
  10. Dai C, Wang Y, Hu L (2015) An improved \(\alpha \)-dominance strategy for many-objective optimization problems. Soft Comput. doi:10.1007/s00500-014-1570-8 (in press)
  11. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: Solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601CrossRefGoogle Scholar
  12. Deb K, Pratap A, Agrawal S, Meyarivan T (2002a) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  13. Deb K, Thiele L, Laumanns M, Zitzler E (2002b) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation, vol 1, pp 825–830Google Scholar
  14. Deb K, Mohan M, Mishra S (2005) Evaluating the \(\epsilon \)-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evol Comput 13(4):501–525CrossRefGoogle Scholar
  15. Derrac J, Garcia S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18CrossRefGoogle Scholar
  16. Fu G, Kapelan Z, Kasprzyk JR, Reed P (2013) Optimal design of water distribution systems using many-objective visual analytics. J Water Resour Plann Manag 139(6):624–633CrossRefGoogle Scholar
  17. Gomes C, Selman B (2001) Algorithm portfolios. Artif Intell 126(1–2):43–62MathSciNetCrossRefMATHGoogle Scholar
  18. Gong D, Wang G, Sun X, Han Y (2015a) A set-based genetic algorithm for solving the many-objective optimization problem. Soft Comput 19(6):1477–1495CrossRefGoogle Scholar
  19. Gong YJ, Chen WN, Zhan ZH, Zhang J, Li Y, Zhang Q (2015b) Distributed evolutionary algorithms and their models: a survey of the state-of-the-art. Appl Soft Comput 34:286–300CrossRefGoogle Scholar
  20. Hadka D, Reed P (2013) Borg: an auto-adaptivemany-objective evolutionary computing framework. Evol Comput 21(2):231–259CrossRefGoogle Scholar
  21. He Z, Yen GG (2015) Many-objective evolutionary algorithm: objective space reduction + diversity improvement. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2433266 (in press)
  22. He Z, Yen GG, Zhang J (2014) Fuzzy-based Pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18(2):269–285CrossRefGoogle Scholar
  23. Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477–506CrossRefMATHGoogle Scholar
  24. Hughes E (2008) Fitness assignment methods for many-objective problems. In: Knowles J, Corne D, Deb K (eds) Multi-objective problem solving from nature: from concepts to applications. Springer, Berlin, pp 307–329Google Scholar
  25. Ishibuchi H, Tanigaki Y, Masuda H, Nojima Y (2014) Distance-based analysis of crossover operators for many-objective knapsack problems. Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics) vol 8672, pp 600–610Google Scholar
  26. Ishibuchi H, Akedo N, Nojima Y (2015) Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems. IEEE Trans Evol Comput 19(2):264–283CrossRefGoogle Scholar
  27. Jiang S, Zhang J, Ong Y, Zhang AN, Tan PS (2015) A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans Cybern 45(10):2202–2213CrossRefGoogle Scholar
  28. Li K, Deb K, Zhang Q, Kwong S (2015a) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evolut Comput 19(5):694–716CrossRefGoogle Scholar
  29. Li M, Yang S, Liu X, Shen R (2013) A comparative study on evolutionary algorithms for many-objective optimization. Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics) vol 7811. LNCS, pp 261–275Google Scholar
  30. Li M, Yang S, Liu X (2014) Shift-based density estimation for pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348–365CrossRefGoogle Scholar
  31. Li M, Yang S, Liu X (2015b) Bi-goal evolution for many-objective optimization problems. Artif Intell 228:45–65MathSciNetCrossRefMATHGoogle Scholar
  32. Lygoe R, Cary M, Fleming PJ (2013) A real-world application of a many-objective optimisation complexity reduction process. In: Proceedings of the 7th international conference on evolutionary multi-criterion optimization, pp 641–655Google Scholar
  33. Ma X, Qi Y, Li L, Liu F, Jiao L, Wu J (2014) MOEA/D with uniform decomposition measurement for many-objective problems. Soft Comput 18(12):2541–2564CrossRefGoogle Scholar
  34. Mallipeddi R, Suganthan P (2010) Ensemble of constraint handling techniques. IEEE Trans Evol Comput 14(4):561–597CrossRefGoogle Scholar
  35. Peng F, Tang K, Chen G, Yao X (2010) Population-based algorithm portfolios for numerical optimization. IEEE Trans Evol Comput 14(5):782–800CrossRefGoogle Scholar
  36. Roy P, Islam M, Murase K, Yao X (2015) Evolutionary path control strategy for solving many-objective optimization problem. IEEE Trans Cybern 45(4):702–715CrossRefGoogle Scholar
  37. Sato H, Aguirre H, Tanaka K (2013) Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems. Ann Math Artif Intell 68(4):197–224MathSciNetCrossRefMATHGoogle Scholar
  38. Saxena D, Duro J, Tiwari A, Deb K, Zhang Q (2013) Objective reduction in many-objective optimization: linear and nonlinear algorithms. IEEE Trans Evol Comput 17(1):77–99CrossRefGoogle Scholar
  39. Singh H, Isaacs A, Ray T (2011) A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Trans Evol Comput 15(4):539–556CrossRefGoogle Scholar
  40. Sun X, Chen Y, Liu Y, Gong D (2015) Indicator-based set evolution particle swarm optimization for many-objective problems. Soft Comput. doi:10.1007/s00500-015-1637-1 (in press)
  41. Talbi EG, Basseur M, Nebro A, Alba E (2012) Multi-objective optimization using metaheuristics: non-standard algorithms. Int Trans Oper Res 19(1–2):283–305MathSciNetCrossRefMATHGoogle Scholar
  42. Tang K, Peng F, Chen G, Yao X (2014) Population-based algorithm portfolios with automated constituent algorithms selection. Inf Sci 279:94–104CrossRefGoogle Scholar
  43. Tusar T, Filipic B (2015) Visualization of Pareto front approximations in evolutionary multiobjective optimization: a critical review and the prosection method. IEEE Trans Evol Comput 19(2):225–245CrossRefGoogle Scholar
  44. Von Lucken C, Baran B, Brizuela C (2014) A survey on multi-objective evolutionary algorithms for many-objective problems. Comput Optim Appl 58(3):707–756MathSciNetMATHGoogle Scholar
  45. Vrugt J, Robinson B (2007) Improved evolutionary optimization from genetically adaptive multimethod search. Proc Natl Acad Sci USA 104(3):708–711CrossRefGoogle Scholar
  46. Walker DJ, Everson RM, Fieldsend JE (2013) Visualising mutually non-dominating solution sets in many-objective optimisation. IEEE Trans Evol Comput 17(2):165–184CrossRefGoogle Scholar
  47. Wang H, Yao X (2014) Corner sort for Pareto-based many-objective optimization. IEEE Trans Cybern 44(1):92–102CrossRefGoogle Scholar
  48. Wang H, Jiao L, Yao X (2015a) Two\_Arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19(4):524–541CrossRefGoogle Scholar
  49. Wang J, Zhong Z, Zhou Y, Zhou Y (2015b) Multiobjective optimization algorithm with objective-wise learning for continuous multiobjective problems. J Ambient Intell Hum Comput 6(5):571–585MathSciNetCrossRefGoogle Scholar
  50. Wang J, Zhou Y, Wang Y, Zhang J, Chen CP, Zheng Z (2015) Multiobjective vehicle routing problems with simultaneous delivery and pickup and time windows: formulation, instances and algorithms. IEEE Trans Cybern (in press)Google Scholar
  51. Wang R, Purshouse R, Fleming P (2013) Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Trans Evol Comput 17(4):474–494CrossRefGoogle Scholar
  52. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1(6):80–83Google Scholar
  53. Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721–736CrossRefGoogle Scholar
  54. Yuan Y, Xu H, Wang B, Yao X (2015a) A new dominance relation based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2420112 (in press)
  55. Yuan Y, Xu H, Wang B, Zhang B, Yao X (2015b) Balancing convergence and diversity in decompisition-based many-objective optimizers. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2443001 (in press)
  56. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  57. Zhang X, Tian Y, Jin Y (2014) A knee point driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput. doi:10.1109/TEVC.2014.2378512 (in press)
  58. Zhao SZ, Suganthan P, Zhang Q (2012) Decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes. IEEE Trans Evol Comput 16(3):442–446CrossRefGoogle Scholar
  59. 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):23–49CrossRefGoogle Scholar
  60. Zhou Y, Wang J (2015) A local search-based multiobjective optimization algorithm for multiobjective vehicle routing problem with time windows. IEEE Syst J 9(3):1100–1113MathSciNetCrossRefGoogle Scholar
  61. Zhu C, Xu L, Goodman E (2015) Generalization of Pareto optimality for many-objective evolutionary optimization. IEEE Trans Evol Comput. doi:10.1109/TEVC.2015.2457245 (in press)

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yalan Zhou
    • 2
  • Jiahai Wang
    • 1
  • Jian Chen
    • 1
  • Shangce Gao
    • 3
  • Luyao Teng
    • 4
  1. 1.Department of Computer ScienceSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.College of InformationGuangdong University of Finance and EconomicsGuangzhouPeople’s Republic of China
  3. 3.Department of Intellectual Information Engineering, Faculty of EngineeringUniversity of ToyamaToyamaJapan
  4. 4.College of Engineering and ScienceVictoria UniversityMelbourneAustralia

Personalised recommendations