Advertisement

Soft Computing

, Volume 22, Issue 16, pp 5491–5512 | Cite as

Evolutionary many-objective optimization based on linear assignment problem transformations

  • Luis Miguel Antonio
  • José A. Molinet Berenguer
  • Carlos A. Coello Coello
Focus
  • 144 Downloads

Abstract

The selection mechanisms that are most commonly adopted by multi-objective evolutionary algorithms (MOEAs) are based on Pareto optimality. However, recent studies have provided theoretical and experimental evidence regarding the unsuitability of Pareto-based selection mechanisms when dealing with problems having four or more objectives. In this paper, we propose a novel MOEA designed for solving many-objective optimization problems. The selection mechanism of our approach is based on the transformation of a multi-objective optimization problem into a linear assignment problem, which is solved by the Kuhn–Munkres’ (Hungarian) algorithm. Our proposed approach is compared with respect to three state-of-the-art MOEAs, designed for solving many-objective optimization problems (i.e., problems having four or more objectives), adopting standard test problems and performance indicators taken from the specialized literature. Since one of our main aims was to analyze the scalability of our proposed approach, its validation was performed adopting test problems having from two to nine objective functions. Our preliminary experimental results indicate that our proposal is very competitive with respect to all the other MOEAs compared, obtaining the best results in several of the test problems adopted, but at a significantly lower computational cost.

Keywords

Multi-objective optimization Many-objective optimization Evolutionary computation 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

We hereby submit the paper entitled “Evolutionary Many-objective Optimization based on Linear Assignment Problem Transformations,” which is submitted for possible publication in this journal. This is an original contribution and is not being considered for possible publication in any other journal.

References

  1. Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795CrossRefGoogle Scholar
  2. Abualigah LM, Khader AT, Hanandeh ES (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci (in press)Google Scholar
  3. Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76CrossRefGoogle Scholar
  4. Berenguer JAM, Coello CAC (2015) Evolutionary many-objective optimization based on Kuhn-Munkres’ algorithm. In: Gaspar-Cunha A, Antunes CH, Coello CAC (eds) Evolutionary multi-criterion optimization, 8th international conference, EMO 2015. Springer. Lecture Notes in Computer Science Vol. 9019, Guimarães, Portugal, pp 3–17Google Scholar
  5. Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653–1669CrossRefzbMATHGoogle Scholar
  6. Bourgeois F, Lassalle JC (1971) An extension of the Munkres algorithm for the assignment problem to rectangular matrices. Commun ACM 14(12):802–804MathSciNetCrossRefzbMATHGoogle Scholar
  7. Bringmann K, Friedrich T (2010) Tight bounds for the approximation ratio of the hypervolume indicator. In: Schaefer R, Cotta C, Kołodziej J, Rudolph G (eds) Parallel Problem Solving from Nature–PPSN XI, 11th International Conference, Proceedings, Part I. Springer, Lecture Notes in Computer Science Vol. 6238, Kraków, Poland, pp 607–616Google Scholar
  8. Bringmann K, Friedrich T (2012) Approximating the least hypervolume contributor: NP-hard in general, but fast in practice. Theoret Comput Sci 425:104–116MathSciNetCrossRefzbMATHGoogle Scholar
  9. Bringmann K, Friedrich T (2012) Convergence of hypervolume-based archiving algorithms II: competitiveness. In: 2012 Genetic and evolutionary computation conference (GECCO’2012). ACM Press, Philadelphia, USA, pp 457–464Google Scholar
  10. Brockhoff D, Friedrich T, Neumann F (2008) Analyzing hypervolume indicator based algorithms. 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, pp 651–660Google Scholar
  11. Coello CAC, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  12. Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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
  14. Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization. Theoretical advances and applications. Springer, Berlin, pp 105–145Google Scholar
  15. Fang KT, Wang Y (1994) Number-theoretic methods in statistics. Chapman & Hall/CRC Monographs on Statistics and Applied Probability. Taylor & FrancisGoogle Scholar
  16. Fleischer M (2003) The measure of pareto optima. Applications to multi-objective metaheuristics. In: Fonseca CM, Fleming PJ, Zitzler E, Deb K, Thiele L (eds) Evolutionary multi-criterion optimization (EMO 2003), Lecture notes in computer science, vol 2632. Springer, Berlin, pp 519–533 (2003)Google Scholar
  17. Gale D, Shapley L (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15MathSciNetCrossRefzbMATHGoogle Scholar
  18. Hammersley JM (1960) Monte-Carlo methods for solving multivariable problems. Ann N Y Acad Sci 86(3):844–874MathSciNetCrossRefzbMATHGoogle Scholar
  19. 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):477–506CrossRefzbMATHGoogle Scholar
  20. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: 2008 IEEE congress on evolutionary computation CEC’2008 (IEEE World Congress on Computational Intelligence). Hong Kong, pp 2424–2431Google Scholar
  21. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: 2008 IEEE congress on evolutionary computation (CEC’2008), pp 2419–2426. IEEE Press, Hong KongGoogle Scholar
  22. 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) Evolutionary multi-criterion optimization EMO’2007, lecture notes in computer science, vol 4403. Springer, Berlin, pp 757–771Google Scholar
  23. Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8(2):149–172CrossRefGoogle Scholar
  24. Kokolo I, Hajime K, Shigenobu K (2001) Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of the Congress on Evolutionary Computation 2001 (CEC’2001), vol 2. IEEE Service Center, Piscataway, New Jersey, pp 957–962Google Scholar
  25. Korobov NM (1959) The approximate computation of multiple integrals. Dokl Akad Nauk SSSR 124:1207–1210MathSciNetzbMATHGoogle Scholar
  26. Kuhn HW (1955) The Hungarian method for the assignment problem. Nav Res Logist Q 2(1–2):83–97MathSciNetCrossRefzbMATHGoogle Scholar
  27. Li B, Li J, Tang K, Yao X (2015) Many-objective evolutionary algorithms: a survey. ACM Comput Surv 48(1):13:1–13:35CrossRefGoogle Scholar
  28. Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13(2):284–302CrossRefGoogle Scholar
  29. Li M, Yang S, Liu X, Shen R (2013) A comparative study on evolutionary algorithms for many-objective optimization. In: Purshouse RC, Fleming PJ, Fonseca CM, Greco S, Shaw J (eds) Evolutionary multi-criterion optimization, 7th international conference, EMO 2013. Springer. Lecture Notes in Computer Science vol 7811, Sheffield, UK, pp 261–275Google Scholar
  30. Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1):32–38MathSciNetCrossRefzbMATHGoogle Scholar
  31. Phan DH, Suzuki J (2013) R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization. In: IEEE congress on evolutionary computation (CEC’2013), pp 1836–1845Google Scholar
  32. Purshouse RC, Fleming PJ (2007) On the evolutionary optimization of many conflicting objectives. IEEE Trans Evolut Algorithms 11(6):770–784CrossRefGoogle Scholar
  33. Rostami S, Neri F (2016) Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm. Integr Comput-Aided Eng 23(4):313–329CrossRefGoogle Scholar
  34. Scheffé H (1958) Experiments with mixtures. J R Stat Soc: Ser B (Methodol) 20(2):344–360MathSciNetzbMATHGoogle Scholar
  35. Steuer RE (1986) Multiple criteria optimization: theory, computation and application. Wiley, New YorkzbMATHGoogle Scholar
  36. Tan YY, Jiao YC, Li H, Wang XK (2013) MOEA/D + uniform design: a new version of MOEA/D for optimization problems with many objectives. Comput Oper Res 40(6):1648–1660MathSciNetCrossRefzbMATHGoogle Scholar
  37. von Lücken C, Baran B, Brizuela C (2014) A survey on multi-objective evolutionary algorithms for many-objective problems. Comput Optim Appl 58(3):707–756MathSciNetzbMATHGoogle Scholar
  38. Wang Y, Fang KT (1990) Number-theoretic method in applied statistics (II). Chin Ann Math Ser B 11:859–914MathSciNetGoogle Scholar
  39. Yevseyeva I, Guerreiro AP, Emmerich MT, Fonseca CM (2014) A Portfolio optimization approach to selection in multiobjective evolutionary algorithms. In: Bartz-Beielstein T, Branke J, Filipič B, Smith J (eds) Parallel problem solving from nature—PPSN XIII, 13th international conference. Springer. Lecture Notes in Computer Science vol 8672, Ljubljana, Slovenia, pp 672–681Google Scholar
  40. Yuan Y, Xu H, Wang B, Yao X (2016) A new dominance relation-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(1):16–37CrossRefGoogle Scholar
  41. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  42. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology (ETH), Zurich, SwitzerlandGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico CityMexico

Personalised recommendations