Evolutionary many-objective optimization based on linear assignment problem transformations
- 42 Downloads
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.
KeywordsMulti-objective optimization Many-objective optimization Evolutionary computation
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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.
- 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
- 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
- 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
- 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
- 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
- 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
- Fang KT, Wang Y (1994) Number-theoretic methods in statistics. Chapman & Hall/CRC Monographs on Statistics and Applied Probability. Taylor & FrancisGoogle Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology (ETH), Zurich, SwitzerlandGoogle Scholar