NSGA-II With Simple Modification Works Well on a Wide Variety of Many-Objective Problems

In the last two decades, the non-dominated sorting genetic algorithm II (NSGA-II) has been the most widely-used evolutionary multi-objective optimization (EMO) algorithm. However, its performance on a wide variety of many-objective test problems has not been examined in the literature. It has been implicitly assumed by EMO researchers that NSGA-II does not work well on many-objective problems. As a result, NSGA-II has always been excluded from performance comparison with recently proposed many-objective EMO algorithms. Recently, it was pointed out that the performance of NSGA-II on many-objective problems is not always bad. In fact, the poor performance of NSGA-II on many-objective problems is mainly due to the existence of dominance resistant solutions. In this article, we show that the negative effect of the dominance resistant solutions can be remedied by slightly modifying objective values of many-objective problems in NSGA-II. Experimental results show that the modified NSGA-II works well on a wide variety of many-objective test problems.

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[3]  Sanaz Mostaghim,et al.  A knee point based evolutionary multi-objective optimization for mission planning problems , 2017, GECCO.

[4]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[5]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[6]  Yali Wang,et al.  Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones , 2020, PPSN.

[7]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[8]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[9]  Peter J. Fleming,et al.  Evolutionary many-objective optimisation: an exploratory analysis , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[10]  Qingfu Zhang,et al.  Stable Matching-Based Selection in Evolutionary Multiobjective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[11]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[12]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[13]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[14]  Sanaz Mostaghim,et al.  Distance Based Ranking in Many-Objective Particle Swarm Optimization , 2008, PPSN.

[15]  Hisao Ishibuchi,et al.  Effects of dominance resistant solutions on the performance of evolutionary multi-objective and many-objective algorithms , 2020, GECCO.

[16]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[17]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[18]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[19]  Hisao Ishibuchi,et al.  Regular Pareto Front Shape is not Realistic , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[20]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.