Many-Objective Problems Are Not Always Difficult for Pareto Dominance-Based Evolutionary Algorithms

1 Recently, it has repeatedly been reported that the search ability of Pareto dominance-based multi-objective evolutionary algorithms severely deteriorates with the increase in the number of objectives. In this paper, we examine the generality of the reported observations through computational experiments on a wide variety of test problems. First, we generate 18 types of test problems by combining various properties of Pareto fronts and feasible regions. Next, we examine the performance of a frequently-used Pareto dominance-based evolutionary algorithm called NSGA-II on the generated test problems in comparison with four decompositionbased algorithms. We observe that the performance of NSGA-II severely degrades for three types of many-objective test problems which are similar to frequently-used DTLZ1-4 test problems with triangular Pareto fronts. However, better results are obtained by NSGA-II than all the examined decomposition-based algorithms for nine types of test problems even when they have ten objectives. Then, we discuss why NSGA-II does not work well on DTLZ type test problems whereas it works well on other test problems.

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

[2]  Yuren Zhou,et al.  A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[3]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

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

[5]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

[6]  Xin Yao,et al.  of Birmingham Quality evaluation of solution sets in multiobjective optimisation , 2019 .

[7]  Carlos A. Brizuela,et al.  A survey on multi-objective evolutionary algorithms for many-objective problems , 2014, Computational Optimization and Applications.

[8]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

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

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

[11]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

[12]  Hisao Ishibuchi,et al.  How to Specify a Reference Point in Hypervolume Calculation for Fair Performance Comparison , 2018, Evolutionary Computation.

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

[14]  Hisao Ishibuchi,et al.  On Scalable Multiobjective Test Problems With Hardly Dominated Boundaries , 2019, IEEE Transactions on Evolutionary Computation.

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

[16]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[17]  Zhang Yi,et al.  IGD Indicator-Based Evolutionary Algorithm for Many-Objective Optimization Problems , 2018, IEEE Transactions on Evolutionary Computation.

[18]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[19]  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.

[20]  Hisao Ishibuchi,et al.  Pareto Fronts of Many-Objective Degenerate Test Problems , 2016, IEEE Transactions on Evolutionary Computation.

[21]  Tao Zhang,et al.  Localized Weighted Sum Method for Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[22]  Hisao Ishibuchi,et al.  Two-Layered Weight Vector Specification in Decomposition-Based Multi-Objective Algorithms for Many-Objective Optimization Problems , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[23]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

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

[25]  Yuren Zhou,et al.  A Many-Objective Evolutionary Algorithm With Pareto-Adaptive Reference Points , 2020, IEEE Transactions on Evolutionary Computation.

[26]  Yuren Zhou,et al.  Evolutionary Many-Objective Optimization Based on Dynamical Decomposition , 2019, IEEE Transactions on Evolutionary Computation.

[27]  David W. Corne,et al.  Techniques for highly multiobjective optimisation: some nondominated points are better than others , 2007, GECCO '07.

[28]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[29]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[30]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[31]  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).

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

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

[34]  Hisao Ishibuchi,et al.  Behavior of Multiobjective Evolutionary Algorithms on Many-Objective Knapsack Problems , 2015, IEEE Transactions on Evolutionary Computation.

[35]  Hisao Ishibuchi,et al.  Modified Distance Calculation in Generational Distance and Inverted Generational Distance , 2015, EMO.

[36]  Kalyanmoy Deb,et al.  An Improved Adaptive Approach for Elitist Nondominated Sorting Genetic Algorithm for Many-Objective Optimization , 2013, EMO.

[37]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

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

[39]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[40]  Carlos A. Coello Coello,et al.  On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem , 2011, IEEE Transactions on Evolutionary Computation.