Searching for Local Pareto Optimal Solutions: A Case Study on Polygon-Based Problems

Local Pareto optimal solutions may exist in multi-modal multi-objective optimization problems. Traditional multi-objective evolutionary algorithms usually try to escape from local Pareto optima. However, these solutions may be good enough for the decision makers and are additional options if Pareto optimal solutions are infeasible. In this paper, we modify our previous double-niched evolutionary algorithm (DNEA) to search for local Pareto optimal solutions. The new version is termed as DNEA-L. We apply DNEA-L to 3- and 4-objective polygon-based problems with local Pareto optima. The experimental results show that DNEA-L is efficient to find a large number of local Pareto optimal solutions with good diversity.

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

[2]  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).

[3]  Kalyanmoy Deb,et al.  Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization , 2008, Eur. J. Oper. Res..

[4]  Hisao Ishibuchi,et al.  A Decomposition-Based Evolutionary Algorithm for Multi-modal Multi-objective Optimization , 2018, PPSN.

[5]  Jing J. Liang,et al.  Multimodal multi-objective optimization: A preliminary study , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[6]  Ofer M. Shir,et al.  Enhancing Decision Space Diversity in Evolutionary Multiobjective Algorithms , 2009, EMO.

[7]  Yaochu Jin,et al.  Evolutionary Multiobjective Blocking Lot-Streaming Flow Shop Scheduling With Machine Breakdowns , 2019, IEEE Transactions on Cybernetics.

[8]  Yieh-Hei Wan.  On local Pareto optima , 1975 .

[9]  Jing J. Liang,et al.  A Multiobjective Particle Swarm Optimizer Using Ring Topology for Solving Multimodal Multiobjective Problems , 2018, IEEE Transactions on Evolutionary Computation.

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

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

[12]  Gary G. Yen,et al.  A Multimodal Multiobjective Evolutionary Algorithm Using Two-Archive and Recombination Strategies , 2019, IEEE Transactions on Evolutionary Computation.

[13]  Gary G. Yen,et al.  Hybrid bi-objective portfolio optimization with pre-selection strategy , 2017, Inf. Sci..

[14]  Hisao Ishibuchi,et al.  A Double-Niched Evolutionary Algorithm and Its Behavior on Polygon-Based Problems , 2018, PPSN.

[15]  Hisao Ishibuchi,et al.  Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space , 2010, PPSN.