On the utilization of pair-potential energy functions in multi-objective optimization

Falcón-Cardona，Jesús Guillermo1; Covantes Osuna，Edgar1; Coello Coello，Carlos A.2,3; Ishibuchi，Hisao4

2023-06-01

10.1016/j.swevo.2023.101308

Swarm and Evolutionary Computation   Impact Factor & Quartile

2210-6502

In evolutionary multi-objective optimization (EMO), the pair-potential energy functions (PPFs) have been used to construct diversity-preserving mechanisms to improve Pareto front approximations. Despite PPFs have shown promising results when dealing with different Pareto front geometries, there are still some open research questions to improve the way we employ them. In this paper, we answer three important questions: (1) what is the effect of a crucial parameter of some PPFs?, (2) how do we set the optimal parameter value?, and (3) what is the best PPF in EMO? To solve these questions, we designed a brand-new fast algorithm to generate an approximate solution to a PPF-based subset selection problem and, then, we conducted a comprehensive parametrical study to predict the optimal parameter values using a deep neural network. To show the effectiveness of the PPF-based diversity-preserving mechanisms, we selected two application cases: the generation of reference point sets of benchmark problems (DTLZ, WFG, IDTLZ, IWFG, IMOP, and Viennet) with different Pareto front shapes, and the definition of a PPF-based archive that can be coupled to any multi-objective evolutionary algorithm to construct well-diversified Pareto front approximations. Using several diversity indicators, it is shown that the utilization of PPF-based mechanisms lead to good Pareto front approximations regardless of the Pareto front shape.

Diversity-oriented optimization Multi-objective optimization Pair-potential energy functions Reference sets

English

Others

Consejo Nacional de Ciencia y Tecnología[2016-01-1920];

2-s2.0-85152230734

Scopus

1.Tecnologico de Monterrey,School of Engineering and Sciences,Monterrey, N.L.,Ave. Eugenio Garza Sada 2501,64849,Mexico
2.CINVESTAV-IPN,Department of Computer Science,Mexico City,Av. IPN 2508, Col. San Pedro Zacatenco,07360,Mexico
3.Basque Center for Applied Mathematics (BCAM) & Ikerbasque,Spain
4.Southern University of Science and Technology,Department of Computer Science and Engineering,Shenzhen,1088 Xueyuan Avenue,518055,China

Falcón-Cardona，Jesús Guillermo,Covantes Osuna，Edgar,Coello Coello，Carlos A.,et al. On the utilization of pair-potential energy functions in multi-objective optimization[J]. Swarm and Evolutionary Computation,2023,79.

Falcón-Cardona，Jesús Guillermo,Covantes Osuna，Edgar,Coello Coello，Carlos A.,&Ishibuchi，Hisao.(2023).On the utilization of pair-potential energy functions in multi-objective optimization.Swarm and Evolutionary Computation,79.

Falcón-Cardona，Jesús Guillermo,et al."On the utilization of pair-potential energy functions in multi-objective optimization".Swarm and Evolutionary Computation 79(2023).