Approximating Pareto Set Topology by Cubic Interpolation on Bi-objective Problems - Archive ouverte HAL
Communication Dans Un Congrès Année : 2019

Approximating Pareto Set Topology by Cubic Interpolation on Bi-objective Problems

Résumé

Difficult Pareto set topology refers to multi-objective problems with geometries of the Pareto set such that neighboring optimal solutions in objective space differ in several or all variables in decision space. These problems can present a tough challenge for evolutionary multi-objective algorithms to find a good approximation of the optimal Pareto set well-distributed in decision and objective space. One important challenge optimizing these problems is to keep or restore diversity in decision space. In this work, we propose a method that learns a model of the topology of the solutions in the population by performing parametric spline interpolations for all variables in decision space. We use Catmull-Rom parametric curves as they allow us to deal with any dimension in decision space. The proposed method is appropriated for bi-objective problems since their optimal set is a one-dimensional curve according to the Karush-Kuhn-Tucker condition. Here, the proposed method is used to promote restarts from solutions generated by the model. We study the effectiveness of the proposed method coupled to NSGA-II and two variations of MOEA/D on problems with difficult Pareto set topology. These algorithms approach very differently the Pareto set. We argue and discuss their behavior and its implications for model building.
Fichier principal
Vignette du fichier
emo2019_yuri.pdf (785.2 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02064548 , version 1 (14-09-2021)

Identifiants

Citer

Yuri Marca, Hernan Aguirre, Saúl Zapotecas Martinez, Arnaud Liefooghe, Bilel Derbel, et al.. Approximating Pareto Set Topology by Cubic Interpolation on Bi-objective Problems. EMO 2019 - International Conference on Evolutionary Multi-Criterion Optimization, Mar 2019, East Lansing, Michigan, United States. pp.386-398, ⟨10.1007/978-3-030-12598-1_31⟩. ⟨hal-02064548⟩
116 Consultations
69 Téléchargements

Altmetric

Partager

More