Repulsion dynamics for uniform Pareto front approximation in multi‐objective optimization problems

PAMM, vol. 23

Abstract

Abstract Scalarization allows to solve a multi‐objective optimization problem by solving many single‐objective sub‐problems, uniquely determined by some parameters. In this work, several adaptive strategies to select such parameters are proposed in order to obtain a uniform approximation of the Pareto front. This is done by introducing a heuristic dynamics where the parameters interact through a binary repulsive potential. The approach aims to minimize the associated energy potential which is used to quantify the diversity of the computed solutions. A stochastic component is also added to overcome non‐optimal energy configurations. Numerical experiments show the validity of the proposed approach for bi‐ and tri‐objectives problems with different Pareto front geometries.

Authors 1

1. Giacomo Borghi corresponding Aachen Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Applied Mathematics (IGPM) RWTH Aachen University Aachen Germany

   Email: [email protected]

   Giacomo Borghi

   Institute for Geometry and Applied Mathematics (IGPM), RWTH Aachen University, Aachen, Germany