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

TL;DR

This paper introduces a novel adaptive scalarization method using repulsive dynamics to achieve a uniform approximation of the Pareto front in multi-objective optimization, demonstrated through numerical experiments.

Contribution

It proposes a new heuristic approach with repulsive interactions and stochastic elements to improve Pareto front coverage in scalarization-based methods.

Findings

Effective in bi-objective problems with diverse Pareto front geometries

Improves solution diversity and uniformity

Validated through numerical experiments

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, we propose several adaptive strategies to select such parameters 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.