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

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