{
  "id": "2211.03378",
  "version": "v1",
  "published": "2022-11-07T09:20:15.000Z",
  "updated": "2022-11-07T09:20:15.000Z",
  "title": "Repulsion dynamics for uniform Pareto front approximation in multi-objective optimization problems",
  "authors": [
    "Giacomo Borghi"
  ],
  "categories": [
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-07T09:20:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C29",
      "90C59",
      "90C26",
      "68T05"
    ],
    "keywords": [
      "uniform pareto front approximation",
      "multi-objective optimization problem",
      "repulsion dynamics",
      "overcome non-optimal energy configurations",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}