The Measure of Pareto Optima Applications to Multi-objective Metaheuristics View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2003

AUTHORS

M. Fleischer

ABSTRACT

This article describes a set function that maps a set of Pareto optimal points to a scalar. A theorem is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a Lebesgue measure, is therefore the best metric to assess the quality of multiobjective optimization algorithms. Moreover, it can be used as the objective function in simulated annealing (SA) to induce convergence in probability to the Pareto optima. An efficient, polynomial-time algorithm for calculating this scalar and an analysis of its complexity is also presented. More... »

PAGES

519-533

References to SciGraph publications

  • 1998. Multiobjective optimization using evolutionary algorithms — A comparative case study in PARALLEL PROBLEM SOLVING FROM NATURE — PPSN V
  • 1990-08. A new approach to the dynamic maintenance of maximal points in a plane in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1996. On the performance assessment and comparison of stochastic multiobjective optimizers in PARALLEL PROBLEM SOLVING FROM NATURE — PPSN IV
  • Book

    TITLE

    Evolutionary Multi-Criterion Optimization

    ISBN

    978-3-540-01869-8
    978-3-540-36970-7

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/3-540-36970-8_37

    DOI

    http://dx.doi.org/10.1007/3-540-36970-8_37

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1019183589


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