The Measure of Pareto Optima: Applications to Multiobjective Metaheuristics

Abstract

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof 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 algorithm for calculating this scalar and analysis of its complexity is presented.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2002
Accession Number
ADA441037

Entities

People

  • Mark Fleischer

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Computer Science
  • Computers
  • Convergence
  • Demographic Cohorts
  • Evolutionary Algorithms
  • Fish
  • Genetic Algorithms
  • Geometry
  • Intervals
  • Iterations
  • Military Research
  • Multiobjective Optimization
  • Optimization
  • Theorems
  • Two Dimensional

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research