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The Measure of Pareto Optima Applications to Multi-objective Metaheuristics

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Evolutionary Multi-Criterion Optimization (EMO 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2632))

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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.

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References

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Author information

Authors and Affiliations

  1. Institute for Systems Research, University of Maryland, College Park

    M. Fleischer

Authors
  1. M. Fleischer
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Editor information

Editors and Affiliations

  1. Faculty of Sciences and Technology, Centre for Intelligent Systems, University of the Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Carlos M. Fonseca

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    Peter J. Fleming

  3. Department of Electrical Engineering, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology, GloriastraĂźe 35, 8092, ZĂĽrich, Switzerland

    Eckart Zitzler  & Lothar Thiele  & 

  4. Department of Mechanical Engineering, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, UP, 208 016, India

    Kalyanmoy Deb

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© 2003 Springer-Verlag Berlin Heidelberg

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Fleischer, M. (2003). The Measure of Pareto Optima Applications to Multi-objective Metaheuristics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_37

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  • DOI: https://doi.org/10.1007/3-540-36970-8_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-01869-8

  • Online ISBN: 978-3-540-36970-7

  • eBook Packages: Springer Book Archive

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