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Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems

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  • Pereyra, Victor

Abstract

In this paper, we consider the problem of generating a well sampled discrete representation of the Pareto manifold or the Pareto front corresponding to the equilibrium points of a multi-objective optimization problem. We show how the introduction of simple additional constraints into a continuation procedure produces equispaced points in either of those two sets. Moreover, we describe in detail a novel algorithm for global continuation that requires two orders of magnitude less function evaluations than evolutionary algorithms commonly used to solve this problem. The performance of the methods is demonstrated on problems from the current literature.

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  • Pereyra, Victor, 2009. "Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1935-1947.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:6:p:1935-1947
    DOI: 10.1016/j.matcom.2007.02.007
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    References listed on IDEAS

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    1. Pereyra, V. & Scherer, G. & Wong, F., 2006. "Variable projections neural network training," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 231-243.
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    Cited by:

    1. Benjamin Martin & Alexandre Goldsztejn & Laurent Granvilliers & Christophe Jermann, 2016. "On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach," Journal of Global Optimization, Springer, vol. 64(1), pages 3-16, January.
    2. Alonso, J.J. & LeGresley, P. & Pereyra, V., 2009. "Aircraft design optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1948-1958.
    3. Clempner, Julio B. & Poznyak, Alexander S., 2016. "Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 142-160.
    4. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.

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    1. Alonso, J.J. & LeGresley, P. & Pereyra, V., 2009. "Aircraft design optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1948-1958.

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