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ParEGO extensions for multi-objective optimization of expensive evaluation functions

Author

Listed:
  • Joan Davins-Valldaura

    (Technocentre)

  • Saïd Moussaoui

    (Ecole Centrale Nantes)

  • Guillermo Pita-Gil

    (Technocentre)

  • Franck Plestan

    (Ecole Centrale Nantes)

Abstract

This paper deals with multi-objective optimization in the case of expensive objective functions. Such a problem arises frequently in engineering applications where the main purpose is to find a set of optimal solutions in a limited global processing time. Several algorithms use linearly combined criteria to use directly mono-objective algorithms. Nevertheless, other algorithms, such as multi-objective evolutionary algorithm (MOEA) and model-based algorithms, propose a strategy based on Pareto dominance to optimize efficiently all criteria. A widely used model-based algorithm for multi-objective optimization is Pareto efficient global optimization (ParEGO). It combines linearly the objective functions with several random weights and maximizes the expected improvement (EI) criterion. However, this algorithm tends to favor parameter values suitable for the reduction of the surrogate model error, rather than finding non-dominated solutions. The contribution of this article is to propose an extension of the ParEGO algorithm for finding the Pareto Front by introducing a double Kriging strategy. Such an innovation allows to calculate a modified EI criterion that jointly accounts for the objective function approximation error and the probability to find Pareto Set solutions. The main feature of the resulting algorithm is to enhance the convergence speed and thus to reduce the total number of function evaluations. This new algorithm is compared against ParEGO and several MOEA algorithms on a standard benchmark problems. Finally, an automotive engineering problem allowing to illustrate the applicability of the proposed approach is given as an example of a real application: the parameter setting of an indirect tire pressure monitoring system.

Suggested Citation

  • Joan Davins-Valldaura & Saïd Moussaoui & Guillermo Pita-Gil & Franck Plestan, 2017. "ParEGO extensions for multi-objective optimization of expensive evaluation functions," Journal of Global Optimization, Springer, vol. 67(1), pages 79-96, January.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-016-0419-3
    DOI: 10.1007/s10898-016-0419-3
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    References listed on IDEAS

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    1. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    2. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    3. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
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    Cited by:

    1. Baquela, Enrique Gabriel & Olivera, Ana Carolina, 2019. "A novel hybrid multi-objective metamodel-based evolutionary optimization algorithm," Operations Research Perspectives, Elsevier, vol. 6(C).

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