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ParEGO extensions for multi-objective optimization of expensive evaluation functions

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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.

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Notes

  1. Several recordings of all vehicle data during real drivings.

  2. When the tire pressure is under a 20% of the nominal pressure.

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Authors and Affiliations

  1. Renault, Technocentre, 78280, Guyancourt, France

    Joan Davins-Valldaura & Guillermo Pita-Gil

  2. IRCCyN, UMR CNRS, Ecole Centrale Nantes, 44321, Nantes, France

    Saïd Moussaoui & Franck Plestan

Authors
  1. Joan Davins-Valldaura
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  2. Saïd Moussaoui
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  3. Guillermo Pita-Gil
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  4. Franck Plestan
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Correspondence to Joan Davins-Valldaura.

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Davins-Valldaura, J., Moussaoui, S., Pita-Gil, G. et al. ParEGO extensions for multi-objective optimization of expensive evaluation functions. J Glob Optim 67, 79–96 (2017). https://doi.org/10.1007/s10898-016-0419-3

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