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Multicriteria optimization with a multiobjective golden section line search

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Abstract

This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions.

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Authors and Affiliations

  1. Departamento de Engenharia Elétrica, Universidade Federal de Minas Gerais, Minas Gerais, Brazil

    Douglas A. G. Vieira & Rodney R. Saldanha

  2. Departamento de Matemática, Universidade Federal de Minas Gerais, Minas Gerais, Brazil

    Ricardo H. C. Takahashi

Authors
  1. Douglas A. G. Vieira
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  2. Ricardo H. C. Takahashi
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  3. Rodney R. Saldanha
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Correspondence to Ricardo H. C. Takahashi.

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Vieira, D.A.G., Takahashi, R.H.C. & Saldanha, R.R. Multicriteria optimization with a multiobjective golden section line search. Math. Program. 131, 131–161 (2012). https://doi.org/10.1007/s10107-010-0347-9

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  • DOI: https://doi.org/10.1007/s10107-010-0347-9

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