Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria

  • Authors:

  • Elizabeth F. Wanner;Frederico G. Guimarães;Ricardo H. C. Takahashi;Peter J. Fleming

  • Affiliations:

  • Departamento de Matemática, Universidade Federal de Ouro Preto, Morro do Cruzeiro, 35400-000, Ouro Preto-MG-Brazil. efwanner@iceb.ufop.br and Department of Automatic Control and Systems Engin ...;Departamento de Engenharia Elétrica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-010, Belo Horizonte-MG-Brazil. fgg@ufmg.br;Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-010, Belo Horizonte-MG-Brazil. taka@mat.ufmg.br;Department of Automatic Control and Systems Engineering, University of Sheffield, S1 3JD, Sheffield-UK. p.fleming@sheffield.ac.uk

  • Venue:
  • Evolutionary Computation
  • Year:
  • 2008

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Abstract

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.