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Solving multiple-objective problems in the objective space

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Abstract

Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, UNICAMP, Campinas, São Paulo, Brazil

    P. A. V. Ferreira (Assistant Professor)

  2. Electrical Engineering Department, Federal University of Ceará, Fortaleza, Ceará, Brazil

    M. E. S. Machado (Lecturer)

Authors
  1. P. A. V. Ferreira
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  2. M. E. S. Machado
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Additional information

Communicated by W. Stadler

This work was partially sponsored by grants from CNPq and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments.

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Ferreira, P.A.V., Machado, M.E.S. Solving multiple-objective problems in the objective space. J Optim Theory Appl 89, 659–680 (1996). https://doi.org/10.1007/BF02275354

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