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Using Weighted-Sum Functions To Compute Nonsupported Efficient Solutions In Multiobjective Combinatorial-{0,1} Problems

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  • CARLOS GOMES DA SILVA

    (School of Technology and Management, Polytechnic Institute of Leiria, Morro do Lena, Alto Vieiro, 2401-951 Leiria, Portugal;
    INESC-Coimbra, Rua Antero de Quental 199, 3000-033 Coimbra, Portugal)

  • JOÃO CLÍMACO

    (INESC-Coimbra, Rua Antero de Quental 199, 3000-033 Coimbra, Portugal;
    Faculty of Economics, University of Coimbra, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal)

Abstract

In multiobjective linear programming, the weighted-sum functions can be used to characterize the entire set of efficient solutions, but in multiobjective combinatorial-{0,1} problems these functions can only determine a small subset of efficient solutions, called supported efficient solutions. In this paper, we show how the entire set of efficient solutions can be found with the same technique by modifying the original problem. An algorithm is proposed. Some results are presented and the effect of some parameters of the proposed algorithm is illustrated with the multiobjective {0,1}-knapsack problem.

Suggested Citation

  • Carlos Gomes Da Silva & João Clímaco, 2013. "Using Weighted-Sum Functions To Compute Nonsupported Efficient Solutions In Multiobjective Combinatorial-{0,1} Problems," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 27-44.
    • Handle: RePEc:wsi:ijitdm:v:12:y:2013:i:01:n:s0219622013500028
    DOI: 10.1142/S0219622013500028
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    Cited by:

    1. Stan Lipovetsky & Igor Mandel, 2017. "Coefficients of Structural Association," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 285-313, March.

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