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Enhancing computations of nondominated solutions in MOLFP via reference points

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  • João Costa
  • Maria Alves

Abstract

In previous work, Costa and Alves (J Math Sci 161:(6)820–831, 2009 ; 2011 ) have presented Branch & Bound and Branch & Cut techniques that allow for the effective computation of nondominated solutions, associated with reference points, of multi-objective linear fractional programming (MOLFP) problems of medium dimensions (ten objective functions, hundreds of variables and constraints). In this paper we present some results that enhance those computations. Firstly, it is proved that the use of a special kind of achievement scalarizing function guarantees that the computation error does not depend on the dimension of the problem. Secondly, a new cut for the Branch & Cut technique is presented. The proof that this new cut is better than the one in Costa and Alves ( 2011 ) is presented, guaranteeing that it reduces the region to explore. Some computational tests to assess the impact of the new cut on the performance of the Branch & Cut technique are presented. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • João Costa & Maria Alves, 2013. "Enhancing computations of nondominated solutions in MOLFP via reference points," Journal of Global Optimization, Springer, vol. 57(3), pages 617-631, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:617-631
    DOI: 10.1007/s10898-013-0074-x
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    References listed on IDEAS

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    1. Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," ERIM Report Series Research in Management ERS-2004-074-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. João Paulo Costa & Maria João Alves, 2011. "A Branch & Cut Algorithm to Compute Nondominated Solutions in MOLFP via Reference Points," Operations Research Proceedings, in: Bo Hu & Karl Morasch & Stefan Pickl & Markus Siegle (ed.), Operations Research Proceedings 2010, pages 353-358, Springer.
    3. Metev, Boyan & Gueorguieva, Dessislava, 2000. "A simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems," European Journal of Operational Research, Elsevier, vol. 126(2), pages 386-390, October.
    4. Jonathan S. H. Kornbluth & Ralph E. Steuer, 1981. "Multiple Objective Linear Fractional Programming," Management Science, INFORMS, vol. 27(9), pages 1024-1039, September.
    5. Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," Econometric Institute Research Papers ERS-2004-074-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Costa, Joao Paulo, 2007. "Computing non-dominated solutions in MOLFP," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1464-1475, September.
    7. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
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