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Finding all nondominated points of multi-objective integer programs

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  • Banu Lokman
  • Murat Köksalan

Abstract

We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
  • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:347-365
    DOI: 10.1007/s10898-012-9955-7
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    References listed on IDEAS

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    1. Laumanns, Marco & Thiele, Lothar & Zitzler, Eckart, 2006. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method," European Journal of Operational Research, Elsevier, vol. 169(3), pages 932-942, March.
    2. Ramos, R. M. & Alonso, S. & Sicilia, J. & Gonzalez, C., 1998. "The problem of the optimal biobjective spanning tree," European Journal of Operational Research, Elsevier, vol. 111(3), pages 617-628, December.
    3. F. Guerriero & R. Musmanno, 2001. "Label Correcting Methods to Solve Multicriteria Shortest Path Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 589-613, December.
    4. Sylva, John & Crema, Alejandro, 2007. "A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1011-1027, August.
    5. Selcen (Pamuk) Phelps & Murat Köksalan, 2003. "An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization," Management Science, INFORMS, vol. 49(12), pages 1726-1738, December.
    6. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    7. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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