Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem
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This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the well-known Set Covering Problem. The proposed approach is a two-phase heuristic method which has the particularity to be a constructive method using the primal-dual Lagrangian relaxation to solve single objective Set Covering problems. The results show that this algorithm finds several potentially supported and unsupported solutions. A comparison with an exact method (up to a medium size), shows that many Pareto-optimal solutions are retrieved and that the other solutions are well spread and close to the optimal ones. Moreover, the method developed compares favorably with the Pareto Memetic Algorithm proposed by Jaszkiewicz.
KeywordsMulti-objective combinatorial optimization Lagrangean relaxation Set covering problem
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- Balas, E., and A. Ho. (1980). “Set Covering Using Cutting Planes, Heuristics and Subgradient Optimisation: A Computational Study.” Mathematical Programming Study, 12, 37–60.Google Scholar
- Caprara, A., M. Fischetti, and P. Toth. (1999). “A Heuristic Method for the Set Covering Problems.” OR 47, 730–743.Google Scholar
- Ceria, S., P. Nobili, and A. Sassano. (1998). “A Lagrangian-Based Heuristic for Large-Scale Set Covering Problems.” Mathematical Programming, 81, 215–228.Google Scholar
- Chvátal, V. (1979). “A Greedy Heuristic for the Set Covering Problem.” Mathematics of Operations Research 4(3), 233–235.Google Scholar
- Ehrgott, M. and X. Gandibleux. (2000). “A Survey and Annoted Bibliography of Multiobjective Combinatorial Optimization.” OR Spektrum, 22, 425–460.Google Scholar
- Gandibleux, X. Personal communication.Google Scholar
- Gandibleux, X., D. Vancoppenolle, and D. Tuyttens. (1998). “A First Making Use of GRASP for Solving MOCO Problems.” In Proceeding of the 14th International Conference on Multiple Criteria Decision-Making pp. 8–12, Charlottesville, USA.Google Scholar
- Jaszkiewicz, A. (2001). “A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm.” Working Paper RA-003/01, Institute of Computing Science, Poznań University of Technology ul.Piotrowo 3a,60-965 Poznań, Poland.Google Scholar
- MCDM society. (2001). http://www.terry.uga.edu/mcdm.
- Nemhauser, G.L. and L.A. Wolsey. (1988). Integer and Combinatorial Optimization. John Wiley and Sons, New York.Google Scholar
- Zitzler, E. (1999). Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.Google Scholar