Abstract
Multiobjective combinatorial problems are commonly encountered in practice and would benefit from the development of metaheuristics where the search effort is interactively guided towards the solutions favored by the decision maker. The present study introduces such an Interactive Genetic Algorithm designed for a general multiobjective combinatorial framework and discusses its behavior in simulations on the Multiobjective Knapsack Problem. The evolution strategies being employed reflect the multiobjective nature of the problem. The fitness of individuals in the population is estimated on the basis of preference information elicited from the decision maker, and continuously updated as the algorithm progresses. The presented results indicate that the algorithm performs well when simulated against decision makers with different underlying utility functions.
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References
Beasley, J. E. and P. C. Chu (1998) “A Genetic Algorithm for the Multidimensional Knapsack Problem,” Journal of Heuristics, vol. 4, pp. 63–86.
Czyzak, P. and A. Jaszkiewicz (1998) “Pareto Simulated Annealing — A Metaheuristic Technique for Multiple-Objective Combinatorial Optimization,” Journal of Multi Criteria Decision Analysis 7, pp. 34–47.
Ehrgott, M. and X. Gandibleux (2000) An Annotated Bibliography of Multiobjective Combinatorial Optimization, Report in Wirtschaftsmathematik, Univarsitat Kaiserslautern.
Gandibleux, X, N. Mezdaoui, and A. Freville (1996) “A Tabu Search Procedure to Solve Multiobjective Combinatorial Optimization Problems,” in Proceedings of MOPGP′96, R. Caballero and R. Steuer (eds.), Springer-Verlag.
Gandibleux, X. and A. Freville (2000) “Tabu Search Based Procedure for Solving the 0-1 Multiobjective Knapsack Problem: the Two Objectives Case,” Journal of Heuristics, to appear.
Klamroth, K. and M.M Wiecek (2000) “Dynamic Programming Approaches to the Multiple Criteria Knapsack Problem,” Naval Research Logistics, to appear.
Korhonen, P., J. Wallenius, and S. Zionts (1984) Solving the Discrete Multiple Criteria Problem Using Convex Cones,” Management Science Vol. 30 No. 11, pp. 1336–1345.
Korhonen, P. and J. Laakso (1986) “A Visual Interactive Method for Solving the Multiple Criteria Problem,” European Journal of Operational Research 24(2), pp. 277–287.
Köksalan, M., M. H. Karwan and S. Zionts (1984) “An Improved Method for Solving Multiple Criteria Problems Involving Discrete Alternatives,” IEEE Transactions on Systems, Man, and Cybernetics Vol. SMC-14, No. 1, pp. 24–34.
Köksalan, M. M. and P. N. S. Sagala (1995) “Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions,” Management Science, Vol. 41, pp. 1158–1171.
Martello, S. and P. Toth (1990) Knapsack Problems: Algorithms and Computer Implementations, John Wiley and Sons, Chichester.
Murata, T. and H. Ishibuchi (1995) “Multiobjective Genetic Algorithms,” Proceedings of the Second IEEE International Conference on Evolutionary Computing, Perth, Australia.
Steuer, R. E. and E.-U. Choo (1983) “An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming,” Mathematical Programming Vol. 26 No. 1, pp. 326–344.
Ulungu E.L. and J. Teghem (1994) “Multi-Objective Combinatorial Optimization Problems: A Survey,” Journal of Multi Criteria Decision Analysis 3, pp. 83–104.
Ulungu, E.L. and J Teghem (1997) “Solving multiobjective Knapsack Problem by a Branch-and-Bound Procedure,” in Multicriteria Analysis, J. Climaco (ed.), Springer-Verlag, Berlin, pp. 269–278.
Ulungu, E.L., J. Teghem, and C. Ost (1998) “Interactive simulated annealing in a multiobjective framework: application to an industrial problem,” Journal of the Operational Research Society 49, pp. 1044–1050.
Ulungu E.L., J. Teghem, P.H. Fortemps and D. Tuyttens (1999) “MOSA Method: A Tool for Solving Multiobjective Combinatorial Optimization Problems, ” Journal of Multi Criteria Decision Analysis 8, pp. 221–236.
Zionts, S. and J. Wallenius (1976) “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science Vol. 22 No. 6, pp. 652–663.
Zionts, S. (1981) “A Multiple Criteria Method for Choosing Among Discrete Alternatives,” European Journal of Operations Research 7, pp. 143–147.
Zionts, S. and J. Wallenius (1983) “An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions,” Management Science Vol. 29 No. 5, pp. 519–529.
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Pamuk, S., Köksalan, M. (2001). An Interactive Genetic Algorithm Applied to the Multiobjective Knapsack Problem. In: Köksalan, M., Zionts, S. (eds) Multiple Criteria Decision Making in the New Millennium. Lecture Notes in Economics and Mathematical Systems, vol 507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56680-6_24
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DOI: https://doi.org/10.1007/978-3-642-56680-6_24
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