Repulsive Assignment Problem
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Standard assignment is the problem of obtaining a matching between two sets of respectively persons and positions so that each person is assigned exactly one position and each position receives exactly one person, while a linear decision maker utility function is maximized. We introduce a variant of the problem where the persons individual utilities are taken into account in a way that a feasible solution must satisfy not only the standard assignment constraints, but also an equilibrium constraint of the complementarity type, which we call repulsive. The equilibrium constraint can be, in turn, transformed into a typically large set of linear constraints. Our problem is NP-hard and it is a special case of the assignment problem with side constraints. We study an exact penalty function approach which motivates a heuristic algorithm. We provide computational experiments that show the usefulness of a heuristic mechanism inspired by the exact approach. The heuristics outperforms a state-of-the-art integer linear programming solver.
KeywordsGeneralized assignment problems Quadratic assignment problems Memetic algorithms Equilibrium constraints
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- 6.Burkard, R.E., Çela, E., Pardalos, P.M., Pitsoulis, L.S.: The quadratic assignment problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 241–337. Kluwer, Boston (1998) Google Scholar
- 8.Martello, S., Toth, P.: Knapsack Problems, Algorithms, and Computer Implementations. Wiley, New York (1974) Google Scholar
- 15.Gaudioso, M., Giallombardo, G., Miglionico, G.: On solving the Lagrangian dual of integer programs via an incremental approach. Comput. Optim. Appl. (2009, to appear) Google Scholar
- 23.Holland, J.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1992) Google Scholar
- 24.Moscato, P., Cotta, C.: A gentle introduction to memetic algorithms. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 105–144. Kluwer, Boston (2003) Google Scholar