Abstract
A variable depth search procedure (abbreviated as VDS) is a generalization of the local search method, which was first successfully applied by Lin and Kernighan to the traveling salesman problem and the graph partitioning problem. The main idea is to adaptively change the size of a neighborhood so that it can effectively traverse a larger search space while keeping the amount of computational time reasonable. In this paper, we propose a heuristic algorithm based on VDS for the generalized assignment problem, which is one of the representative combinatorial optimization problems known to be NP-hard. To the authors’ knowledge, most of the previously proposed algorithms (with some exceptions) conduct the search within the feasible region; however, there are instances for which the search within the feasible region is not advantageous because the feasible region is very small or is combinatorially complicated to search. Therefore, we allow our algorithm to search within the infeasible region as well. We also incorporate an adaptive use of two different neighborhoods, shift and swap, within the sequence of neighborhood moves in VDS. Computational experiments exhibit good prospects of the proposed algorithm.
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References
M.M. Amini and M. Racer, “A Hybrid Heuristic for the Generalized Assignment Problem,” European J. Oper. Res., 87 (1995) 343–348.
P.C. Chu and J.E. Beasley, “A Genetic Algorithm for the Generalized Assignment Problem,” Computers Oper. Res., 24 (1997) 17–23.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, (Freeman, 1979).
B.W. Kernighan and S. Lin, “An Efficient Heuristic Procedure for Partitioning Graphs,” Bell Syst. Tech. J., 49 (1970) 291–307.
M. Laguna, J.P. Kelly, J.L. González-Velarde and F. Glover, “Tabu Search for the Multilevel Generalized Assignment Problem,” European J. Oper. Res., 82 (1995) 176–189.
S. Lin and B.W. Kernighan, “An Effective Heuristic Algorithm for the Traveling Salesman Problem,” Oper. Res., 21 (1973) 498–516.
S. Martello and P. Toth, “An Algorithm for the Generalized Assignment Problem,” Proc. IFORS, (1981) 589–603.
S. Martello and P. Toth, Knapsack Problems: Algorithms and Computer Implementations, (John Wiley & Sons, 1990).
K. Nonobe and T. Ibaraki, “A Tabu Search Approach to the CSP (Constraint Satisfaction Problem) as a General Problem Solver,” European J. Oper. Res., 106 (1998) 599–623.
I.H. Osman, “Heuristics for the Generalized Assignment Problem: Simulated Annealing and Tabu Search Approaches,” OR Spektrum, 17 (1995) 211–225.
M. Racer and M.M. Amini, “A Robust Heuristic for the Generalized Assignment Problem,” Ann. Oper. Res., 50 (1994) 487–503.
S. Sahni and T. Gonzalez, “P-Complete Approximation Problems,” J. ACM, 23 (1976) 555–565.
T. Yamaguchi, “A Variable Depth Search for the Generalized Assignment Problem (in Japanese),” Graduate Thesis, Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 1996.
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© 1999 Springer Science+Business Media New York
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Yagiura, M., Yamaguchi, T., Ibaraki, T. (1999). A Variable Depth Search Algorithm for the Generalized Assignment Problem. In: VoĂź, S., Martello, S., Osman, I.H., Roucairol, C. (eds) Meta-Heuristics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5775-3_31
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DOI: https://doi.org/10.1007/978-1-4615-5775-3_31
Publisher Name: Springer, Boston, MA
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