On the Convergence of Tabu Search
- Saïd Hanafi
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The Tabu Search (TS) meta-heuristic has proved highly successful for solving combinatorial and nonlinear problems. A key aspect of TS consists of using adaptive forms of memory to forbid the search process to revisit solutions already examined unless the trajectory to reach it is different. In Glover (ORSA Journal on Computing, 1990, 2, 4–32) a special memory design was proposed together with a choice rule for handling the situation where the method was compelled to revisit solutions already encountered. This proposal, which specified the exploration should resume from the earliest solution visited in the past, as accompanied by the conjecture that such a choice has implications for finiteness in the zero-one integer program and optimal set membership examples. Up to now numerous applications of TS in various areas of research are available, however, we are aware of only a few results concerning the convergence of TS. In this paper, we prove that Glover's conjecture is true if the neighborhood employed is strongly connected, yielding a “reversible” path from each solution to every other solution.
- Aboudi, R. and K. Jörnsten. (1994). “Tabu Search for General Zero-One Integer Programs Using the Pivot and Complement Heuristic.” ORSA Journal of Computing 6, 82–93.
- Balas, E. and C.H. Martin. (1980). “Pivot and Complement—A Heuristic for 0-1 Programming.” Management Science Research 26, 86–96.
- Dammeyer, F., P. Forst, and S. Voß. (1991). “On the Cancellation Sequence Method of Tabu Search.” ORSA Journal on Computing 3, 262–265.
- Dammeyer, F. and S. Voß. (1993). “Dynamic Tabu List Management using the Reverse Elimination Method.” Annals of Operations Research 41, 31–46.
- Feo, T.A., M.G.C. Resende, and S.H. Smith. (1994). “A Greedy Randomized Adaptive Search for Maximum Independent Set.” Operations Research 42, 860.
- Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. San Fransisco: W.H. Freeman and Company.
- Glover, F. (1989). “Tabu Search, Part 1.” ORSA Journal on Computing 1, 190–206.
- Glover, F. (1990). “Tabu Search, Part 2.” ORSA Journal on Computing 2, 4–32.
- Glover, F. and M. Laguna. (1997). Tabu Search. Dordrecht: Kluwer Academic Publishers.
- Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley.
- Hanafi, S., and A. Fréville. (1996). “An Efficient Tabu Search Approach for the 0-1 Multidimensional Knapsack Problem.” In Fred Glover (ed.), Special Issue on Tabu Search, to appear in European Journal of Operational Research.
- Hanafi, S., A. Fréville, and A. El Abdellaoui. (1995). “Comparison of Heuristics for the 0-1 Multidimensional Kanapsack Problem.” In I.H. Osman and J.P. Kelly (eds.), Metaheuristics: Theory and Applications. Dordrecht: Kluwer, pp. 449–466.
- Hübscher, R. and F. Glover. (1994). “Applying Tabu Search with Influential Diversification to Multiprocessor Scheduling.” Computer and Operation Research 13, 877–884.
- Kirkpatrick, S., C.D. Gelatt, and M.P. Vechi. (1983). “Optimization by Simulated Annealing.” Science 220, 671–680.
- Lin, S. and B.W. Kernighan. (1973). “An Effective Heuristic Algorithm for the Traveling Salesman Problem.” Operations Research 21, 443–452.
- Lokketangen, A. and F. Glover. (1996). “Solving Zero-One Mixed Integer Programming Problems Using Tabu Search.” Working paper, University of Colorado, USA.
- Mladenovic, N. and P. Hansen. (1996). “Variable Neighborhood Search.” Les Cahiers du GERAD, G-96-49.
- Osman, I.H. and G. Laporte. (1996). “Meta-Heuristics: A Biography.” Annals Opnl. Res. 63, 513–628.
- Reeves, C. (1993). Modern Heuristic Techniques for Combinatorial Problems. Oxford: Blackwell.
- On the Convergence of Tabu Search
Journal of Heuristics
Volume 7, Issue 1 , pp 47-58
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- Kluwer Academic Publishers
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- tabu search
- Saïd Hanafi (1)
- Author Affiliations
- 1. LAMIH-Recherche Operationnelle et Informatique UMR CNRS 8530, Universite de Valenciennes, LeMont Houy, F-59313, Valenciennes Cedex 9-, France