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Extension of Reverse Elimination Method Through a Dynamic Managementof the Tabu List

Published online by Cambridge University Press:  15 August 2002

Saïd Hanafi  and
Arnaud Fréville
Saïd Hanafi
Affiliation:
LAMIH, UMR 8530 du CNRS, ROI – Groupe Recherche Opérationnelle et Informatique, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont Houy, 59313 Valenciennes Cedex, France; [email protected].
Arnaud Fréville
Affiliation:
LAMIH, UMR 8530 du CNRS, ROI – Groupe Recherche Opérationnelle et Informatique, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont Houy, 59313 Valenciennes Cedex, France; [email protected].
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Abstract

The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called REM-t method proposed by Glover (1990) where t is an integer parameter which controls the number of tabu attributes. A suitable adjustment of this parameter t can be designed in order to create a balance between diversification and intensification. In this paper, new dynamic rules for controlling the adjustment of the parameter t, are proposed. Finally, to illustrate the differences between the variants proposed for managing the tabu list, we test some of them on the 0–1 multidimensional knapsack problem.

Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 2: ROADEF'99 , April 2001 , pp. 251 - 267
Copyright
© EDP Sciences, 2001

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References

Aboudi, R. and Jörnsten, K., Tabu Search for General Zero-One Integer Programs Using the Pivot and Complement Heuristic. ORSA J. Comput. 6 (1994) 82-93. CrossRef
Battiti, R. and Tecchiolli, G., The Reactive Tabu Search. ORSA J. Comput. 6 (1994) 126-140. CrossRef
Dammeyer, F. and Voss, S., Dynamic Tabu List Management using the Reverse Elimination Method. Ann. Oper. Res. 41 (1993) 31-46. CrossRef
Fréville, A. and Plateau, G., Heuristics and Reduction Methods for Multiple Constraints 0-1 Linear Programming Problems. European J. Oper. Res. 24 (1986) 206-215. CrossRef
Fréville, A. and Plateau, G., Hard 0-1 Multiknapsack Test Problems for Size Reduction Methods. Investigacion Oper. 1 (1990) 251-270.
Glover, F., Tabu Search, Part 1. ORSA J. Comput. 1 (1989) 190-206. CrossRef
Glover, F., Tabu Search, Part 2. ORSA J. Comput. 2 (1990) 4-32. CrossRef
F. Glover and S. Hanafi, Tabu Search and Finite Convergence, Working paper, LAMIH-UMR CNRS N° 8530. University of Valenciennes, France, presented at INFORMS Meeting, 25-28 October 1998, USA.
F. Glover and G.A. Kochenberger, Critical Events Tabu Search for Multidimensional Knapsack Problems, in Metaheuristics: Theory and Applications, edited by I.H. Osman and J.P. Kelly. Kluwer (1996) 407-428.
F. Glover and M. Laguna, Tabu Search. Kluwer Academic Publishers (1997).
S. Hanafi, On the Convergence of Tabu Search. J. Heuristics (to appear).
Hanafi, S. and Fréville, A., An efficient Tabu Search Approach for the 0-1 Multidimensional Knapsack Problem. European J. Oper. Res. 106 (1998) 659-675. CrossRef
S. Hanafi, A. Fréville and A. El Abdellaoui, Comparison of Heuristics for the 0-1 Multi-dimensional Knapsack Problem, in Metaheuristics: Theory and Applications, edited by I.H. Osman and J.P. Kelly. Kluwer (1996) 449-466.
Hübscher, R. and Glover, F., Applying Tabu Search with influential diversification to multiprocessor scheduling. Comput. Oper. Res. 13 (1994) 877-884. CrossRef
A. Lokketangen and F. Glover, Probabilistic Move Selection in Tabu Search for Zero-One Mixed Integer Programming Problems, in Metaheuristics: Theory and Applications, edited by I.H. Osman and J.P. Kelly. Kluwer (1996) 467-488.
Lorie, J. and Savage, L.J., Three Problems in Capital Rationing. J. Bus. 28 (1955) 229-239. CrossRef
Nonobe, K. and Ibaraki, T., Tabu Search Approach, A to the CSP (Constraint Satisfaction Problem) as a General Problem Solver. European J. Oper. Res. 106 (1998) 599-623. CrossRef