Journal of Heuristics

, Volume 6, Issue 3, pp 361–383 | Cite as

Tabu Search Based Procedure for Solving the 0-1 MultiObjective Knapsack Problem: The Two Objectives Case

  • Xavier Gandibleux
  • Arnaud Freville
Article

Abstract

We consider in this paper the solving of 0-1 knapsack problems with multiple linear objectives. We present a tabu search approach to generate a good approximation of the efficient set. The heuristic scheme is included in a redu tion decision space framework. The case of two objectives is developed in this paper. TS principles viewed into the multiobjective context are discussed. According to a prospective way, several variations of the algorithm are investigate. Numerical experiments are reported and compared with available exact efficient solutions. Intuitive justifications for the observed empirical behavior of the procedure and open questions are discussed.

multi-objective programming knapsack problem tabu search decision space reduction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben Abdelaziz, F., S. Krichen, and J. Chaouachi. (1999). “An Hybrid Metaheuristic for the MultiObjective Knapsack Problem. ” In St. Voss, S. Martello, I. Osman, and C. Roucairol (eds.), Meta-Heuristics-Advances and Trends in Local Search Paradigms for Optimization. Kluwer, pp. 205–212.Google Scholar
  2. Brandimarte, P. and M. Calderini. (1995). “A Hierarchical Bicriterion Approach to Integrated Process Plan Selection and Job Shop scheduling. ” Int. J. Prod. Res. 33(1), 161–181.Google Scholar
  3. Czyzak, P. and A. Jaszkiewicz. (1998). “Pareto Simulated Annealing-A Metaheuristic Technique for Multiple Objective Combinatorial Optimization. ” Journal of Multicriteria Decision Analysis 7, 34–47.Google Scholar
  4. Dahl, G., K. Jornsten, and A. Lokketangen. (1995). “A Tabu Search Approach to the Channel Minimization Problem. ” ICOTA'95, 9p.Google Scholar
  5. Fréville, A. and G. Plateau. (1993). “Sac-à-dos multidimensionnel en variables 0–1: encadrement de la somme des variables à l'optimum. ” RAIRO 27(2), 169–187.Google Scholar
  6. Fréville, A. and G. Plateau. (1994). “An Efficient Preprocessing Procedure for the Multidimensional 0–1 Knapsack Problem. ” Discrete Applied Mathematics, 189–212.Google Scholar
  7. Gandibleux, X., N. Mezdaoui, and A. Fréville. (1997a). “A Multi-Objective Tabu Search Procedure to Solve Combinatorial Optimization Problems. ” In R. Caballero, F. Ruiz, and R. Steuer (eds.), Advances in Multiple Objective and Goal Programming. Lecture Notes 455 in Economics and Mathematical Systems, Springer, pp. 291–300.Google Scholar
  8. Gandibleux, X., N. Mezdaoui, and E.L.B. Ulungu. (1997b). “Simulated Annealing Versus Tabu Search Multi-Objective Approaches to the MultiObjective KnapSack Problem. ” 13th International Conference on Multiple Criteria Decision-Making, Jan. 6–10, 1997, Cape Town, South Africa.Google Scholar
  9. Geoffrion, A.M. (1974). “Lagrangean Relaxation for Integer Programming. ” Mathematical Programming Study 2, 82–114.Google Scholar
  10. Glover, Fr. (1965). “A Multiphase Dual Algorithm for the Zero-One Integer Programming Problem. ” Operations Research 13(6), 879–919.Google Scholar
  11. Habenicht, W. (1982). “Quad Trees. A Data Structure for Discrete Vector Optimization Problems. ” In P. Hansen (ed.), Springer-Verlag, pp. 136–145. Lecture Notes “Essays and surveys on MCDM”.Google Scholar
  12. Hansen, M.P. (1997). “Tabu Search for MultiObjective Optimization: MOTS. ” 13th International Conference on Multiple Criteria Decision-Making, Jan. 6–10, 1997, Cape Town, South Africa.Google Scholar
  13. Hertz, A., B. Jaumard, C.C. Ribeiro, and W.P. Formosinho. (1994). “A MultiCriteria Tabu Search Aproach to Cell Formation Problems in Group Technology with Multiple Objectives. ” Recherche Opérationnelle-Operations Research 28(3), 303–328.Google Scholar
  14. Malakooti, B., J. Wang, and E.C. Tandler. (1990). “A Sensor-Based Accelerated Approach for Multi-Attribute Machinability and Tool Life Evaluation. ” International Journal of Production Research 28, 2373.Google Scholar
  15. Martello, S. and P. Toth. (1990). Knapsack Problems: Algorithms and Computer Implementations. New York: Wiley.Google Scholar
  16. Martello, S., D. Pisinger, and P. Toth. (1997). “New Trends in Exact Algorithms for the 0–1 Knapsack Problem. ” EURO/INFORMS-97, Barcelona, Spain, pp. 151–160.Google Scholar
  17. Mezdaoui, N., X. Gandibleux, and A. Fréville. (1997). “Decision Space Exploration Techniques in the MultiObjective Tabu Search Procedure Applied on the 0–1 MOKP. ” EURO XV-INFORMS XXXIV, July 14–17, 1997, Barcelona, Spain.Google Scholar
  18. Osman, I. and G. Laporte. (1996). “Metaheuristics: A Bibliography. ” Annals of Operations Research 63, 513–623.Google Scholar
  19. Reeves, C. (1995). Modern Heuristic Techniques for Combinatorial Problems. London: McGrawHill.Google Scholar
  20. Roy, B. and D. Bouyssou. (1993). Aide multicritère à la décision: méthode et cas. Gestion, Economica.Google Scholar
  21. Savelsberg, M.W.P. (1994). “Preprocessing and Probing Techniques for Mixed Integer Programming Problems. ” ORSA Journal on Computing 6(4), 445–454.Google Scholar
  22. Schaffer, J.D. (1985). “Multiple Objective Optimization using Vector Evaluated Genetic Algorithms. ” In Proc. of 1st Int. Conf. on G.A. and Their Applications, 1985, pp. 93–100.Google Scholar
  23. Serafini, P. (1992). “Simulated Annealing for Multi Objective Optimization Problems. ” 10th Int. Conf. on MCDM Proc., Vol. 1, July 19–24, 1992, Taipei, Taiwan, pp. 87–96.Google Scholar
  24. Steuer, R. (1986). Multiple Criteria Optimization: Theory, Computation and Application. New York: Wiley.Google Scholar
  25. Sun, M. and R. Steuer. (1995). “Quad-Trees and Linear Lists for Identifying Non Dominated Criterion Vectors. ” Informs, Journal on Computing 8(4), Fall 1996.Google Scholar
  26. Teghem, J and E.L. Ulungu. (1997). “Bicriteria Assigment Problem. ” MAMDM Int. Conf, May 14–16, 1997, Mons, Belgium, pp. 144–147.Google Scholar
  27. Ulungu, E.L.B. and J. Teghem. (1994). “Multi-Objective Combinatorial Optimization Problems: A Survey. ” Journal of Multi-Criteria Decision Analysis 3, 83–104.Google Scholar
  28. Ulungu, E.L. and J. Teghem. (1995). “The Two Phases Method: An Efficient Procedure to Solve Bi-Objective Combinatorial Optimization Problems. ” Foundations of Computing and Decision Sciences 20(2), 149–165, 1995.Google Scholar
  29. Ulungu, E.L.B., J. Teghem, and Ph. Fortemps. (1995). “Heuristics for Multi-objective Combinatorial Optimization Problems by Simulated Annealing. ” In J. Gu, G.C.Q. Wei, and Sh. Wang (eds.), MCDM: Theory and Applications SCI-TECH Information Services, pp. 228–238.Google Scholar
  30. Vanderpooten, D. (1990). “Multiobjective Programming: Basic Concepts and Approaches. ” In R. Slowinski and J. Teghem (eds.), Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty Kluwer, pp. 7–22.Google Scholar
  31. Van Wassenhove, L. and L. Gelders. (1980). “Solving a Bicriterion Scheduling Problem. ” European Journal of Operational Research 4, 42–48.Google Scholar
  32. WWW Site, LAMIH-ROAD, UVHC, numerical instances for MultiObjective MetaHeuristics. http://www.univ-valenciennes.fr/ROAD/MCDM.html, Université de Valenciennes.Google Scholar
  33. Yu, G. (1990). “Algorithms for Optimizing Piecewise Linear Functions and for Degree Constrained Minimum Spanning Tree Problems. ” PhD, 09–11–01, Wharton School, University of Pennsylvania.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Xavier Gandibleux
    • 1
  • Arnaud Freville
    • 2
  1. 1.LAMIH-ROAD, UMR CNRS 8530University of ValenciennesValenciennes CedexFrance
  2. 2.LAMIH-ROAD, UMR CNRS 8530University of ValenciennesValenciennes CedexFrance

Personalised recommendations