Annals of Operations Research

, Volume 131, Issue 1–4, pp 259–282 | Cite as

Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem

  • Gintaras Palubeckis
Article

Abstract

This paper describes and experimentally compares five rather different multistart tabu search strategies for the unconstrained binary quadratic optimization problem: a random restart procedure, an application of a deterministic heuristic to specially constructed subproblems, an application of a randomized procedure to the full problem, a constructive procedure using tabu search adaptive memory, and an approach based on solving perturbed problems. In the solution improvement phase a modification of a standard tabu search implementation is used. A computational trick applied to this modification – mapping of the current solution to the zero vector – allowed to significantly reduce the time complexity of the search. Computational results are provided for the 25 largest problem instances from the OR-Library and, in addition, for the 18 randomly generated larger and more dense problems. For 9 instances from the OR-Library new best solutions were found.

binary quadratic optimization tabu search multistart strategies heuristics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alidaee, B., G. Kochenberger, and A. Ahmadian. (1994). “0—1 Quadratic Programming Approach for the Optimal Solution of Two Scheduling Problems.” International Journal of Systems Science 25, 401-408.Google Scholar
  2. Barahona, F., M. Grötschel, M. Jünger, and G. Reinelt. (1988). “An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design.” Operations Research 36, 493-513.Google Scholar
  3. Barahona, F., M. Jünger, and G. Reinelt. (1989). “Experiments in Quadratic 0—1 Programming.” Mathematical Programming 44, 127-137.CrossRefGoogle Scholar
  4. Beasley, J.E. (1996). “Obtaining Test Problems Via Internet.” Journal of Global Optimization 8, 429-433.Google Scholar
  5. Beasley, J.E. (1998). “Heuristic Algorithms for the Unconstrained Binary Quadratic Programming Problem.” Working paper, The Management School, Imperial College, London, England.Google Scholar
  6. Billionnet, A., and A. Sutter. (1994). “Minimization of a Quadratic Pseudo-Boolean Function.” European Journal of Operational Research 78, 106-115.CrossRefGoogle Scholar
  7. Boros, E., and P.L. Hammer. (1991). “The Max-Cut Problem and Quadratic 0—1 Optimization: Polyhedral Aspects, Relaxations and Bounds.” Annals of Operations Research 33, 151-180.CrossRefGoogle Scholar
  8. Carter, M.W. (1984). “The Indefinite Zero—One Quadratic Problem.” Discrete Applied Mathematics 7, 23- 44.CrossRefGoogle Scholar
  9. Çela, E. (1998). The Quadratic Assignment Problem: Theory and Algorithms. Dordrecht: Kluwer Academic.Google Scholar
  10. Charon, I., and O. Hudry. (1993). “The Noising Method: A New Method for Combinatorial Optimization.” Operations Research Letters 14, 133-137.CrossRefGoogle Scholar
  11. Codenotti, B., G. Manzini, L. Margara, and G. Resta. (1996). “Perturbation: An Efficient Technique for the Solution of Very Large Instances of the Euclidean TSP.” INFORMS Journal on Computing 8, 125-133.Google Scholar
  12. Dearing, P.M., P.L. Hammer, and B. Simeone. (1988). “Boolean and Graph-Theoretic Formulations of the Simple Plant Location Problem.” RUTCOR Research Report 3-88, Rutgers University, New Brunswick, USA.Google Scholar
  13. De Simone, C., M. Diehl, M. Jünger, P. Mutzel, G. Reinelt, and G. Rinaldi. (1995). “Exact Ground States of Ising Spin Glasses: New Experimental ResultsWith a Branch and Cut Algorithm.” Journal of Statistical Physics 80, 487-496.Google Scholar
  14. Feo, T.A., and M.G.C. Resende. (1995). “Greedy Randomized Adaptive Search Procedures.” Journal of Global Optimization 6, 109-133.CrossRefGoogle Scholar
  15. Fleurent, C., and F. Glover. (1999). “Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory.” INFORMS Journal on Computing 11, 198-204.Google Scholar
  16. Gallo, G., P.L. Hammer, and B. Simeone. (1980). “Quadratic Knapsack Problems.”Mathematical Programming 12, 132-149.Google Scholar
  17. Glover, F. (1977). “Heuristics for Integer Programming Using Surrogate Constraints.” Decision Sciences 8, 156-166.Google Scholar
  18. Glover, F. (1986). “Future Paths for Integer Programming and Links to Artificial Intelligence.” Computers and Operations Research 13, 533-549.Google Scholar
  19. Glover, F., B. Alidaee, C. Rego, and G. Kochenberger. (2002). “One-Pass Heuristics for Large-Scale Unconstrained Binary Quadratic Problems.” European Journal of Operational Research 137, 272-287.CrossRefGoogle Scholar
  20. Glover, F., G.A. Kochenberger, and B. Alidaee. (1998). “Adaptive Memory Tabu Search for Binary Quadratic Programs.” Management Science 44, 336-345.Google Scholar
  21. Glover, F., and M. Laguna. (1997). Tabu Search.Hingham, MA: Kluwer Academic.Google Scholar
  22. Hammer, P.L. (1968). “Plant Location — A Pseudo-Boolean Approach.” Israel Journal of Technology 6, 330-332.Google Scholar
  23. Hammer, P., and S. Rudeanu. (1968). Boolean Methods in Operations Research.New York: Springer.Google Scholar
  24. Hansen, P. (1979). “Methods of Nonlinear 0—1 Programming.” Annals of Discrete Mathematics 5, 53-70.Google Scholar
  25. Helmberg, C., and F. Rendl. (1998). “Solving Quadratic (0,1)-Problems by Semidefinite Programs and Cutting Planes.” Mathematical Programming 82, 291-315.Google Scholar
  26. Jünger, M., A. Martin, G. Reinelt, and R. Weismantel. (1994). “Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits.” Mathematical Programming 63, 257-279.CrossRefGoogle Scholar
  27. Krarup, J., and P.M. Pruzan. (1978). “Computer-Aided Layout Design.” Mathematical Programming Study 9, 75-94.Google Scholar
  28. Laughunn, D.J. (1970). “Quadratic Binary Programming.” Operations Research 14, 454-461.Google Scholar
  29. Li, Y., P.M. Pardalos, and M.G.C. Resende. (1994). “A Greedy Randomized Adaptive Search Procedure for the Quadratic Assignment Problem.” In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 16. Providence, RI: Amer. Math. Soc., pp. 237-261.Google Scholar
  30. Lodi, A., K. Allemand, and T.M. Liebling. (1999). “An Evolutionary Heuristic for Quadratic 0—1 Programming.” European Journal of Operational Research 119, 662-670.CrossRefGoogle Scholar
  31. McBride, R.D., and J.S. Yormark. (1980). “An Implicit Enumeration Algorithm for Quadratic Integer Programming.” Management Science 26, 282-296.Google Scholar
  32. Merz, P., and B. Freisleben. (1999). “Genetic Algorithms for Binary Quadratic Programming.” In W. Banzhaf, J. Daida, A.E. Eiben, M.H. Garzon, V. Honavar, M. Jakiela, and R.E. Smith (eds.), Proceedings of the Genetic and Evolutionary Computation Conference, Vol. 1. Orlando, FL: Morgan Kaufmann, pp. 417-424.Google Scholar
  33. Palubeckis, G. (1992). “Heuristics with a Worst-Case Bound for Unconstrained Quadratic 0—1 Programming.” Informatica 3, 225-240.Google Scholar
  34. Palubeckis, G. (1995). “A Heuristic-Based Branch and Bound Algorithm for Unconstrained Quadratic Zero—One Programming.” Computing 54, 283-301.CrossRefGoogle Scholar
  35. Pardalos, P.M. (1991). “Construction of Test Problems in Quadratic Bivalent Programming.” ACM Transactions on Mathematical Software 17, 74-87.CrossRefGoogle Scholar
  36. Pardalos, P.M., and S. Jha. (1991). “Graph Separation Techniques for Quadratic Zero—One Programming.” Computers and Mathematics with Applications 21, 107-113.Google Scholar
  37. Pardalos, P.M., and G.P. Rodgers. (1990). “Computational Aspects of a Branch and Bound Algorithm for Quadratic Zero—One Programming.” Computing 45, 131-144.CrossRefGoogle Scholar
  38. Pardalos, P.M., and G.P. Rodgers. (1992). “A Branch and Bound Algorithm for the Maximum Clique Problem.” Computers and Operations Research 19, 363-375.CrossRefGoogle Scholar
  39. Pardalos, P.M., and J. Xue. (1994). “The Maximum Clique Problem.” Journal of Global Optimization 4, 301-328.Google Scholar
  40. Picard, J.C., and H.D. Ratliff. (1975). “Minimum Cuts and Related Problems.” Networks 5, 357-370.Google Scholar
  41. Poljak, S., and Z. Tuza. (1995). “Maximum Cuts and Large Bipartite Subgraphs.” In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 20. Providence, RI: Amer. Math. Soc., pp. 181-244.Google Scholar
  42. Shih, M., and E.S. Kuh. (1993). “Quadratic Boolean Programming for Performance-Driven System Par282 PALUBECKIS titioning.” In Proceedings of the 30th ACM/IEEE Design Automation Conference, Dallas, TX. ACM Press, pp. 761-765.Google Scholar
  43. Skorin-Kapov, J. (1990). “Tabu Search Applied to the Quadratic Assignment Problem.” ORSA Journal on Computing 2, 33-45.Google Scholar
  44. Storer, R.H., S.D. Wu, and R. Vaccari. (1992). “New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling.” Management Science 38, 1495-1509.Google Scholar
  45. Warszawski, A. (1974). “Pseudo-Boolean Solutions to Multidimensional Location Problems.” Operations Research 22, 1081-1085.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Gintaras Palubeckis
    • 1
  1. 1.Department of Practical InformaticsKaunas University of TechnologyKaunasLithuania

Personalised recommendations