Journal of Heuristics

, Volume 4, Issue 1, pp 5–23

Tabu Search When Noise is Present: An Illustration in the Context of Cause and Effect Analysis

  • Daniel Costa
  • Edward A. Silver


In the field of combinatorial optimization, it may be possible to more accurately represent reality through stochastic models rather than deterministic ones. When randomness is present in a problem, algorithm designers face new difficulties which complicate their task significantly. Finding a proper mathematical formulation and a fast evaluation of the objective function are two major issues. In this paper we propose a new tabu search algorithm based on sampling and statistical tests. The algorithm is shown to perform well in a stochastic environment where the quality of feasible solutions cannot be computed easily. This new search principle is illustrated in the field of cause and effect analysis where the true cause of an undesirable effect needs to be eliminated. A set of n potential causes is identified and each of them is assumed to be the true cause with a given probability. The time to investigate a cause is a random variable with a known probability distribution. Associated with each cause is the reward obtained if the cause is really the true cause. The decision problem is to sequence the n potential causes so as to maximize the expected reward realized before a specified time horizon.

cause and effect analysis sampling statistical tests stochastic combinatorial optimization tabu search 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andradottir, S. (1995). “A Method for Discrete Stochastic Optimization,” Management Science41, 1946-1961.Google Scholar
  2. Barton, R. and J. Ivey. (1996). “Nelder-Mead Simplex Modifications for Simulation Optimization,” Management Science42, 954-973.Google Scholar
  3. Bellalouna, M., C. Murat, and V.Th. Paschos. (1995). “Probabilistic Combinatorial Optimization Problems on Graphs: A New Domain in Operational Research,” European Journal of Operational Research87, 693-706.Google Scholar
  4. Benton, W.C. and M.D. Rossetti. (1993). “The Vehicle Scheduling Problem with Intermittent Customer Demands,” Computers and Operations Research19(6), 521-531.Google Scholar
  5. Bertsimas, D.J. and D. Simchi-Levi. (1996). “A New Generation ofVehicle Routing Research: Robust Algorithms, Addressing Uncertainty,” Operations Research44(2), 286-304.Google Scholar
  6. Chun, Y.H., H. Moskowitz, and R. Plante. (1995). “Sequencing a Set of Alternatives Under Time Constraints,” Journal of the Operational Research Society46(9), 1133-1144.Google Scholar
  7. Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W.H. Freeman.Google Scholar
  8. Gendreau, M., G. Laporte, and R. Séguin. (1995). “An Exact Algorithm for the Vehicle Routing Problem with Stochastic Demands and Customers,” Transportation Science29, 143-155.Google Scholar
  9. Gendreau, M., G. Laporte, and R. Séguin. (1996). “A Tabu Search Heuristic for the Vehicle Routing Problem with Stochastic Demands and Customers,” Operations Research44(3), 469-477.Google Scholar
  10. Gibbons, J.D. (1985). “Nonparametric Statistical Inference,” Statistics: Textbooks and Monographs. New York: Marcel Dekker Inc., vol. 85.Google Scholar
  11. Glover, F. (1986). “Future Paths for Integer Programming and Links to Artificial Intelligence,” Computers and Operations Research13(5), 533-549.Google Scholar
  12. Glover, F. (1995). “Tabu Search Fundamentals and Uses,” Research Report, School of Business, University of Colorado, Boulder.Google Scholar
  13. Glover, F. (1996). “Tabu Search and Adaptive Memory Programming-Advances, Applications and Challenges.” In Barr, Helgason, and Kennington (eds.), Interfaces in Computer Science and Operations Research. Kluwer Academic Publishers (to appear).Google Scholar
  14. Glover, F. and M. Laguna. (1993a). “Tabu Search.” In C.R. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems. Oxford: Blackwell Scientific Publishing, pp. 70-141.Google Scholar
  15. Glover, F., M. Laguna, E. Taillard, and D. de Werra. (eds.) (1993b). “Tabu Search,” Annals of Operations Research, vol. 41.Google Scholar
  16. Hansen, P. and B. Jaumard. (1990). “Algorithms for the Maximum Satisfiability Problem,” Computing44, 279-303.Google Scholar
  17. Hertz, A., E. Taillard, and D. de Werra. (1997). “Tabu Search.” In E.H.L. Aarts and J.K. Lenstra (eds.), Local Search in Combinatorial Optimization. New York: Wiley.Google Scholar
  18. Ibaraki, T. (1987a). “Enumerative Approaches to Combinatorial Optimization-Part I,” Annals of Operations Research, vol. 10.Google Scholar
  19. Ibaraki, T. (1987b). “Enumerative Approaches to Combinatorial Optimization-Part II,” Annals of Operations Research, vol. 11.Google Scholar
  20. Jaillet, P. (1988). “A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers are Visited,” Operations Research36(6), 929-936.Google Scholar
  21. Johnson, R.A. and G.K. Bhattacharyya. (1992). Statistics: Principles and Methods(2nd edition). New York: Wiley.Google Scholar
  22. Jönsson, H. and E.A. Silver. (1996). “Some Insight Regarding Selecting Sets of Scenarios in Combinatorial Stochastic Problems,” International Journal of Production Economics45, 463-472.Google Scholar
  23. Kinderman, A.J. and J.G. Ramage. (1976). “Computer Generation of Normal Random Variables,” Journal of the American Statistical Association71, 893-896.Google Scholar
  24. Law, A.M. and W.D. Kelton. (1991). Simulation Modeling and Analysis(2nd edition). New York: McGraw-Hill.Google Scholar
  25. Osman, I.H. and G. Laporte. (1996). “Metaheuristics: A Bibliography,” Annals of Operations Research63, 513-623.Google Scholar
  26. Rohleder, T.R. and E.A. Silver. (1997). “A Tutorial on Business Process Improvement,” Journal of Operations Management15, 139-154.Google Scholar
  27. Saliby, E. (1990). “Descriptive Sampling: A Better Approach to Monte Carlo Simulation,” Journal of the Operational Research Society41, 1133-1142.Google Scholar
  28. Silver, E.A. and T.R. Rohleder. (1997). “Some Simple Mathematical Aids for Cause-and-Effect Analyses,” Journal of Quality Technology(to appear).Google Scholar
  29. Yan, Di and H. Mukai. (1992). “Stochastic Discrete Optimization,” SIAM Journal of Control and Optimization30, 594-612.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Daniel Costa
    • 1
  • Edward A. Silver
    • 2
  1. 1.Groupe de StatistiqueUniversité de NeuchâtelNeuchâtelSwitzerland
  2. 2.Faculty of ManagementUniversity of CalgaryCalgaryCanada

Personalised recommendations