Annals of Operations Research

, Volume 183, Issue 1, pp 163–173 | Cite as

The case for strategic oscillation

Article

Abstract

We study a “hard” optimization problem for metaheuristic search, where a natural neighborhood (that consists of moves for flipping the values of zero-one variables) confronts two local optima, separated by a maximum possible number of moves in the feasible space. Once a descent method reaches the first local optimum, all sequences of feasible moves to reach the second, which is the global optimum, must ultimately pass through solutions that are progressively worse until reaching the worst solution of all, which is adjacent to the global optimum.

We show how certain alternative neighborhoods can locate the global more readily, but disclose that each of these approaches encounters serious difficulties by slightly changing the problem formulation. We also identify other possible approaches that seem at first to be promising but turn out to have deficiencies.

Finally, we observe that a strategic oscillation approach for transitioning between feasible and infeasible space overcomes these difficulties, reinforcing recent published observations about the utility of solution trajectories that alternate between feasibility and infeasibility. We also sketch features of such an approach that have implications for future research.

Keywords

Zero-one optimization Strategic oscillation Hard problems Global minima Tabu search 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beasley, J. (1993). Lagrangian relaxation. In Modern heuristic techniques for combinatorial problems (pp. 243–303). New York: Wiley. Google Scholar
  2. Eckstein, J., & Nediak, M. (2007). Pivot, cut and dive: a heuristic for mixed 0-1 integer programming. Journal of Heuristics, 13(5), 471–503. CrossRefGoogle Scholar
  3. Freville, A., & Plateau, G. (1986). Heuristics and reduction methods for multiple constraint 0-1 linear programming problems. European Journal of Operational Research, 24, 206–215. CrossRefGoogle Scholar
  4. Galinier, P., & Hao, J.-K. (2004). A general approach for constraint solving by local search. Journal of Mathematical Modelling and Algorithms, 3(1), 73–88. CrossRefGoogle Scholar
  5. Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1), 156–166. CrossRefGoogle Scholar
  6. Glover, F. (1995). Tabu thresholding: improved search by nonmonotonic trajectories. ORSA Journal on Computing, 7(3), 426–442. Google Scholar
  7. Glover, F. (2000). Multi-start and strategic oscillation methods—principles to exploit adaptive memory. In M. Laguna & J.L. Gonzales Velarde (Eds.), Computing tools for modeling, optimization and simulation: interfaces in computer science and operations research (pp. 1–24). Norwell: Kluwer Academic. Google Scholar
  8. Glover, F. (2003). Tutorial on surrogate constraint approaches for optimization in graphs. Journal of Heuristics, 9(3), 175–227. CrossRefGoogle Scholar
  9. Glover, F. (2006). Parametric tabu search for mixed integer programs. Computers and Operations Research, 33(9), 2449–2494. CrossRefGoogle Scholar
  10. Glover, F. (2007). Infeasible/feasible search trajectories and directional rounding in integer programming. Journal of Heuristics, 13(6), 505–542. CrossRefGoogle Scholar
  11. Glover, F. (2008). Inequalities and target objectives for metaheuristic search—part I: mixed binary optimization. In P. Siarry & Z. Michalewicz (Eds.), Advances in metaheuristics for hard optimization (pp. 439–474). New York: Springer. CrossRefGoogle Scholar
  12. Glover, F., & Laguna, M. (1997). Tabu search. Norwell: Kluwer Academic. Google Scholar
  13. Glover, F., Kochenberger, G., Alidaee, B., & Amini, M. M. (1999). Tabu with search critical event memory: an enhanced application for binary quadratic programs. In S. Voss, S. Martello, I. Osman & C. Roucairol (Eds.), MetaHeuristics: advances and trends in local search paradigms for optimization (pp. 93–110). Boston: Kluwer Academic. Google Scholar
  14. Hvattum, L. M., Lokketangen, A., & Glover, F. (2005). New heuristics and adaptive memory procedures for Boolean optimization problems. In J.K. Karlof (Ed.), Integer programming theory and practice (pp. 1–18). Google Scholar
  15. Kelly, J., Golden, B., & Assad, A. (1993). Large scale controlled rounding using tabu search with strategic oscillation. Annals of Operations Research, 41, 69–84. CrossRefGoogle Scholar
  16. Lü, Z., & Hao, J.-K. (2008). Adaptive tabu search for course timetabling. European Journal of Operational Research. doi:10.1016/j.ejor.2008.12.007. Google Scholar
  17. Nonobe, K., & Ibaraki, T. (1998). A tabu search approach for the constraint satisfaction problem as a general problem solver. European Journal of Operational Research, 106, 599–623. CrossRefGoogle Scholar
  18. Nonobe, K., & Ibaraki, T. (2001). An improved tabu search method for the weighted constraint satisfaction problem. INFOR, 39, 131–151. Google Scholar
  19. Osman, I. H. (1993). Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of Operations Research, 41, 421–451. CrossRefGoogle Scholar
  20. Reeves, C. R. (2006). Fitness landscapes. In Search Methodologies. Berlin: Springer, Chap. 19. Google Scholar
  21. Rego, C. (2005). RAMP: a new metaheuristic framework for combinatorial optimization. In C. Rego & B. Alidaee (Eds.), Metaheuristic optimization via memory and evolution: tabu search and scatter search (pp. 441–460). Norwell: Kluwer Academic. CrossRefGoogle Scholar
  22. Rego, C., & Alidaee, B. (2005). Metaheuristic optimization via memory and evolution: tabu search and scatter search. Norwell: Kluwer Academic. Google Scholar
  23. Vasquez, M., & Hao, J.-K. (2001a). A heuristic approach for antenna positioning in cellular networks. Journal of Heuristics, 7(5), 443–472. CrossRefGoogle Scholar
  24. Vasquez, M., & Hao, J.-K. (2001b). A ‘logic-constrained’ knapsack formulation and a Tabu algorithm for the daily photograph scheduling of an earth observation satellite. Computational Optimization and Applications, 20(2), 137–157. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.OptTek Systems, Inc.BoulderUSA
  2. 2.LERIA, UFR SciencesUniversité d’AngersAngers Cedex 01France

Personalised recommendations