Journal of Scheduling

, Volume 14, Issue 2, pp 121–140 | Cite as

Understanding the behavior of Solution-Guided Search for job-shop scheduling

Article

Abstract

This paper investigates reasons behind the behavior of constructive Solution-Guided Search (SGS) on job-shop scheduling optimization problems. In particular, two, not mutually exclusive, hypotheses are investigated: (1) Like randomized restart, SGS exploits heavy-tailed distributions of search cost; and (2) Like local search, SGS exploits search space structure such as the clustering of high-quality solutions. Theoretical and experimental evidence strongly support both hypotheses. Unexpectedly, the experiments into the second hypothesis indicate that the performance of randomized restart and standard chronological backtracking are also correlated with search space structure. This result leaves open the question of finding the mechanism by which such structure is exploited as well as suggesting a deeper connection between the performance of constructive and local search.

Keywords

Search Empirical analysis Algorithm behavior Constraint programming 

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References

  1. Achlioptas, D., Gomes, C. P., Kautz, H. A., & Selman, B. (2000). Generating satisfiable problem instances. In Proceedings of the seventeenth national conference on artificial intelligence (pp. 256–261). Google Scholar
  2. Baptista, L., & Silva, J. P. M. (2000). Using randomization and learning to solve hard real-world instances of satisfiability. In Principles and practice of constraint programming (pp. 489–494). Google Scholar
  3. Beck, J. C. (1999). Texture measurements as a basis for heuristic commitment techniques in constraint-directed scheduling. PhD thesis, University of Toronto. Google Scholar
  4. Beck, J. C. (2005). Multi-point constructive search. In Proceedings of the eleventh international conference on principles and practice of constraint programming (CP’05) (pp. 737–741). Google Scholar
  5. Beck, J. C. (2005). Multi-point constructive search: Extended remix. In Proceedings of the CP2005 workshop on local search techniques for constraint satisfaction (pp. 17–31). Google Scholar
  6. Beck, J. C. (2006). An empirical study of multi-point constructive search for constraint-based scheduling. In Proceedings of the sixteenth international on automated planning and scheduling (ICAPS06) (pp. 274–283). Google Scholar
  7. Beck, J. C. (2007). Solution-guided multi-point constructive search for job shop scheduling. Journal of Artificial Intelligence Research, 29, 49–77. Google Scholar
  8. Beck, J. C., & Fox, M. S. (2000). Dynamic problem structure analysis as a basis for constraint-directed scheduling heuristics. Artificial Intelligence, 117(1), 31–81. CrossRefGoogle Scholar
  9. Beck, J. C., & Watson, J.-P. (2003). Adaptive search algorithms and fitness-distance correlation. In Proceedings of the fifth metaheuristics international conference. Google Scholar
  10. Blazewicz, J., Domschke, W., & Pesch, E. (1996). The job shop scheduling problem: Conventional and new solution techniques. European Journal of Operational Research, 93(1), 1–33. CrossRefGoogle Scholar
  11. Chen, H., Gomes, C. P., & Selman, B. (2001). Formal models of heavy-tailed behavior in combinatorial search. In CP’01: Proceedings of the 7th international conference on principles and practice of constraint programming (pp. 408–421). London: Springer. Google Scholar
  12. Clark, D. A., Frank, J., Gent, I. P., MacIntyre, E., Tomov, N., & Walsh, T. (1996). Local search and the number of solutions. In Proceedings of the second international conference on principles and practice of constraint programming (CP’96) (pp. 119–133). Berlin: Springer. Google Scholar
  13. Gent, I. P., MacIntyre, E., Prosser, P., & Walsh, T. (1996). The constrainedness of search. In Proceedings of the thirteenth national conference on artificial intelligence (AAAI-96) (Vol. 1, pp. 246–252). Google Scholar
  14. Gomes, C. P., & Selman, B. (1999). Search strategies for hybrid search spaces. In Proceedings of the 11th IEEE international conference on tools with artificial intelligence (p. 359). Los Alamitos: IEEE Computer Society. CrossRefGoogle Scholar
  15. Gomes, C. P., Selman, B., & Kautz, H. (1998). Boosting combinatorial search through randomization. In Proceedings of the fifteenth national conference on artificial intelligence (AAAI-98) (pp. 431–437). Google Scholar
  16. Gomes, C. P., Selman, B., Crato, N., & Kautz, H. A. (2000). Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. Journal of Automated Reasoning, 24(1/2), 67–100. CrossRefGoogle Scholar
  17. Gomes, C. P., Fernàndes, C., Selman, B., & Bessiere, C. (2004). Statistical regimes across constrainedness regions. In Proceedings of the tenth international conference on the principles and practice of constraint programming (CP2004) (pp. 32–46). Google Scholar
  18. Gomes, C. P., Fernández, C., Selman, B., & Bessière, C. (2005). Statistical regimes across constrainedness regions. Constraints, 10(4), 317–337. CrossRefGoogle Scholar
  19. Heckman, I. (2007). Empirical analysis of solution guided multi-point constructive search. Master’s thesis, Department of Computer Science, University of Toronto. Google Scholar
  20. Heckman, I., & Beck, J. C. (2007). Fitness-distance correlation and solution-guided multi-point constructive search. In L. Perron & M. Trick (Eds.), Proceedings of the fourth international conference on integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR’07) (pp. 112–126). Berlin: Springer. Google Scholar
  21. Jones, T., & Forrest, S. (1995). Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In L. Eshelman (Ed.), Proceedings of the sixth international conference on genetic algorithms (pp. 184–192). San Francisco: Morgan Kaufmann. Google Scholar
  22. Laarhoven, P. J. M., Aarts, E. H. L., & Lenstra, J. K. (1992). Job shop scheduling by simulated annealing. Operations Research, 40(1), 113–125. CrossRefGoogle Scholar
  23. Laborie, P. (2003). Algorithms for propagating resource constraints in AI planning and scheduling: Existing approaches and new results. Artificial Intelligence, 143, 151–188. CrossRefGoogle Scholar
  24. Le Pape, C. (1994). Implementation of resource constraints in ILOG Schedule: A library for the development of constraint-based scheduling systems. Intelligent Systems Engineering, 3(2), 55–66. CrossRefGoogle Scholar
  25. Luby, M., Sinclair, A., & Zuckerman, D. (1993). Optimal speedup of Las Vegas algorithms. Information Processing Letters, 47, 173–180. CrossRefGoogle Scholar
  26. Mattfeld, D. C., Bierwirth, C., & Kopfer, H. (1999). A search space analysis of the job shop scheduling problem. Annals of Operations Research, 86, 441–453. CrossRefGoogle Scholar
  27. Mitchell, D., Selman, B., & Levesque, H. (1992). Hard and easy distributions of SAT problems. In Proceedings of the tenth national conference on artificial intelligence (AAAI-92) (pp. 459–465). Google Scholar
  28. Nuijten, W. P. M. (1994). Time and resource constrained scheduling: a constraint satisfaction approach. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology. Google Scholar
  29. Parkes, A. J. (1997). Clustering at the phase transition. In Proceedings of the fourteenth national conference on artificial intelligence (AAAI-97) (pp. 340–345). Providence, RI. Google Scholar
  30. Scheduler (2006). ILOG Scheduler 6.2 User’s manual and reference manual. ILOG, S.A. Google Scholar
  31. Singer, J., Gent, I. P., & Smaill, A. (2000). Backbone fragility and local search cost peak. Journal of Artificial Intelligence Research, 12, 235–270. Google Scholar
  32. Smith, B. M., & Dyer, M. E. (1996). Locating the phase transition in constraint satisfaction problems. Artificial Intelligence, 81, 155–181. CrossRefGoogle Scholar
  33. Watson, J.-P. (2003). Empirical modeling and analysis of local search algorithms for the job-shop scheduling problem. PhD thesis, Dept. of Computer Science, Colorado State University. Google Scholar
  34. Watson, J.-P., & Beck, J. C. (2008). A hybrid constraint programming/local search approach to the job-shop scheduling problem. In Proceedings of the fifth international conference on integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR’08) (pp. 263–277). Google Scholar
  35. Watson, J.-P., Barbulescu, L., Whitley, L. D., & Howe, A. E. (2002). Contrasting structured and random permutation flow-shop scheduling problems: search-space topology and algorithm performance. INFORMS Journal on Computing, 14(2), 98–123. CrossRefGoogle Scholar
  36. Watson, J.-P., Beck, J. C., Howe, A. E., & Whitley, L. D. (2003). Problem difficulty for tabu search in job-shop scheduling. Artificial Intelligence, 143(2), 189–217. CrossRefGoogle Scholar
  37. Williams, R., Gomes, C., & Selman, B. (2003). On the connections between backdoors, restarts, and heavy-tailedness in combinatorial search. In Proceedings of sixth international conference on theory and applications of satisfiability testing (SAT-03). Google Scholar
  38. Wu, H., & van Beek, P. (2007). On universal restart strategies for backtracking search. In Proceedings of the thirteenth international conference on the principles and practice of constraint programming (CP 2007) (pp. 681–695). Google Scholar
  39. Yokoo, M. (1997). Why adding more constraints makes a problem easier for hill-climbing algorithms: Analyzing landscapes of CSPs. In Principles and practice of constraint programming (pp. 356–370). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.Department of Mechanical & Industrial EngineeringUniversity of TorontoTorontoCanada

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