Journal of Intelligent Manufacturing

, Volume 21, Issue 1, pp 17–30 | Cite as

Iterative flattening search for resource constrained scheduling

  • Angelo Oddi
  • Amedeo Cesta
  • Nicola Policella
  • Stephen F. Smith
Article

Abstract

Iterative flattening search (ifs) is a meta-heuristic strategy for solving multi-capacity scheduling problems. Given an initial solution, ifs iteratively applies: (1) a relaxation-step, in which a subset of scheduling decisions are randomly retracted from the current solution; and (2) a flattening-step, in which a new solution is incrementally recomputed from this partial schedule. Whenever a better solution is found, it is retained, and, upon termination, the best solution found during the search is returned. Prior research has shown ifs to be an effective and scalable heuristic procedure for minimizing schedule makespan in multi-capacity resource settings. In this paper we experimentally investigate the impact on ifs performance of algorithmic variants of the flattening step. The variants considered are distinguished by different computational requirements and correspondingly vary in the type and depth of search performed. The analysis is centered around the idea that given a time bound to the overall optimization procedure, the ifs optimization process is driven by two different and contrasting mechanisms: the random sampling performed by iteratively applying the “relaxation/flattening” cycle and the search conducted within the constituent flattening procedure. On one hand, one might expect that efficiency of the flattening process is key: the faster the flattening procedure, the greater the number of iterations (and number of sampled solutions) for a given time bound; and hence the greater the probability of finding better quality solutions. On the other hand, the use of more accurate (and more costly) flattening procedures can increase the probability of obtaining better quality solutions even if their greater computational cost reduces the number of ifs iterations. Comparative results on well-studied benchmark problems are presented that clarify this tradeoff with respect to previously proposed flattening strategies, identify qualitative guidelines for the design of effective ifs procedures, and suggest some new directions for future work in this area.

Keywords

Scheduling Meta-heuristics Iterative sampling 

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References

  1. Adams J., Balas E., Zawack D. (1988) The shifting bottleneck procedure for job shop scheduling. Management Science 34(3): 391–401CrossRefGoogle Scholar
  2. Blazewicz J., Lenstra J.K., Rinnoy Kan A.H.G. (1983) Scheduling projects subject to resource constraints: Classification and complexity. Discrete Applied Mathematics 5(1): 11–24CrossRefGoogle Scholar
  3. Blum C., Roli A. (2003) Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys 35(3): 268–308CrossRefGoogle Scholar
  4. Cesta, A., Oddi, A., & Smith, S. F. (1998). Profile based algorithms to solve multiple capacitated metric scheduling problems. In AIPS-98. Proceedings of the 4th International Conference on Artificial Intelligence Planning Systems (pp. 214–223).Google Scholar
  5. Cesta, A., Oddi, A., & Smith, S. F. (2000) Iterative flattening: A scalable method for solving multi-capacity scheduling problems. In AAAI00. Proceedings of the 17th National Conference on Artificial Intelligence (pp. 742–747).Google Scholar
  6. Cesta A., Oddi A., Smith S.F. (2002) A constraint-based method for project scheduling with time windows. Journal of Heuristics 8(1): 109–136CrossRefGoogle Scholar
  7. Dechter R., Meiri I., Pearl J. (1991) Temporal constraint networks. Artificial Intelligence 49: 61–95CrossRefGoogle Scholar
  8. Dorndorf U., Pesch E., Phan Huy T. (2000) A branch-and-bound algorithm for the resource-constrained project scheduling problem. Mathematical Methods of Operations Research 52: 413–439CrossRefGoogle Scholar
  9. Godard, D., Laborie, P., & Nuitjen, W. (2005). Randomized large neighborhood search for cumulative scheduling. In ICAPS-05. Proceedings of the 15th International Conference on Automated Planning & Scheduling (pp. 81–89).Google Scholar
  10. Gomes, C. P. (2003). Complete randomized backtrack search. In M. Milano (Ed.), Constraint and integer programming: Toward a unified methodology (pp. 233–283). Kluwer.Google Scholar
  11. Hoos H.H., Stützle T. (2005) Stochastic local search. Foundations and applications. San Francisco, Morgan Kaufmann.Google Scholar
  12. Jacobs L.W., Brusco M.J. (1995) A local search heuristic for large set-covering problems. Naval Research Logistic Quarterly 42(7): 1129–1140CrossRefGoogle Scholar
  13. Kolisch R. (1996) Serial and parallel resource-constrained project scheduling methods revised: Theory and computation. European Journal of Operational Research 90: 320–333CrossRefGoogle Scholar
  14. Langley, P. (1992). Systematic and nonsystematic search strategies. In AIPS92. Proceedings of the First International Conference on Artificial Intelligence Planning Systems (pp. 145–152). San Francisco: Morgan Kaufmann Publishers Inc.Google Scholar
  15. Lawrence, S. (1984). Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques (supplement). Technical report, Graduate School of Industrial Administration, Carnegie Mellon University.Google Scholar
  16. 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): 55–66CrossRefGoogle Scholar
  17. Lourenco H.R., Martin O., Stutzle T. (2002) Iterated local search. In: Glover F., Kochenberger G. (eds) Handbook of metaheuristics, international series in operations research & management science (Vol. 57). Academic Publishers, Norwell, MA, pp 321–353Google Scholar
  18. Marchiori, E., & Steenbeek, A. (1998). An iterated heuristic algorithm for the set covering problem. In Proceedings WAE’98, Saarbrücken, Germany, August 20–22 (pp. 155–166).Google Scholar
  19. Michel, L., & Van Hentenryck, P. (2004). Iterative relaxations for iterative flattening in cumulative scheduling. In ICAPS04. Proceedings of the 14th International Conference on Automated Planning & Scheduling (pp. 200–208).Google Scholar
  20. Nuijten W.P.M., Aarts E.H.L. (1996) A computational study of constraint satisfaction for multiple capacitated job shop scheduling. European Journal of Operational Research 90(2): 269–284CrossRefGoogle Scholar
  21. Oddi A., Cesta A., Policella N., Smith S.F. (2008) Combining variants of iterative flattening search. Journal of Engineering Applications of Artificial Intelligence 21(5): 683–690CrossRefGoogle Scholar
  22. Policella N., Cesta A., Oddi A., Smith S.F. (2007) From precedence constraint posting to partial order schedules. AI Communications 20(3): 163–180Google Scholar
  23. Prestwich, S. (2000). A hybrid search architecture applied to hard random 3-SAT and low-autocorrelation binary sequences. In 2000CP00. The 6th International Conference on Principles and Practice of Constraint Programming, LNCS (Vol. 1894, pp. 337–352). Springer-Verlag.Google Scholar
  24. Resende, M. G. C., & Ribeiro, C. C. (2002). Greedy randomized adaptive search procedures. In F. Glover & G. Kochenberger (Eds.), State of the art handbook in metaheuristics. Kluwer.Google Scholar
  25. Ruiz R., Stützle T. (2007) A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research 177(3): 2033–2049CrossRefGoogle Scholar
  26. Ruiz R., Stützle T. (2008) An iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objective. European Journal of Operational Research 187(3): 1143–1159CrossRefGoogle Scholar
  27. Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In CP98. The 4th International Conference on Principles and Practice of Constraint Programming, LNCS (Vol. 1520, pp. 417–431). Springer-Verlag.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Angelo Oddi
    • 1
  • Amedeo Cesta
    • 1
  • Nicola Policella
    • 2
  • Stephen F. Smith
    • 3
  1. 1.ISTC-CNRNational Research Council of ItalyRomeItaly
  2. 2.European Space AgencyDarmstadtGermany
  3. 3.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

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