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Journal of Scheduling

, Volume 16, Issue 4, pp 369–383 | Cite as

Multi-criteria scheduling: an agent-based approach for expert knowledge integration

  • Christian Grimme
  • Joachim Lepping
  • Uwe Schwiegelshohn
Article

Abstract

In this work, we present an agent-based approach to multi-criteria combinatorial optimization. It allows to flexibly combine elementary heuristics that may be optimal for corresponding single-criterion problems.

We optimize an instance of the scheduling problem 1|d j |∑C j ,L max and show that the modular building block architecture of our optimization model and the distribution of acting entities enables the easy integration of problem specific expert knowledge. We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures. In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to solve fractions of the complete problem. We show that we can approximate both single-criterion problems such as P m |d j |∑U j as well as more challenging multi-criteria scheduling problems, like P m ||C max,∑C j and P m |d j |C max,∑C j ,∑U j . The latter problems are evaluated with extensive simulations comparing the standard multi-criteria evolutionary algorithm NSGA-2 and the new agent-based model.

Keywords

Multi-criteria scheduling Predator–prey model Parallel machine scheduling Evolutionary multi-criteria optimization 

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References

  1. Bartz-Beielstein, T., Lasarczyk, C. W. G., & Preuss, M. (2005). Sequential parameter optimization. In IEEE congress on evolutionary computation (Vol. 1, pp. 773–780). New York: IEEE Press. Google Scholar
  2. Chen, C. L., & Bulfin, R. L. (1993). Complexity of single machine multi-criteria scheduling problems. European Journal of Operational Research, 70, 115–125. CrossRefGoogle Scholar
  3. Coello, C. A. C., Lamont, G. B., & Veldhuizen, D. A. V. (2007). Evolutionary algorithms for solving multi-objective problems. Genetic and evolutionary computation (2nd ed.). New York: Springer. Google Scholar
  4. Conover, W. J., Johnson, M. E., & Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics, 4(23), 351–361. CrossRefGoogle Scholar
  5. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization (1st ed.). New York: Wiley. Google Scholar
  6. Deb, K., Agrawal, S., Pratab, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In M. Schoenauer et al. (Eds.), Lecture notes in computer science: Vol. 1917. Proceedings of the conference on parallel problem solving from nature (pp. 849–858). Berlin: Springer. Google Scholar
  7. Durillo, J., Nebro, A., & Alba, E. (2010). The jMetal framework for multi-objective optimization: design and architecture. In IEEE congress on evolutionary computation (Vol. 5467, pp. 4138–4325). Barcelona, Spain. Berlin: Springer. Google Scholar
  8. Dutot, P. F., Rzadca, K., Saule, E., & Trystram, D. (2010). Multi-objective scheduling. In Introduction to scheduling, (1st ed.). (pp. 219–251). Boca Raton: CRC Press. Google Scholar
  9. Emmerich, M., Beume, N., & Naujoks, B. (2005). An EMO algorithm using the hypervolume measure as selection criterion. In Proceedings of the international conference on evolutionary multi-criterion optimization (pp. 62–76). CrossRefGoogle Scholar
  10. Fligner, M. A., & Killeen, T. J. (1976). Distribution-free two-sample tests for scale. Journal of the American Statistical Association, 71(353), 210–213. CrossRefGoogle Scholar
  11. Garey, M. R., & Johnson, D. S. (1978). “Strong” NP-completeness results: motivation, examples, and implications. Journal of the ACM, 25(3), 499–508. CrossRefGoogle Scholar
  12. Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17, 416–429. CrossRefGoogle Scholar
  13. Graham, R. L., Lawer, E. L., Lenstra, J. K., & Kan, A. H. G. R. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326. CrossRefGoogle Scholar
  14. Grimme, C., & Lepping, J. (2007). Designing multi-objective variation operators using a predator–prey approach. In Lecture notes in computer science: Vol. 4403. Proceedings of the international conference on evolutionary multi-criterion optimization (pp. 21–35). Berlin: Springer. CrossRefGoogle Scholar
  15. Grimme, C., Lepping, J., & Papaspyrou, A. (2007). Exploring the behavior of building blocks for multi-objective variation operator design using predator–prey dynamics. In D. Thierens et al. (Eds.), Proceedings of the genetic and evolutionary computation conference (pp. 805–812). New York: ACM. Google Scholar
  16. Hoogeveen, H. (2005). Multicriteria scheduling. European Journal of Operational Research, 167(3), 592–623. CrossRefGoogle Scholar
  17. Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness (Management Science Research Project, Research Report 43), University of California, Los Angeles. Google Scholar
  18. Knowles, J., & Corne, D. (2000). Approximating the nondominated front using the Pareto archived evolution strategies. Evolutionary Computation, 8(2), 149–172. CrossRefGoogle Scholar
  19. Knowles, J., & Corne, D. (2007). Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In Proceedings of the 4th international conference on evolutionary multi-criterion optimization (pp. 757–771). Berlin: Springer. CrossRefGoogle Scholar
  20. Laumanns, M., Rudolph, G., & Schwefel, H. P. (1998). A spatial predator–prey approach to multi-objective optimization: a preliminary study. In T. Bäck et al. (Eds.), Proceedings of the conference on parallel problem solving from nature (pp. 241–249). Berlin: Springer. CrossRefGoogle Scholar
  21. Moore, J. M. (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109. CrossRefGoogle Scholar
  22. Pinedo, M. (2009). Scheduling: theory, algorithms, and systems (3rd ed.). Berlin: Springer. Google Scholar
  23. Schwefel, H. P. (1995). Evolution and optimum seeking (1st ed.). New York: Wiley. Google Scholar
  24. Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3, 59–66. CrossRefGoogle Scholar
  25. Stein, C., & Wein, J. (1997). On the existence of schedules that are near-optimal for both makespan and total weighted completion time. Operations Research Letters, 21, 115–122. CrossRefGoogle Scholar
  26. Süer, G. A., Báez, E., & Czajkiewicz, Z. (1993). Minimizing the number of tardy jobs in identical machine scheduling. Computers & Industrial Engineering, 25(1–4), 243–246. CrossRefGoogle Scholar
  27. T’kindt, V., & Billaut, J. C. (2006). Multicriteria scheduling. Theory, models and algorithms (2nd ed.). Berlin: Springer. Google Scholar
  28. van den Akker, M., & Hoogeveen, H. (2008). Minimizing the number of late jobs in a stochastic setting using a chance constraint. Journal of Scheduling, 11(1), 59–69. CrossRefGoogle Scholar
  29. van Wassenhove, L. N., & Gelders, F. (1980). Solving a bicriterion scheduling problem. European Journal of Operational Research, 2(4), 281–290. CrossRefGoogle Scholar
  30. Vincent, T. L., & Grantham, W. J. (1981). Optimality in parametric systems (1st ed.). New York: Wiley. Google Scholar
  31. Zitzler, E. (1999). Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, ETH Zürich. Google Scholar
  32. Zitzler, E., & Thiele, L. (1999). Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3(4), 257–271. CrossRefGoogle Scholar
  33. Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm (Technical Report 103). Computer Engineering and Communication Networks Lab (TIK), ETH Zürich. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Christian Grimme
    • 1
  • Joachim Lepping
    • 2
  • Uwe Schwiegelshohn
    • 1
  1. 1.Robotics Research InstituteTU Dortmund UniversityDortmundGermany
  2. 2.ENSIMAG—antenne de MontbonnotINRIA Rhône-Alpes, Grenoble UniversityMontbonnot Saint MartinFrance

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