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.
Similar content being viewed by others
References
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.
Chen, C. L., & Bulfin, R. L. (1993). Complexity of single machine multi-criteria scheduling problems. European Journal of Operational Research, 70, 115–125.
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.
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.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization (1st ed.). New York: Wiley.
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.
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.
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.
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).
Fligner, M. A., & Killeen, T. J. (1976). Distribution-free two-sample tests for scale. Journal of the American Statistical Association, 71(353), 210–213.
Garey, M. R., & Johnson, D. S. (1978). “Strong” NP-completeness results: motivation, examples, and implications. Journal of the ACM, 25(3), 499–508.
Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17, 416–429.
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.
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.
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.
Hoogeveen, H. (2005). Multicriteria scheduling. European Journal of Operational Research, 167(3), 592–623.
Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness (Management Science Research Project, Research Report 43), University of California, Los Angeles.
Knowles, J., & Corne, D. (2000). Approximating the nondominated front using the Pareto archived evolution strategies. Evolutionary Computation, 8(2), 149–172.
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.
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.
Moore, J. M. (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109.
Pinedo, M. (2009). Scheduling: theory, algorithms, and systems (3rd ed.). Berlin: Springer.
Schwefel, H. P. (1995). Evolution and optimum seeking (1st ed.). New York: Wiley.
Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3, 59–66.
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.
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.
T’kindt, V., & Billaut, J. C. (2006). Multicriteria scheduling. Theory, models and algorithms (2nd ed.). Berlin: Springer.
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.
van Wassenhove, L. N., & Gelders, F. (1980). Solving a bicriterion scheduling problem. European Journal of Operational Research, 2(4), 281–290.
Vincent, T. L., & Grantham, W. J. (1981). Optimality in parametric systems (1st ed.). New York: Wiley.
Zitzler, E. (1999). Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, ETH Zürich.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grimme, C., Lepping, J. & Schwiegelshohn, U. Multi-criteria scheduling: an agent-based approach for expert knowledge integration. J Sched 16, 369–383 (2013). https://doi.org/10.1007/s10951-011-0256-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-011-0256-7