Abstract
The importance of multi-objective optimization is globably established nowadays. Furthermore, a great part of real-world problems are subject to uncertainties due to, e.g., noisy or approximated fitness function(s), varying parameters or dynamic environments. Moreover, although evolutionary algorithms are commonly used to solve multi-objective problems on the one hand and to solve stochastic problems on the other hand, very few approaches combine simultaneously these two aspects. Thus, flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are, by nature, multi-objective and are subjected to a wide range of uncertainties. However, these two features have never been investigated at the same time.
In this paper, we present and adopt a proactive stochastic approach where processing times are represented by random variables. Then, we propose several multi-objective methods that are able to handle any type of probability distribution. Finally, we experiment these methods on a stochastic bi-objective flow-shop problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Babbar, M., Lakshmikantha, A., Goldberg, D.E.: A Modified NSGA-II to Solve Noisy Multiobjective Problems. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 21–27. Springer, Heidelberg (2003)
Basseur, M., Zitzler, E.: Handling Uncertainty in Indicator-Based Multiobjective Optimization. International Journal of Computational Intelligence Research 2(3), 255–272 (2006)
Cunningham, A.A., Dutta, S.K.: Scheduling jobs with exponentially distributed processing times on two machines of a flow shop. Naval Research Logistics Quarterly 16, 69–81 (1973)
Dauzère-Pérès, S., Castagliola, P., Lahlou, C.: Niveau de service en ordonnancement stochastique. In: Billaut, J.-C., et al. (eds.) Flexibilité et robustesse en ordonnancement, pp. 97–113. Hermès, Paris (2004)
Deb, K., Gupta, H.: Searching for Robust Pareto-Optimal Solutions in Multi-Objective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 150–164. Springer, Heidelberg (2005)
Dudek, R.A., Panwalkar, S.S., Smith, M.L.: The Lessons of Flowshop Scheduling Research. Operations Research 40(1), 7–13 (1992)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey. Annals of Discrete Mathematics 5, 287–326 (1979)
Hughes, E.J.: Evolutionary Multi-Objective Ranking with Uncertainty and Noise. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 329–343. Springer, Heidelberg (2001)
Ishibuchi, H., Murata, T.: A Multi-Objective Genetic Local Search Algorithm and Its Application to Flowshop Scheduling. IEEE Transactions on Systems, Man and Cybernetics 28, 392–403 (1998)
Jin, Y., Branke, J.: Evolutionary Optimization in Uncertain Environments - A Survey. IEEE Transactions on Evolutionary Computation 9, 303–317 (2005)
Keijzer, M., Merelo, J.J., Romero, G., Schoenauer, M.: Evolving Objects: A General Purpose Evolutionary Computation Library. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 231–244. Springer, Heidelberg (2002)
Kouvelis, P., Daniels, R.L., Vairaktarakis, G.: Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Transactions 32(5), 421–432 (2000)
Ku, P.S., Niu, S.C.: On Johnson’s Two-Machine Flow Shop with Random Processing Times. Operations Research 34, 130–136 (1986)
Landa Silva, J.D., Burke, E.K., Petrovic, S.: An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling. In: Gandibleux, X., et al. (eds.) Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, vol. 535, pp. 91–129. Springer, Berlin (2004)
Meunier, H., Talbi, E.-G., Reininger, P.: A multiobjective genetic algorithm for radio network optimization. In: Proc. of the 2000 Congress on Evolutionary Computation (CEC’00), pp. 317–324. IEEE Computer Society Press, Los Alamitos (2000)
T’kindt, V., Billaut, J.-C.: Multicriteria Scheduling - Theory, Models and Algorithms. Springer, Berlin (2002)
Taillard, E.D.: Benchmarks for Basic Scheduling Problems. European Journal of Operational Research 64, 278–285 (1993)
Teich, J.: Pareto-Front Exploration with Uncertain Objectives. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 314–328. Springer, Heidelberg (2001)
Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Liefooghe, A., Basseur, M., Jourdan, L., Talbi, EG. (2007). Combinatorial Optimization of Stochastic Multi-objective Problems: An Application to the Flow-Shop Scheduling Problem. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-70928-2_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70927-5
Online ISBN: 978-3-540-70928-2
eBook Packages: Computer ScienceComputer Science (R0)