A genetic solution based on lexicographical goal programming for a multiobjective job shop with uncertainty
In this work we consider a multiobjective job shop problem with uncertain durations and crisp due dates. Ill-known durations are modelled as fuzzy numbers. We take a fuzzy goal programming approach to propose a generic multiobjective model based on lexicographical minimisation of expected values. To solve the resulting problem, we propose a genetic algorithm searching in the space of possibly active schedules. Experimental results are presented for several problem instances, solved by the GA according to the proposed model, considering three objectives: makespan, tardiness and idleness. The results illustrate the potential of the proposed multiobjective model and genetic algorithm.
KeywordsJob shop Scheduling Uncertain duration Multiobjective optimisation
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- Bierwirth C. (1995) A generalized permutation approach to jobshop scheduling with genetic algorithms. OR Spectrum 17: 87–92Google Scholar
- Brucker P., Knust S. (2006) Complex scheduling. Springer, NYGoogle Scholar
- Dubois D., Prade H. (1988) Possibility theory: An approach to computerized processing of uncertainty. Plenum Press, New YorkGoogle Scholar
- Fayad, C., & Petrovic, S. (2005). A fuzzy genetic algorithm for real-world job-shop scheduling. Innovations in applied artificial intelligence. Lecture Notes in Computer Science (Vol. 3533, pp. 524–533). Bari: Springer.Google Scholar
- González Rodríguez, I., Vela, C. R., & Puente, J. (2006). Study of objective functions in fuzzy job-shop problem. ICAISC 2006. Lecture Notes in Artificial Intelligence (vol. 4029, pp.360–369). Zakopane: Springer.Google Scholar
- González Rodríguez I., Vela C.R., Puente J. (2007) A genetic solution for multiobjective fuzzy job shop based on lexicographical goal programming. In: Salido M.A., Fdez-Olivares J.(eds) Proceedings of the Workshop on Planning, Scheduling and Constraint Satisfaction. Salamanca, Spain, pp 93–104Google Scholar
- González Rodríguez, I., Vela, C. R., & Puente, J. (2007b). A memetic approach to fuzzy job shop based on expectation model. In Proceedings of IEEE International Conference on Fuzzy Systems, FUZZ-IEEE2007 (pp. 692–697). London.Google Scholar
- Mattfeld D.C. (1995) Evolutionary search and the job shop investigations on genetic algorithms for production scheduling. Springer-Verlag, NYGoogle Scholar
- Słowiński, R., Hapke, M. (eds) (2000) Scheduling under fuzziness (vol. 37 of Studies in Fuzziness and Soft Computing. Physica-Verlag, HeidelbergGoogle Scholar
- Varela, R., Serrano, D., & Sierra, M. (2005). New codification schemas for scheduling with genetic algorithms. Artificial intelligence and knowledge engineering applications: A bioinspiried approach. Lecture Notes in Computer Science (Vol. 3562, pp. 11–20). Las Palmas: Springer.Google Scholar