Abstract
In this paper we consider a variant of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. Solutions to this problem are fuzzy schedules, which we argue should be seen as predictive schedules, thus establishing links with the concept of robustness and a measure thereof. We propose a particle swarm optimization (PSO) approach to minimise the schedule’s expected makespan, using priorities to represent particle position, as well as a decoding algorithm to generate schedules in a subset of possibly active ones. Our proposal is evaluated on a varied set of several benchmark problems. The experimental study includes a parametric analysis, results of the PSO compared with the state-of-the-art, and an empirical study of the robustness of taking into account uncertainty along the scheduling process.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Ahmadizar F, Farahani MH (2012) A novel hybrid genetic algorithm for the open shop scheduling problem. Int J Adv Manuf Technol 62:775–787
Bidot J, Vidal T, Laboire P (2009) A theoretic and practical framework for scheduling in stochastic environment. J Sched 12:315–344
Blum C (2005) Beam-ACO—hybridizing ant colony optimization with beam search: an application to open shop scheduling. Comput Oper Res 32(6):1565–1591
Brucker P, Hunrink J, Jurisch B, Wöstmann B (1997) A branch & bound algorithm for the open-shop problem. Discrete App Math 76:43–59
Dubois D, Fargier H, Fortemps P (2008) Scheduling under flexible constraints and uncertain data: the fuzzy approach. In: Production scheduling, chap. 11, Wiley, Weinheim, p 301–332
Dubois D, Fargier H, Fortemps P (2003) Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge. Eur J Oper Res 147:231–252
Dubois D, Prade H (1986) Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York
Fortemps P (1997) Jobshop scheduling with imprecise durations: a fuzzy approach. IEEE Trans Fuzzy Syst 7:557–569
Giffler B, Thompson GL (1960) Algorithms for solving production scheduling problems. Oper Res 8:487–503
Gonçalves J, Mendes J, de M RM (2005) A hybrid genetic algorithm for the job shop scheduling problem. Eur J Oper Res 167:77–95
González-Rodríguez I, Palacios JJ, Vela CR, Puente J (2010) Heuristic local search for fuzzy open shop scheduling. In: Proceedings IEEE International conference on fuzzy systems, FUZZ-IEEE2010. pp 1858–1865. IEEE
González-Rodríguez I, Puente J, Vela CR, Varela R (2008) Semantics of schedules for the fuzzy job shop problem. IEEE Trans Syst Man Cybern Part A 38(3):655–666
González-Rodríguez I, Vela CR, Puente J (2007) 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. IEEE, London
Graham R, Lawler E, Lenstra J, Rinnooy Kan A (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discret Math 4:287–326
Guéret C, Prins C (1998) Classical and new heuristics for the open-shop problem: a computational evaluation. Eur J Oper Res 107:306–314
Herroelen W, Leus R (2005) Project scheduling under uncertainty: Survey and research potentials. Eur J Oper Res 165:289–306
Hu Y, Yin M, Li X (2011) A novel objective function for job-shop scheduling problem with fuzzy processing time and fuzzy due date using differential evolution algorithm. Int J Adv Manuf Technol 56:1125–1138
Huang YM, Lin JC (2011) A new bee colony optimization algorithm with idle-time-based filtering scheme for open shop-scheduling problems. Expert Syst Appl 38(5):5438–5447
Kalaï R, Lamboray C, Vanderpooten D (2012) Lexicographic α-robustness: an alternative to min-max criteria. Eur J Oper Res 220:722–728
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks. pp 1942–1948. IEEE Press, New Jersey
Konno T, Ishii H (2000) An open shop scheduling problem with fuzzy allowable time and fuzzy resource constraint. Fuzzy Sets Syst 109:141–147
Lei D (2010) Solving fuzzy job shop scheduling problems using random key genetic algorithm. International Int J Adv Manuf Technol 49:253–262
Liaw CF (1999) A tabu search algorithm for the open shop scheduling problem. Comput Oper Res 26:109–126
Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10:445–450
Noori-Darvish S, Mahdavi I, Mahdavi-Amiri N (2012) A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due-dates. Appl Soft Comput 12:1399–1416
Palacios JJ, Puente J, Vela CR, González-Rodríguez I (2009) A genetic algorithm for the open shop problem with uncertain durations. In: Proceedings of IWINAC 2009, Part I. Lecture notes in computer science, vol 5601, pp 255–264. Springer
Pinedo ML (2008) Scheduling: theory, algorithms, and systems, 3rd edn. Springer, Secaucus
Puente J, Vela CR, González-Rodríguez I (2010) Fast local search for fuzzy job shop scheduling. In: Proceedings of 19th European conference on artificial intelligence, ECAI 2010. pp 739–744. IOS Press
Sha DY, Cheng-Yu H (2006) A modified parameterized active schedule generation algorithm for the job shop scheduling problem. In: Proceedings of the 36th international conference on computers and industrial engineering, ICCIE2006. pp 702–712
Sha DY, Cheng-Yu H (2008) A new particle swarm optimization for the open shop scheduling problem. Comput Oper Res 35:3243–3261
Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64:278–285
Tavakkoli-Moghaddam R, Safei N, Kah M (2008) Accessing feasible space in a generalized job shop scheduling problem with the fuzzy processing times: a fuzzy-neural approach. J Oper Res Soc 59:431–442
Zheng Y, Li Y, Lei D (2011) Swarm-based neighbourhood search for fuzzy job shop scheduling. Int J Innovative Comput Appl 3(3):144–151
Acknowledgments
This work Has been funded by the Spanish Ministry of Science and Education under research grants MEC-FEDER TIN2010-20976-C02-02 and MTM2010-16051 and by the Principality of Asturias (Spain) under grant Severo Ochoa BP13106.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Palacios, J.J., González-Rodríguez, I., Vela, C.R. et al. Robust swarm optimisation for fuzzy open shop scheduling. Nat Comput 13, 145–156 (2014). https://doi.org/10.1007/s11047-014-9413-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-014-9413-1