Abstract
When solving a scheduling problem, users are often interested in finding a schedule optimizing a given objective function. However, in some settings there can be hard constraints that make the problem unfeasible. In this paper we focus on the task of repairing infeasibility in job shop scheduling problems with a hard constraint on the makespan. In this context, earlier work addressed the problem of computing the largest subset of the jobs that can be scheduled within the makespan constraint. Herein, we face a more general weighted version of the problem, consisting in computing a feasible subset of jobs maximizing their weighted sum. To this aim, we propose an efficient memetic algorithm, that combines a genetic algorithm with a local search method, also proposed in the paper. The results from an experimental study show the practical suitability of our approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allahverdi A, Aydilek H (2014) Total completion time with makespan constraint in no-wait flowshops with setup times. Eur J Oper Res 238(3):724–734
Ansótegui C, Bonet ML, Levy J (2013) SAT-based MaxSAT algorithms. Artif Intell 196:77–105
Artigues C, Lopez P, Ayache P (2005) Schedule generation schemes for the job shop problem with sequence-dependent setup times: dominance properties and computational analysis. Ann Oper Res 138:21–52
Bailey J, Stuckey PJ (2005) Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: PADL, pp 174–186
Beasley JE (1990) Or-library: distributing test problems by electronic mail. J Oper Res Soc 41(11):1069–1072
Bierwirth C (1995) A generalized permutation approach to job shop scheduling with genetic algorithms. OR Spectr 17:87–92
Brucker P, Knust S (2006) Complex scheduling. Springer, Berlin
Choi JY (2015) Minimizing total weighted completion time under makespan constraint for two-agent scheduling with job-dependent aging effects. Comput Ind Eng 83:237–243
Dawande M, Gavirneni S, Rachamadugu R (2006) Scheduling a two-stage flowshop under makespan constraint. Math Comput Model 44(1):73–84
Garey M, Johnson D, Sethi R (1976) The complexity of flowshop and jobshop scheduling. Math Oper Res 1(2):117–129
Giffler B, Thompson GL (1960) Algorithms for solving production scheduling problems. Oper Res 8:487–503
Graham R, Lawler E, Lenstra J, Kan A (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326
Marques-Silva J, Heras F, Janota M, Previti A, Belov A (2013) On computing minimal correction subsets. In: Proceedings of IJCAI, pp 615–622
Marques-Silva J, Janota M, Mencía C (2017) Minimal sets on propositional formulae. Problems and reductions. Artif Intell 252:22–50
Mencía C, Sierra MR, Varela R (2013) Depth-first heuristic search for the job shop scheduling problem. Ann OR 206(1):265–296
Mencía R, Sierra MR, Mencía C, Varela R (2015a) Memetic algorithms for the job shop scheduling problem with operators. Appl Soft Comput 34:94–105
Mencía R, Sierra MR, Mencía C, Varela R (2015b) Schedule generation schemes and genetic algorithm for the scheduling problem with skilled operators and arbitrary precedence relations. In: Proceedings of ICAPS. AAAI Press, pp 165–173
Mencía C, Sierra MR, Mencía R, Varela R (2019a) Evolutionary one-machine scheduling in the context of electric vehicles charging. Integr Comput Aided Eng 26:49–63
Mencía R, Mencía C, Varela R (2019b) Repairing infeasibility in scheduling via genetic algorithms. In: From bioinspired systems and biomedical applications to machine learning—8th international work-conference on the interplay between natural and artificial computation, IWINAC 2019, Almería, Spain, 3–7 June 2019, Proceedings, Part II, pp 254–263
Nowicki E, Smutnicki C (2005) An advanced tabu search algorithm for the job shop problem. J Sched 8:145–159
Ono I, Yamamura M, Kobayashi S (1996) A genetic algorithm for job-shop scheduling problems using job-based order crossover. In: Proceedings of 1996 IEEE international conference on evolutionary computation, pp 547–552
Palacios JJ, Vela CR, Rodríguez IG, Puente J (2014) Schedule generation schemes for job shop problems with fuzziness. In: Proceedings of ECAI, pp 687–692 (2014)
Previti A, Mencía C, Järvisalo M, Marques-Silva J (2018) Premise set caching for enumerating minimal correction subsets. In: Proceedings of AAAI, pp 6633–6640
Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285
Talbi E (2009) Metaheuristics: from design to implementation. Wiley, New York
Van Laarhoven P, Aarts E, Lenstra K (1992) Job shop scheduling by simulated annealing. Oper Res 40:113–125
Zhang CY, Li P, Rao Y, Guan Z (2008) A very fast TS/SA algorithm for the job shop scheduling problem. Comput Oper Res 35:282–294
Acknowledgements
This research is supported by the Spanish Government under Project TIN2016-79190-R and by the Principality of Asturias under Grant IDI/2018/000176.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mencía, R., Mencía, C. & Varela, R. A memetic algorithm for restoring feasibility in scheduling with limited makespan. Nat Comput 21, 577–587 (2022). https://doi.org/10.1007/s11047-020-09796-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-020-09796-1