Abstract
As a novel evolutionary technique, grouping evolutionary strategy (GES) has proved efficient and effective on grouping problems in which the task is to partition a set of items into disjoint groups. This paper investigates the first application of GES to tackle the parallel-machines scheduling problem as a well-known grouping problem in which machines can be treated as groups and jobs can be regarded as the items and the task is to partition a set of jobs into disjoint groups (and process all jobs in a same group by the same machines) to minimize makespan (C max) criterion. The main features of GES algorithm that make it different from the typical evolutionary approaches proposed for the parallel-machines scheduling problem, lie in exploiting a suitable chromosomal representation and a well-designed mutation operator that works with the set of jobs assigned to each machine instead of jobs isolatedly, and uses a two-phase procedure to generate the new schedules more effectively. In addition, we hybridized GES with an efficient local search heuristic and proved that it has an important descent property. To verify the performance of our proposed algorithm, comparisons are made using available methodologies in the literature. Computational results signify that the proposed approach is fast and competitive in providing high quality results.
Similar content being viewed by others
References
Abdulhamid SM, Abd Latiff MS, Madni SHH, Abdullahi M (2016) Fault tolerance aware scheduling technique for cloud computing environment using dynamic clustering algorithm. Neural Comput Appl. doi:10.1007/s00521-016-2448-8
Abdullahi M, Ngadi MA, Abdulhamid SM (2016) Symbiotic organism search optimization based task scheduling in cloud computing environment. Future Gener Comput Syst 56(1):640–650
Balin S (2011) Non-identical parallel machine scheduling using genetic algorithm. Expert Syst Appl 38(6):6814–6821
Bathrinath S, Sankar SS, Ponnambalam SG, Kannan BKV (2013) Bi-objective optimization in identical parallel machine scheduling problem. In: Swarm, evolutionary, and memetic computing. Springer International Publishing, pp. 377–388
Bathrinath S, Sankar SS, Ponnambalam SG, Leno IJ (2015) VNS-based heuristic for identical parallel machine scheduling problem. In: Artificial intelligence and evolutionary algorithms in engineering systems. Springer India, pp 693–699
Chen J, Pan QK, Wang L, Li JQ (2012) A hybrid dynamic harmony search algorithm for identical parallel machines scheduling. Eng Optim 44(2):209–224
Coffman EG, Garey MR, Johnson DS (1978) An application of bin-packing to multi-processor scheduling. SIAM J Comput 7:1–17
Dell’Amico M, Martello S (2005) A note on exact algorithms for the identical parallel machine scheduling problem. Eur J Oper Res 160(2):576–578
Dell’Amico M, Martello S (1995) Optimal scheduling of tasks on identical parallel processors. ORSA J Comput 7(2):191–200
Diana ROM, de França Filho MF, de Souza SR, de Almeida Vitor JF (2015) An immune-inspired algorithm for an unrelated parallel machines’ scheduling problem with sequence and machine dependent setup-times for makespan minimisation. Neurocomputing 163:94–105
Falkenauer E (1994) New representation and operators for GAs applied to grouping problems. Evol Comput 2:123–144
Fatemi Ghomi SMT, Jolai Ghazvini F (1998) A pairwise interchange algorithm for parallel machine scheduling. Prod Plan Control 9:685–689
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco
Gharbi A, Haouari M (2007) An approximate decomposition algorithm for scheduling on parallel machines with heads and tails. Comput Oper Res 34:868–883
Graham RL (1969) Bounds on multiprocessor timing anomalies. SIAM J Appl Math 17:416–429
Gupta JND, Ruiz-Torres AJ (2001) A LISTFIT heuristic for minimizing makespan on identical parallel machines. Prod Plan Control 12:28–36
Hashemian N, Diallo C, Vizvári B (2014) Makespan minimization for parallel machines scheduling with multiple availability constraints. Ann Oper Res 213(1):173–186
Husseinzadeh Kashan A (2014) League championship algorithm (LCA): a new algorithm for global optimization inspired by sport championships. Appl Soft Comput 16:171–200
Husseinzadeh Kashan A (2015) A new metaheuristic for optimization: optics inspired optimization (OIO). Comput Oper Res 55:99–125
Husseinzadeh Kashan A, Karimi B (2009) A discrete particle swarm optimization algorithm for scheduling parallel machines. Comput Ind Eng 56:216–223
Husseinzadeh Kashan A, Karimi B (2009) An improved mixed integer linear formulation and lower bounds for minimizing makespan on a flow shop with batch processing machines. Int J Adv Manuf Technol 40:582–594
Husseinzadeh Kashan A, Karimi B (2010) A new algorithm for constrained optimization inspired by the sport league championships. In: IEEE world congress on computational intelligence, WCCI 2010, pp 487–494
Husseinzadeh Kashan A, Karimi B, Jenabi M (2008) A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes. Comput Oper Res 35:1084–1098
Husseinzadeh Kashan A, Jenabi M, Husseinzadeh Kashan M (2009) A new solution approach for grouping problems based on evolution strategies. In: International conference of soft computing and pattern recognition
Husseinzadeh Kashan A, Rezaee B, Karimiyan S (2013) An efficient approach for unsupervised fuzzy clustering based on grouping evolution strategy. Pattern Recogn 46:1240–1254
Husseinzadeh Kashan A, Akbari AA, Ostadi B (2015) Grouping evolution strategies: an effective approach for grouping problems. Appl Math Model 2015(39):2703–2720
Husseinzadeh Kashan A, Tavakkoli-Moghaddam R, Gen M (2016) A warfare inspired optimization algorithm: the find-fix-finish-exploit-analyze (F3EA) metaheuristic algorithm. In: Tenth international conference on management science and engineering management, ICMSEM 2016, pp 393–408
Iori M, Martello S (2008) Scatter search algorithms for identical parallel machine scheduling problems. In: Metaheuristics for scheduling in industrial and manufacturing applications. Springer, Berlin, pp 41–59
Jing C, Guang-Liang L, Ran L (2011) Discrete harmony search algorithm for identical parallel machine scheduling problem. In: IEEE control conference (CCC), 2011 30th Chinese, pp 5457–5461
Kedia SK (1971) A job scheduling problem with parallel processors. Technical Report. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor
Kowalczyk D, Leus R (2016) An exact algorithm for parallel machine scheduling with conflicts. J Sched 1–18
Kuruvilla A, Paletta G (2015) Minimizing makespan on identical parallel machines. Int J Oper Res Inf Syst (IJORIS) 6(1):19–29
Lee CY, Massey JD (1988) Multiprocessor scheduling: combining LPT and MULTIFIT. Discrete Appl Math 20:233–242
Lee WC, Wu CC, Chen P (2006) A simulated annealing approach to makespan minimization on identical parallel machines. Int J Adv Manuf Technol 31:328–334
Low C, Wu GH (2016) Unrelated parallel-machine scheduling with controllable processing times and eligibility constraints to minimize the makespan. J Ind Prod Eng 33(4):286–293
Mellouli R, Sadfi C, Chu C, Kacem I (2009) Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times. Eur J Oper Res 197(3):1150–1165
Min L, Cheng W (1999) A genetic algorithm for minimizing the makespan in the case of scheduling identical parallel machines. Artif Intell Eng 13(4):399–403
Mokotoff E (2004) An exact algorithm for the identical parallel machine scheduling problem. Eur J Oper Res 152(3):758–769
Pakzad-Moghaddam SH (2016) A Lévy flight embedded particle swarm optimization for multi-objective parallel-machine scheduling with learning and adapting considerations. Comput Ind Eng 91:109–128
Rechenberg I (1964) Cybernetic solution path of an experimental problem. Library Translation 1122, August 1965. Famborough Hants: royal aircraft establishment. English translation of lecture given at the Annual Conference of the WGLR, Berlin, 1964
Rechenberg I (1973) Evolutionsstrategie: optimierung technischer systeme nach den prinzipien der biologischen evolution. Frommann-Holzboog, Stuttgart
Zarandi MF, Kayvanfar V (2014) A bi-objective identical parallel machine scheduling problem with controllable processing times: a just-in-time approach. Int J Adv Manuf Technol 1–19
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kashan, A.H., Keshmiry, M., Dahooie, J.H. et al. A simple yet effective grouping evolutionary strategy (GES) algorithm for scheduling parallel machines. Neural Comput & Applic 30, 1925–1938 (2018). https://doi.org/10.1007/s00521-016-2789-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-016-2789-3