Abstract
In this study, a distributed flow shop scheduling problem with batch delivery constraints is investigated. The objective is to minimize the makespan and energy consumptions simultaneously. To this end, a hybrid algorithm combining the wale optimization algorithm (WOA) with local search heuristics is developed. In the proposed algorithm, each solution is represented by three vectors, namely a job scheduling sequence vector, batch assignment vector, and a factory assignment vector. Then, an efficient neighborhood structure is applied in the proposed algorithm to enhance search abilities. Furthermore, the simulated annealing algorithm and clustering method are embedded to improve the global search abilities of the algorithm. Finally, 30 instances are generated based on realistic application to test the performance of the algorithm. After detailed comparisons with three efficient algorithms, i.e., ABC-Y, ICA-K, and IWOANS, the superiority of the proposed algorithm is verified.












Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abdel-Basset M, Manogaran G, El-Shahat D et al (2018) A hybrid whale optimization algorithm based on local search strategy for the permutation flow shop scheduling problem. Futur Gener Comput Syst 85:129–145
Agnetis A, Aloulou MA, Fu LL (2016) Production and interplant batch delivery scheduling: dominance and cooperation. Int J Prod Econ 182:38–49
Akbalik A, Rapine C (2018) Lot sizing problem with multi-mode replenishment and batch delivery. Omega 81:123–133
Ark OA (2020) Population-based Tabu search with evolutionary strategies for permutation flow shop scheduling problems under effects of position-dependent learning and linear deterioration. Soft Comput 25:1501–1518
Bargaoui H, Driss OB, Ghdira K (2017) A novel chemical reaction optimization for the distributed permutation flowshop scheduling problem with makespan criterion. Comput Ind Eng 111:239–250
Basir SA, Mazdeh MM, Namakshenas M (2018a) Bi-level genetic algorithms for a two-stage assembly flow-shop scheduling problem with batch delivery system. Comput Ind Eng 126:217–231
Basir SA, Mazdeh MM, Namakshenas M (2018b) Bi-level genetic algorithms for a two-stage assembly flow-shop scheduling problem with batch delivery system. Comput Ind Eng 126:217–231
Chen TL, Cheng CY, Chou YH (2018) Multi-objective genetic algorithm for energy-efficient hybrid flow shop scheduling with lot streaming. Ann Oper Res 290:1–24
Deng J, Wang L (2017) A competitive memetic algorithm for multi-objective distributed permutation flow shop scheduling problem. Swarm Evol Comput 32:121–131
Fu M, Zhonghua H, Zhijun G et al (2017) Whale optimization algorithm for flexible flow shop scheduling with setup times. In: 2017 9th international conference on modelling, identification and control (ICMIC). IEEE, pp 157–162
Gao J, Chen R, Deng W (2013) An efficient tabu search algorithm for the distributed permutation flowshop scheduling problem. Int J Prod Res 51(3):641–651
Gonzalez-Neira EM, Ferone D, Hatami S et al (2017) A biased-randomized simheuristic for the distributed assembly permutation flowshop problem with stochastic processing times. Simul Model Pract Theory 79:23–36
Hasanien HM (2018) Performance improvement of photovoltaic power systems using an optimal control strategy based on whale optimization algorithm. Electric Power Syst Res 157:168–176
Hatami S, Ruiz R, Andrs-Romano C (2015) Heuristics and metaheuristics for the distributed assembly permutation flowshop scheduling problem with sequence dependent setup times. Int J Prod Econ 169:76–88
Jiang T, Zhang C, Zhu H et al (2018) Energy-efficient scheduling for a job shop using an improved whale optimization algorithm. Mathematics 6(11):220
Jiang T, Zhang C, Sun QM (2019) Green job shop scheduling problem with discrete whale optimization algorithm. IEEE Access 7:43153–43166
Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42:21–57
Kazemi H, Mazdeh MM, Rostami M (2017) The two stage assembly flow-shop scheduling problem with batching and delivery. Eng Appl Artif Intell 63:98–107
Kong L, Li H, Luo H et al (2018) Sustainable performance of just-in-time (JIT) management in time-dependent batch delivery scheduling of precast construction. J Clean Prod 193:684–701
Li J, Liu Z, Li C, Zheng Z (2020) Improved artificial immune system algorithm for type-2 fuzzy flexible job shop scheduling problem. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.3016225
Li J, Du Y, Gao K, Duan P, Gong D, Pan Q, Suganthan P (2021) A hybrid iterated greedy algorithm for a crane transportation flexible job shop problem. IEEE Trans Autom Sci Eng. https://doi.org/10.1109/TASE.2021.3062979
Liao CJ, Tjandradjaja E, Chung TP (2012) An approach using particle swarm optimization and bottleneck heuristic to solve hybrid flow shop scheduling problem. Appl Soft Comput 12(6):1755–1764
Luan F, Cai Z, Wu S et al (2019) Improved whale algorithm for solving the flexible job shop scheduling problem. Mathematics 7(5):384
Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312
Marandi F, Ghomi SMTF (2019) Network configuration multi-factory scheduling with batch delivery: a learning-oriented simulated annealing approach. Comput Ind Eng 132:293–310
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Nasiri J, Khiyabani FM (2018) A whale optimization algorithm (WOA) approach for clustering. Cogent Math Stat 5(1):1483565
Noroozi A, Mazdeh MM, Heydari M et al (2018) Coordinating order acceptance and integrated production-distribution scheduling with batch delivery considering third party logistics distribution. J Manuf Syst 46:29–45
Peng K, Pan QK, Gao L et al (2018) An improved artificial bee colony algorithm for realworld hybrid flowshop rescheduling in steelmaking-refining-continuous casting process. Comput Ind Eng 122:235–250
Prakash DB, Lakshminarayana C (2017) Optimal siting of capacitors in radial distribution network using whale optimization algorithm. Alex Eng J 56(4):499–509
Prakash DB, Lakshminarayana C (2018) Multiple DG placements in radial distributionsystem for multi objectives using whale optimization algorithm. Alex Eng J 57(4):2797–2806
Qi X, Yuan J (2017) A further study on two-agent scheduling on an unbounded serial-batch machine with batch delivery cost. Comput Ind Eng 111:458–462
Rifai AP, Nguyen HT, Dawal SZM (2016) Multi-objective adaptive large neighborhood search for distributed reentrant permutation flow shop scheduling. Appl Soft Comput 40:42–57
Seidgar H, Fazlollahtabar H, Zandieh M et al (2019) Scheduling two-stage assembly flow shop with random machines breakdowns: integrated new self-adapted differential evolutionary and simulation approach. Soft Comput 24:1–25
Shao W, Pi D, Shao Z (2019) A pareto-based estimation of distribution algorithm for solving multiobjective distributed no-wait flow-shop scheduling problem with sequence dependent setup time. IEEE Trans Autom Sci Eng 16:1344–1360
Shaya S, Komakib GM, Vahid K (2018) Multi objective two-stage assembly flow shop with release time. Comput Ind Eng 124:276–292
Shen L, Gupta JND, Buscher U (2014) Flow shop batching and scheduling with s uencedependent setup times. J Sched 17(4):353–370
Sun Y, Wang X, Chen Y et al (2018) A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst Appl 114:563–577
Wang K, Luo H, Liu F et al (2017) Permutation flow shop scheduling with batch delivery to multiple customers in supply chains. IEEE Trans Syst Man Cybern Syst 48(10):1826–1837
Wang S, Wu R, Chu F et al (2019) Variable neighborhood search-based methods for integrated hybrid flow shop scheduling with distribution. Soft Comput 24:1–20
Yin Y, Wang Y, Cheng TCE et al (2016) Two-agent single-machine scheduling to minimize the batch delivery cost. Comput Ind Eng 92:16–30
Ying KC, Lin SW, Cheng CY et al (2017) Iterated reference greedy algorithm for solving distributed no-idle permutation flowshop scheduling problems. Comput Ind Eng 110:413–423
Yurtkuran A, Yagmahan B, Emel E (2018) A novel artificial bee colony algorithm for the workforce scheduling and balancing problem in sub-assembly lines with limited buffers. Appl Soft Comput 73:767–782
Zhang G, Xing K (2018) Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment. Comput Ind Eng 125:423–433
Zhang G, Xing K, Cao F (2018) Discrete differential evolution algorithm for distributed blocking flowshop scheduling with makespan criterion. Eng Appl Artif Intell 76:96–107
Acknowledgements
This research is partially supported by major basic research projects in Shandong (ZR2018ZB0419), and a Grant of Key Laboratory of Intelligent Optimization and Control with Big Data.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Human and animal rights
This article does not contain any studies with human participants or animals performed by any of the authors.
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
Li, Q., Li, J., Zhang, X. et al. A wale optimization algorithm for distributed flow shop with batch delivery. Soft Comput 25, 13181–13194 (2021). https://doi.org/10.1007/s00500-021-06099-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-021-06099-0