Abstract
Distributed welding flow shop scheduling problem is an extension of distributed permutation flow shop scheduling problem, which possesses a set of identical factories of welding flow shop. On account of several machines can process one job simultaneously in welding shop, increasing the amount of machines can short the processing time of operation while waste more energy consumption at the same time. Thus, energy-efficient is of great significance to take total energy consumption into account in scheduling. A multi-objective mixed integer programming model for energy-efficient scheduling of distributed welding flow shop is presented based on three sub-problems with allocating jobs among factories, scheduling the jobs in each factory and determining the amount of machines upon each job. A multi-objective whale swarm algorithm is proposed to optimize the total energy consumption and makespan simultaneously. In the proposed algorithm, a new initialization method is designed to improve the quality of the initial solution. And various update operators, as well as local search, are designed according to the feature of the problem. To conduct the experiment, diversified indicators are applied to evaluate the proposed algorithm and other MOEAs performance. And the experiment results demonstrate the effectiveness of the proposed method. The proposed algorithm is applied in the real-life case with great performance compared with other MOEAs.
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References
Cai, X., Sun, H., & Fan, Z. (2018). A diversity indicator based on reference vectors for many-objective optimization. Information Sciences, 430–431, 467–486.
Chan, F. T. S., Prakash, A., Ma, H. L., & Wong, C. S. (2013). A hybrid Tabu sample-sort simulated annealing approach for solving distributed scheduling problem. International Journal of Production Research, 51(9), 2602–2619.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
Ding, J.-Y., Song, S., & Wu, C. (2016). Carbon-efficient scheduling of flow shops by multi-objective optimization. European Journal of Operational Research, 248(3), 758–771.
Fernandez-Viagas, V., & Framinan, J. (2014). A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem. International Journal of Production Research, 53, 1111–1123.
Fernandez-Viagas, V., Perez-Gonzalez, P., & Framinan, J. M. (2018). The distributed permutation flow shop to minimise the total flowtime. Computers and Industrial Engineering, 118, 464–477.
Fu, Y., Tian, G., Fathollahi-Fard, A. M., Ahmadi, A., & Zhang, C. (2019). Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. Journal of Cleaner Production, 226, 515–525.
Gao, H., Kwong, S., Fan, B., & Wang, R. (2014). A hybrid particle-swarm tabu search algorithm for solving job shop scheduling problems. IEEE Transactions on Industrial Informatics, 10(4), 2044–2054.
Gao, J., & Chen, R. (2011). A hybrid genetic algorithm for the distributed permutation flowshop scheduling problem. International Journal of Computational Intelligence Systems, 4(4), 497–508.
Gao, J., Chen, R., & Deng, W. (2013). An efficient tabu search algorithm for the distributed permutation flowshop scheduling problem. International Journal of Production Research, 51(3), 641–651.
Garey, M. R., Johnson, D. S., & Sethi, R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of operations research, 2(1), 117–129.
Goldberg, D. E. & Lingle, R. (1985). Alleles, loci, and the traveling salesman problem. In: Proceedings of an international conference on genetic algorithms and their applications (Vol. 154, pp. 154–159): Lawrence Erlbaum, Hillsdale, NJ.
Grobler, J., Engelbrecht, A. P., Kok, S., & Yadavalli, S. (2010). Metaheuristics for the multi-objective FJSP with sequence-dependent set-up times, auxiliary resources and machine down time. Annals of Operations Research, 180(1), 165–196.
Hansen, P., Mladenovic, N., & Perez, J. A. M. (2010). Variable neighbourhood search: methods and applications. Annals of Operations Research, 175(1), 367–407.
Kahn, K. B., Castellion, G., & Griffin, A. (2005). The PDMA handbook of new product development. Hoboken, NJ: Wiley.
Li, M., & Yao, X. (2019). Quality evaluation of solution sets in multiobjective optimisation: a survey. ACM Computing Surveys, 52(2), 26.
Li, X., Gao, L., Pan, Q., Wan, L., & Chao, K. (2019a). An effective hybrid genetic algorithm and variable neighborhood search for integrated process planning and scheduling in a packaging machine workshop. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(10), 1933–1944.
Li, X., Lu, C., Gao, L., Xiao, S., & Wen, L. (2018). An effective multiobjective algorithm for energy-efficient scheduling in a real-life welding shop. IEEE Transactions on Industrial Informatics, 14(12), 5400–5409.
Li, X., Xiao, S., Wang, C., & Yi, J. (2019b). Mathematical modeling and a discrete artificial bee colony algorithm for the welding shop scheduling problem. Memetic Computing, 11, 1–19.
Lin, S., Ying, K., & Huang, C. (2013). Minimising makespan in distributed permutation flowshops using a modified iterated greedy algorithm. International Journal of Production Research, 51(16), 5029–5038.
Lu, C., Gao, L., Li, X., Pan, Q., & Wang, Q. (2017a). Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm. Journal of Cleaner Production, 144, 228–238.
Lu, C., Gao, L., Li, X., & Xiao, S. (2017b). A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry. Engineering Applications of Artificial Intelligence, 57, 61–79.
Lu, C., Gao, L., Li, X., Zheng, J., & Gong, W. (2018). A multi-objective approach to welding shop scheduling for makespan, noise pollution and energy consumption. Journal of Cleaner Production, 196, 773–787.
Lu, C., Xiao, S., Li, X., & Gao, L. (2016). An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production. Advances in Engineering Software, 99, 161–176.
Marichelvam, M. K., & Prabaharan, T. (2015). Solving realistic industrial scheduling problems using a multi-objective improved hybrid particle swarm optimisation algorithm. International Journal of Operational Research, 23(1), 94–129.
Naderi, B., & Ruiz, R. (2010). The distributed permutation flowshop scheduling problem. Computers and Operations Research, 37(4), 754–768.
Naderi, B., & Ruiz, R. (2014). A scatter search algorithm for the distributed permutation flowshop scheduling problem. European Journal of Operational Research, 239(2), 323–334.
Nanda, S. J., & Panda, G. (2014). A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm and Evolutionary Computation, 16, 1–18.
Pan, Q., Gao, L., Wang, L., Liang, J., & Li, X. (2019). Effective heuristics and metaheuristics to minimize total flowtime for the distributed permutation flowshop problem. Expert Systems with Applications, 124, 309–324.
Pei, J., Cheng, B. Y., Liu, X. B., Pardalos, P. M., & Kong, M. (2019). Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Annals of Operations Research, 272(1–2), 217–241.
Peng, K., Pan, Q.-K., Gao, L., Li, X., Das, S., & Zhang, B. (2019). A multi-start variable neighbourhood descent algorithm for hybrid flowshop rescheduling. Swarm and Evolutionary Computation, 45, 92–112.
Qingfu Zhang, H. L. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731.
Ruiz, R., Pan, Q.-K. & Naderi, B. (2018). Iterated Greedy methods for the distributed permutation flowshop scheduling problem. Omega 18: 213-222.
Shao, W., Pi, D., & Shao, Z. (2017). Optimization of makespan for the distributed no-wait flow shop scheduling problem with iterated greedy algorithms. Knowledge-Based Systems, 137, 163–181.
Shrivastava, A., Krones, M., & Pfefferkorn, F. E. (2015). Comparison of energy consumption and environmental impact of friction stir welding and gas metal arc welding for aluminum. CIRP Journal of Manufacturing Science and Technology, 9, 159–168.
Si, L., Pan, Y., & Yang, Q. (2010). The current situation and development of arc welding energy. Electric Welder, 40(6), 108–132.
Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64(2), 425–434.
Wang, G., Gao, L., Li, X., Li, P., & Tasgetiren, M. F. (2020). Energy-efficient distributed permutation flow shop scheduling problem using a multi-objective whale swarm algorithm. Swarm and Evolutionary Computation, 57, 100716.
Wang, G., Li, X., Gao, L., & Li, P. (2019). A multi-objective whale swarm algorithm for energy-efficient distributed permutation flow shop scheduling problem with sequence dependent setup times. IFAC-PapersOnLine, 52(13), 235–240.
Wang, S., Wang, L., Liu, M., & Xu, Y. (2013). An effective estimation of distribution algorithm for solving the distributed permutation flow-shop scheduling problem. International Journal of Production Economics, 145(1), 387–396.
Zeng, B., Li, X., Gao, L., Zhang, Y., & Dong, H. (2019). Whale swarm algorithm with the mechanism of identifying and escaping from extreme points for multimodal function optimization. Neural Computing and Applications, 32, 1–21.
Zhang, G., Xing, K., & Cao, F. (2018). Discrete differential evolution algorithm for distributed blocking flowshop scheduling with makespan criterion. Engineering Applications of Artificial Intelligence, 76, 96–107.
Zitzler, E., & Thiele, L. (1999). Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3(4), 257–271.
Zitzler E. M. L., & Lothar, T. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-report, 103.
Acknowledgments
This work was supported by National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 51825502), National Natural Science Foundation of China (Grant No. 51775216), Natural Science Foundation of Hubei Province (Grant No. 2018CFA078) and Program for HUST Academic Frontier Youth Team (Grant No. 2017QYTD04).
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Wang, G., Li, X., Gao, L. et al. An effective multi-objective whale swarm algorithm for energy-efficient scheduling of distributed welding flow shop. Ann Oper Res 310, 223–255 (2022). https://doi.org/10.1007/s10479-021-03952-1
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DOI: https://doi.org/10.1007/s10479-021-03952-1