Modeling and solving for bi-objective cutting parallel machine scheduling problem
- 26 Downloads
This paper addresses a bi-objective cutting parallel machine scheduling problem aiming to minimize the total makespan and total tardiness. This problem is inspired from a structural metal-cutting plant that combines identical and unrelated parallel machine scheduling problems. To formulate this complicated problem, a new mixed-integer programming (MIP) model is presented in consideration of total makespan and total tardiness. The machine-job-dependent processing times are considered along with the setup times, pickup times, different delivery times, and machine eligibility constraints. Owing to the complex characteristics of the problem, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII) with an embedded variable neighborhood structure strategy (VNSGAIII) is developed. A number of randomly generated datasets are used to test the performance of VNSGAIII in comparison with NSGAII, and NSGAIII on solving the engineering problem addressed herein. The experimental results demonstrate that the suggested VNSGAIII statistically outperforms the compared algorithms, especially in the distribution of Pareto solutions. The ε-constrained method is implemented in the direct MIP model by CPLEX for comparison with the proposed evolutionary algorithms. The proposed algorithm performs efficiently when obtaining the Pareto solutions.
KeywordsParallel machine scheduling problem NSGA III Bi-objective problem Makespan Tardiness
This work is supported by the National Natural Science Foundation of China (Grant No. 51675206); the open fund project of the Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance (Grant No. 2017KJX10) and the new intelligent manufacturing models for rail transit shield machine funded by Ministry of Industry and Information Technology of China. All supports are gratefully acknowledged.
- Asefi, H., Jolai, F., Rabiee, M., & Tayebi Araghi, M. E. (2014). A hybrid NSGA-II and VNS for solving a bi-objective no-wait flexible flowshop scheduling problem. The International Journal of Advanced Manufacturing Technology, 75(5–8), 1017–1033. https://doi.org/10.1007/s00170-014-6177-9.CrossRefGoogle Scholar
- Berrichi, A., Amodeo, L., Yalaoui, F., Châtelet, E., & Mezghiche, M. (2008). Bi-objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem. Journal of Intelligent Manufacturing, 20(4), 389–400. https://doi.org/10.1007/s10845-008-0113-5.CrossRefGoogle Scholar
- Deb, K., & Jain, H. (2014). An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18(4), 577–601. https://doi.org/10.1109/tevc.2013.2281535.CrossRefGoogle Scholar
- Jain, H., & Deb, K. (2014). An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation, 18(4), 602–622. https://doi.org/10.1109/tevc.2013.2281534.CrossRefGoogle Scholar
- Liao, T. W., & Su, P. (2017). Parallel machine scheduling in fuzzy environment with hybrid ant colony optimization including a comparison of fuzzy number ranking methods in consideration of spread of fuzziness. Applied Soft Computing, 56, 65–81. https://doi.org/10.1016/j.asoc.2017.03.004.CrossRefGoogle Scholar
- Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11), 4.Google Scholar
- Mokotoff, E. (2001). Parallel-machine scheduling problems: A survey. Asia-Pacific Journal of Operational Research, 18, 50.Google Scholar
- Rajkanth, R., Rajendran, C., & Ziegler, H. (2016). Heuristics to minimize the completion time variance of jobs on a single machine and on identical parallel machines. The International Journal of Advanced Manufacturing Technology, 88(5–8), 1923–1936. https://doi.org/10.1007/s00170-016-8879-7.Google Scholar
- Sadati, A., Tavakkoli-Moghaddam, R., Naderi, B., & Mohammadi, M. (2017). Solving a new multi-objective unrelated parallel machines scheduling problem by hybrid teaching-learning based optimization. International Journal of Engineering, 30(2), 10. https://doi.org/10.5829/idosi.ije.2017.30(02b).Google Scholar
- Shahvari, O., & Logendran, R. (2017). An enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes. Computers & Operations Research, 77, 154–176. https://doi.org/10.1016/j.cor.2016.07.021.CrossRefGoogle Scholar
- Tseng, C.-T., Lee, C.-H., Chiu, Y.-S. P., & Lu, W.-T. (2016). A discrete electromagnetism-like mechanism for parallel machine scheduling under a grade of service provision. International Journal of Production Research, 55(11), 3149–3163. https://doi.org/10.1080/00207543.2016.1265683.CrossRefGoogle Scholar