MILP modeling and optimization of flexible job shop scheduling problem with preventive maintenance

作     者：Zhao, Lixin Cheng, Weiyao Meng, Leilei Zhang, Chaoyong Ren, Yaping Zhang, Biao Duan, Peng 

作者机构：Liaocheng Univ Sch Comp Sci Liaocheng 252000 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China Jinan Univ Sch Intelligent Syst Sci & Engn Dept Ind Engn Zhuhai 519070 Peoples R China 

出 版 物：《COMPUTERS & INDUSTRIAL ENGINEERING》 (Comput Ind Eng)

年 卷 期：2025年第201卷

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Funds for the National Natural Science Foundation of China [52205529, 62303204] Natural Science Foundation of Shandong Province [ZR2021QE195, ZR2021QF036] Youth Innovation Team Program of Shandong Higher Education Institution [2023KJ206] Guangyue Youth Scholar Innovation Talent Program from Liaocheng University [LCUGYTD2022-03] Foundation of Young Talent of Lifting engineering for Science and Technology in Shandong, China [SDAST2024QTA074] 

主　　题：Flexible job shop scheduling Preventative maintenance Mixed-integer linear programming Collaborative variable neighbourhood search algorithm Q -learning 

摘      要：This study investigated the flexible job shop scheduling problem considering preventive maintenance (FJSP-PM), which can be categorised into two types: FJSP-PM with a fixed maintenance strategy (FJSP-FPM) and FJSP-PM with a periodic maintenance strategy (FJSP-PPM). The objective is to minimize the makespan. To prove the optimality of small-sized instances, for the first time, two mixed-integer linear programming (MILP) models for each problem are established based on different modeling approaches. A Q-learning-based collaborative variable neighbourhood search algorithm (CVNS-Q) is proposed to efficiently obtain approximate optimal solutions for large-sized instances. In the CVNS-Q, eight neighbourhoods are utilized. Two VNS modules are used to guide the evolution of the two individuals, and a Q-learning algorithm guide the selection of neighbourhoods. In addition, a restart strategy is designed to reduce the possibility of sinking into local optima. The effectiveness of the MILP model and CVNS-Q is evaluated using 20 benchmark instances.