This study focuses on the flexible job shop scheduling problem with sequence-dependent setup times (FJSP-SDST), and the goal is minimizing the makespan. To solve FJSP-SDST, first, we develop a constraint programming (CP) model to obtain optimal solutions. Due to the NP-hardness of FJSP-SDST, a CP assisted meta-heuristic algorithm (C-VNS-CP) is designed to make use of the advantages of both CP model and cooperative variable neighborhood search (C-VNS). The C-VNS-CP algorithm consists of two stages. The first stage involves C-VNS, for which eight neighborhood structures are defined. In the second stage, CP is used to further optimize the good solution obtained from C-VNS. In order to prove the efficiency of the C-VNS algorithm, CP model, and C-VNS-CP algorithm, experiments of 20 instances are conducted.

With a decentral and global economy, distributed scheduling problems are getting a lot of attention. This paper addresses a distributed flexible job shop scheduling problem (DFJSP) with minimizing makespan, in which three subproblems, namely operations sequencing, factory selection and machine selection must be determined. To solve the DFJSP, a novel mixed-integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard characteristic of DFJSP, a hybrid algorithm (GA-VNS-CP) of genetic algorithm (GA), variable neighborhood search (VNS) and constraint programming (CP). Specifically, the GA-VNS-CP is divided into two stages. The first stage uses the hybrid meta-heuristic algorithms of GA and VNS (GA-VNS), and the VNS is designed to improve the local search ability of GA. In GA-VNS, the encoding only considers the factory selection and the operations sequencing problems, and the machine selection problem is determined by the decoding rule. Because the solution space may be limited by the decoding rule, the second stage uses the CP to extend the solution and further improve the solution. Numerical experiments based on benchmark instances are conducted to evaluate the effectiveness of the MILP model, VNS, CP and GA-VNS-CP. The experimental results show effectiveness of the MILP model, VNS and CP. Moreover, the GA-VNS-CP algorithm has better performance than traditional algorithms and improves 6 current best solutions for benchmark instances

This article discusses the ecological vehicle routing problem with a stop at a refueling station titled Green-Vehicle Routing Problem. In this problem, the refueling stations and the limit of fuel tank capacity are considered for the construction of a tour. We propose a variable neighborhood search to solve the problem. We tested and compared the performance of our algorithm intensively on datasets existing in the literature.