A hybrid estimation of distribution algorithm for distributed flexible job shop scheduling with crane transportations

Abstract

Distributed flexible job shop scheduling has attracted research interest due to the development of global manufacturing. However, constraints including crane transportation and energy consumption should be considered with the realistic requirements. To address this issue, first, we modeled the problem by utilizing an integer programming method, wherein the makespan and energy consumptions during the machine process and crane transportation are optimized simultaneously. Afterward, a hybrid algorithm consisting of estimation of distribution algorithm (EDA) and variable neighborhood search (VNS) was proposed to solve the problem, where an identification rule of four crane conditions was designed to make fitness calculation feasible. In EDA component, the parameters in probability matrices are set to be self-adaptive for stable convergence to obtain better output. Moreover, a probability mechanism was applied to control the activity of the EDA component. In VNS component, five problem-specific neighborhood structures including global and local strategies are employed to enhance exploitation ability. The simulation tests results confirmed that the proposed hybrid EDA-VNS algorithm can solve the considered problem with high efficiency compared with other competitive algorithms, and the proposed improving strategies are verified to have significance in better performance.