A Hybrid Estimation-of-Distribution Algorithm for Scheduling Flexible Job Shop With Limited Buffers Based on Petri Nets

This article focuses on the production scheduling problem in the flexible job shop (FJS) environment with limited buffers. Limited manufacturing resources and buffers may lead to blockage and deadlock phenomenon. In order to establish production scheduling with minimum makespan, the timed Petri net (PN) model of a production process is established. Based on this PN model, a novel Hybrid Estimation-of-Distribution Algorithm (HEDA) is proposed for solving the considered scheduling problem. A candidate solution for the problem is coded as an individual that consists of a route sequence for processing jobs and a permutation with repetition of jobs. A deadlock prevention policy is used to check the feasibility of individuals, such that it can be decoded into a feasible sequence of transitions, i.e., a feasible schedule. By using an effective voting procedure of elite individuals, two probability models in HEDA corresponding to different subsections of individuals are constructed. Based on the probability models, offspring individuals are then produced. As an improvement strategy, simulated-annealing-based local search is designed and incorporated into HEDA to enhance the entire algorithm's search ability. The proposed hybrid HEDA is tested on FJS examples. The results show its feasibility and effectiveness.