Integrated scheduling of multi-constraint open shop and vehicle routing: Mathematical model and learning-driven brain storm optimization algorithm

Abstract

Recent years have witnessed a surge of interest in integrated production and distribution scheduling problems which can achieve an overall optimization of the production and distribution activities. However, integrated scheduling of open shop and distribution receives rare attention in existing studies. This work proposes an integrated scheduling problem of multi-constraint open shop and vehicle routing to minimize maximum completion time, where group and transportation operations are considered together in the production process. All jobs are divided into multiple groups, and then handled in an open shop with multiple machines. Subsequently, the jobs are delivered to their corresponding customers. First, a mixed integer programming model is formulated to define the problem. Second, a Q-learning-driven brain storm optimization algorithm is developed to address the formulated model. A Q-learning method is employed to choose search strategies for generating new individuals rather than using fixed probability parameters straightforwardly as basic brain storm optimizers. In addition, the solution encoding, heuristic decoding, population initialization, clustering, new individual generation and selection methods are specially devised in consideration of problem-specific knowledge. At last, the developed model and algorithm are verified by addressing a set of benchmark instances, and comparison experiments are conducted with an exact solver CPLEX and four meta-heuristics from existing literature. The results validate the competitive advantages of the formulated model and algorithm in solving the considered problems. 2024