Toward automated algorithm configuration for distributed hybrid flow shop scheduling with multiprocessor tasks

Abstract

Due to the large volume of requests and the need to speed up the provision of services, production companies are migrating from a single service center to distributed centers. To support this migration, it is necessary to make intelligence decisions that benefit from automatic design of search algorithms. Considering these, this paper addresses the distributed hybrid flow shop scheduling problem with multiprocessor tasks (DHFSP-MT) as an extension of the hybrid flow shop scheduling problem with multiprocessor tasks (HFSP-MT) to minimize the maximum completion time among distributed factories. To provide effective decision support, we apply a novel framework called conditional markov chain search (CMCS) to automate the generation of heuristics, which is presented for the first time in the distributed shop scheduling problem to the best of our knowledge. We express the HFSP-MT as a markov decision process (MDP) and solve it through a hybrid Q-learning-local search algorithm. By using the characteristics of the problem under study, we introduce two new concepts, weight and impact, which are used to develop an initial construction algorithm and two local search methods. To balance jobs between factories at runtime, we propose a load balancing method, which transfers selected jobs from certain source factories to destination factories. We compare the proposed CMCS with two state-of-the-art metaheuristic algorithms from the literature using publicly available benchmark instances. The computational results show that the proposed CMCS provides better performance than that of the existing algorithms on solving the considered DHFSP-MT.