Solving Distributed Hybrid Flowshop Scheduling Problems by a Hybrid Brain Storm Optimization Algorithm

With the trend of manufacturing globalization, distributed production has attracted wide attention from the industry and academia. Nevertheless, there has been little research on the distributed hybrid flowshop scheduling (DHFS) problem. To make up for the gap, this study aims to solve the DHFS problem, in which multiple factories with hybrid flowshop scheduling (HFS) problems are considered. This problem consists of two subproblems: 1) how to choose a factory for each job and 2) how to schedule all jobs within the assigned factories. To solve the DHFS problem, a mathematical model is formulated. Then, inspired by successful applications of brain storm optimization (BSO) algorithm in different fields, we try to solve the DHFS with a hybrid BSO (HBSO). In the proposed algorithm, firstly, a new approach to calculate the distance in the procedure of clustering is embedded. Then, a novel constructive heuristic based on the Nawaz-Enscore-Ham (NEH) method, called distributed NEH, is proposed. Moreover, an improved crossover operator based on the partial-mapped crossover (PMX) is designed for the distributed scheduling problem. Finally, the 20 large-scale instances based on the realistic production data are randomly generated to test the performance of the proposed algorithm. The experimental results verify that the proposed algorithm is efficient and effective for solving the considered DHFS problems in comparison with the other recently published efficient algorithms.