A Bi-Population Cooperative Memetic Algorithm for Distributed Hybrid Flow-Shop Scheduling

In the context of globalization and decentralized economies, the distributed manufacturing and scheduling systems have become emerging in large enterprises. This article addresses the distributed hybrid flow-shop scheduling problem (DHFSP) with heterogeneous factories to minimize makespan. Different from single-factory scheduling problem, DHFSP contains several strongly coupled sub-problems, i.e., factory assignment of jobs and the job sequencing in each hybrid flow-shop. In this article, we present a mixed integer linear programming model for the DHFSP and make a first attempt to propose a bi-population cooperative memetic algorithm (BCMA) for solving such a strongly NP-hard problem. The proposed optimization framework comprises collaborative initialization, bi-population cooperation and local intensification. To generate diverse solutions with small makespan, two knowledge-based heuristics are designed for collaborative initialization by utilizing the lower bound of the problem and the historic information of elite solutions during search process. To balance exploration and exploitation, two populations are evolved in a cooperative way. To further enhance the optimization capability, intensification search with multiple problem-specific operators is incorporated. The effect of parameter setting is investigated and extensive computational tests are carried out. The comparative results show that the BCMA is more effective than both the Math solver Gurobi and the existing iterated greedy algorithm, and the effectiveness of each specific design is also verified in solving DHFSP.