An improved migrating birds optimization for an integrated lot-streaming flow shop scheduling problem

Lot-streaming is an effective technology to enhance the production efficiency by splitting a job or a lot into several sublots. It is commonly assumed that lot-splitting (i.e. job-splitting) is specified in advance and fixed during the optimization procedure in recent studies on lot-streaming flow shop scheduling problems. In many real-world production processes, however, it is not easy to determine the optimal lot-splitting beforehand. Therefore, in this paper we consider an integrated lot-streaming flow shop scheduling problem in which lot-splitting and job scheduling are needed to be optimized simultaneously. We provide a mathematical model for the problem and present an improved migrating birds optimization (IMMBO) to minimize the maximum completion time or makespan. In the IMMBO algorithm, a harmony search based scheme is designed to construct neighborhood of solutions, which makes good use of optimization information from the population and can tune the search scope adaptively. Moreover, a leaping mechanism is introduced to avoid being trapped in the local optimum. Extensive numerical simulations are conducted and comparisons with other state-of-the-art algorithms verify the effectiveness of the proposed IMMBO algorithm.