Memetic discrete differential evolution with domain knowledge for blocking scheduling distributed flow shop with lot-streaming constraints

Abstract

This article addresses the blocking distributed flow shop scheduling problem with lot-streaming (BDFSPL) with the objective of minimizing the maximum completion time, or makespan. In many realistic conditions, a job is divided into multiple continuous processed sublots. This pattern achieves operation overlap on consecutive machines and decreases the completion time of the whole job. Moreover, there are no buffers between machines, potentially causing finished sublots to be blocked on the current machine until the downstream machine is available. This is the first study to consider distributed production, blocking constraints, and lot-streaming together. To address this problem, we formulate a mathematical model for BDFSPL and propose a memetic discrete differential evolution (MDDE) algorithm. First, the MDDE algorithm partitions the entire population into three subpopulations based on solution quality, and each subpopulation evolves independently through adaptive scale and parameter adjustment. Second, four discrete mathematical operators are proposed to generate new individuals, and based on these operators, discrete mutation, crossover, and selection operations of MDDE are designed. Additionally, a crucial path-based local search strategy, informed by the domain knowledge of the best individual, is embedded into MDDE to enhance the exploitation capacity. To validate MDDE’s effectiveness, comprehensive experiments with several related algorithms on extensive testing instances are carried out, and the parameters of the MDDE algorithm are calibrated by employing a design of experiments. The comparison results demonstrate the effectiveness and efficiency of the proposed MDDE algorithm for the BDFSPL.