Matrix and Learning-Assisted Distributed Dual-Space Memetic Algorithm for Customized Distributed Blocking Flowshop Scheduling Problem

Compared to existing distributed flowshop scheduling problems (DFSPs), this article addresses a more realistic DFSP, which further integrates intermachine blocking constraints and two customized processing stages of assembly and differentiation. The manufacturing process includes job fabrication in distributed blocking flowshops, job-to-product assembly on an assembling machine, and product fine-processing on differentiation machines. A novel evolutionary framework is proposed, including continuous space exploration, discrete space exploitation, and dual-space knowledge migration. This framework has advanced features of distribution, memetic evolution, and dual-space coevolution, and can serve as a unified model to construct algorithms for different optimization problems. Based on this evolutionary framework, a matrix and learning assisted distributed dual-space memetic algorithm (DDMA) is proposed to address the studied problem. In DDMA, exploratory population is represented as a real-valued matrix, where individuals are defined as different identities that will dynamically adjust with evolution. In accordance with identity differences, exploratory population is heterogeneously evolved in the continuous search space by a matrix-assisted evolutionary optimizer. The exploitative population consists of elite individuals, which are represented as discrete permutations. It is evolved in parallel with exploratory population and in the discrete search space by a learning-assisted evolutionary optimizer, including a reinforcement learning-based multineighborhood local search and a statistical learning-based enhanced local search. To communicate the superior evolutionary information obtained by exploration and exploitation, an adaptive knowledge migration across continuous and discrete search spaces is proposed based on the impact of migration on the population diversity. The computational results demonstrate the superiority of DDMA over state-of-the-art algorithms.