A Shuffled Frog Leaping Algorithm with Q-Learning for Distributed Hybrid Flow Shop Scheduling Problem with Missing Operations

Distributed manufacturing introduces new challenges to traditional production shop scheduling, and the combination of machine learning and metaheuristic algorithms offers new approaches to solve these problems. To address the distributed hybrid flow shop scheduling problem with missing operations (MDHFSP), a shuffled frog leaping algorithm with Q-learning (QSFLA) is proposed to minimize the maximum completion time. A dual-string encoding method is proposed to represent factory assignment and job sequencing, with heuristic methods utilized during decoding to determine machine assignments. The state set is constructed based on changes in the minimum and average objective values of solutions in the population, while the action set is built from different optimized solutions and learned solutions during the memeplex search process. Symmetry-driven Q-learning is employed to dynamically adjust the optimization objects based on the state of the population. Testing on 140 benchmarks and a real-life example shows that symmetry-driven Q-learning plays a positive role within QSFLA, and QSFLA effectively solves the MDHFSP.