Ensemble evolutionary algorithms equipped with Q-learning strategy for solving distributed heterogeneous permutation flowshop scheduling problems considering sequence-dependent setup time

A distributed heterogeneous permutation flowshop scheduling problem with sequence-dependent setup times (DHPFSP-SDST) is addressed, which well reflects real-world scenarios in heterogeneous factories. The objective is to minimise the maximum completion time (makespan) by assigning jobs to factories, and sequencing them within each factory. First, a mathematical model to describe the DHPFSP-SDST is established. Second, four meta-heuristics, including genetic algorithms, differential evolution, artificial bee colony, and iterated greedy (IG) algorithms are improved to optimally solve the concerned problem compared with the other existing optimisers in the literature. The Nawaz-Enscore-Ham (NEH) heuristic is employed for generating an initial solution. Then, five local search operators are designed based on the problem characteristics to enhance algorithms' performance. To choose the local search operators appropriately during iterations, Q-learning-based strategy is adopted. Finally, extensive numerical experiments are conducted on 72 instances using 5 optimisers. The obtained optimisation results and comparisons prove that the improved IG algorithm along with Q-learning based local search selection strategy shows better performance with respect to its peers. The proposed algorithm exhibits higher efficiency for scheduling the concerned problems.