HGNP: A PCA-based heterogeneous graph neural network for a family distributed flexible job shop

Abstract

The distributed flexible job shop scheduling problem (DFJSP) has gained increasing attention in recent years. Meanwhile, the family setup time constraint exists in many realistic manufacturing systems, e.g., prefabricated components system. In this study, first, a mixed integer programming (MIP) model is formulated for the DFJSP with family setup time. To minimize the makespan, a hybrid heterogeneous graph neural network with a principal component analysis (PCA)-based transform mechanism (HGNP) is proposed. In the proposed algorithm, a novel state representation is designed, which combines the features of operation, machine and factory assignment. Then, a multilayer perceptron (MLP) mechanism is used for the operation embedding, and graph attention networks (GATs) are embedded for the machine and factory embeddings. Next, a PCA-based transform mechanism is developed to further fuse all the three embeddings. To improve the solution performance, a simple enhanced local search method is developed. Three different scale of instances are generated to test the performance of HGNP, including small instances to test the effectiveness of the mathematical model, medium and large instances to test the efficiency, and extended public instances to test the generalization abilities. Experimental results and comparisons with different types of state-of-the-art algorithms show the competitiveness and efficiency of the proposed algorithm, both in performance and generalization capabilities.