Integrating Machine Learning and Mathematical Optimization for Job Shop Scheduling

Job-shop scheduling is an important but difficult combinatorial optimization problem for low-volume and high-variety manufacturing, with solutions required to be obtained quickly at the beginning of each shift. In view of the increasing demand for customized products, problem sizes are growing. A promising direction is to take advantage of Machine Learning (ML). Direct learning to predict solutions for job-shop scheduling, however, suffers from major difficulties when problem scales are large. In this paper, a Deep Neural Network (DNN) is synergistically integrated within the decomposition and coordination framework of Surrogate Lagrangian Relaxation (SLR) to predict good-enough solutions for subproblems. Since a subproblem is associated with a single part, learning difficulties caused by large scales are overcome. Nevertheless, the learning still presents challenges. Because of the high-variety nature of parts, the DNN is desired to be able to generalize to solve all possible parts. To this end, our idea is to establish "surrogate" part subproblems that are easier to learn, develop a DNN based on Pointer Network to learn to predict their solutions, and calculate the solutions of the original part subproblems based on the predictions. Moreover, a masking mechanism is developed such that all the predictions are feasible. Numerical results demonstrate that good-enough subproblem solutions are predicted in many iterations, and high-quality solutions of the overall problem are obtained in a computationally efficient manner. The performance of the method is further improved through continuous learning. Note to Practitioners-Scheduling is important for the planning and operation of job shops, and high-quality schedules need to be obtained quickly at the beginning of each shift. To take advantage of ML, in this paper, a DNN is integrated within our recent decomposition and coordination approach to learn to predict "good-enough" solutions to part subproblems. To be able to predict solutions for parts of various characteristics", surrogate" part subproblems that are easier to learn are established, and a generic "pointer network" is developed to learn to predict their solutions. To satisfy the constraints of the surrogate part subproblems, the pointer network is enhanced with a novel "masking mechanism" such that all the predictions are feasible. The solutions to the original part subproblems are calculated based on the predictions. Testing results demonstrate that subproblem solutions are efficiently obtained based on predictions, and the high-quality solutions of the overall problem are thus efficiently obtained. Through continuous learning, the performance of the method is further improved. Python codes and datasets are submitted together with the paper.