<p>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 these 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. </p>

<p>Job-shop scheduling is an important but difficult integer 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 of customized products, problem sizes are growing. Machine learning (ML) is a promising solution methodology. Direct learning solutions, however, is difficult because of the NP-hard nature of the problem. In this paper, ML and the decomposition and coordination approach of Surrogate Lagrangian Relaxation are synergistically integrated. ML is used to learn and predict “good enough” solutions of part subproblems, which are not NP-hard. Nevertheless, the task is still challenging in view of the quite different parts to be scheduled from shift to shift, the complicated tardiness-related objective function, and many part-level constraints. To address these issues, a generic pointer network is developed for all parts after part subproblems are innovatively reformulated to be at a much simplified and streamlined level. The pointer network is also novelly enhanced with a masking mechanism so that predictions satisfy all part-level constraints. Numerical results demonstrate that the enhanced pointer network can learn and predict subproblem solutions well, and that near-optimal solutions of large problems are efficiently obtained. The performance of the method is expected to further improve through continual learning.  </p>

<p>Job-shop scheduling is an important but difficult integer 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 of customized products, problem sizes are growing. Machine learning (ML) is a promising solution methodology. Direct learning solutions, however, is difficult because of the NP-hard nature of the problem. In this paper, ML and the decomposition and coordination approach of Surrogate Lagrangian Relaxation are synergistically integrated. ML is used to learn and predict “good enough” solutions of part subproblems, which are not NP-hard. Nevertheless, the task is still challenging in view of the quite different parts to be scheduled from shift to shift, the complicated tardiness-related objective function, and many part-level constraints. To address these issues, a generic pointer network is developed for all parts after part subproblems are innovatively reformulated to be at a much simplified and streamlined level. The pointer network is also novelly enhanced with a masking mechanism so that predictions satisfy all part-level constraints. Numerical results demonstrate that the enhanced pointer network can learn and predict subproblem solutions well, and that near-optimal solutions of large problems are efficiently obtained. The performance of the method is expected to further improve through continual learning.  </p>

<p>Job-shop scheduling is an important but difficult integer 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 of customized products, problem sizes are growing. Machine learning (ML) is a promising solution methodology. Direct learning solutions, however, is difficult because of the NP-hard nature of the problem. In this paper, ML and the decomposition and coordination approach of Surrogate Lagrangian Relaxation are synergistically integrated. ML is used to learn and predict “good enough” solutions of part subproblems, which are not NP-hard. Nevertheless, the task is still challenging in view of the quite different parts to be scheduled from shift to shift, the complicated tardiness-related objective function, and many part-level constraints. To address these issues, a generic pointer network is developed for all parts after part subproblems are innovatively reformulated to be at a much simplified and streamlined level. The pointer network is also novelly enhanced with a masking mechanism so that predictions satisfy all part-level constraints. Numerical results demonstrate that the enhanced pointer network can learn and predict subproblem solutions well, and that near-optimal solutions of large problems are efficiently obtained. The performance of the method is expected to further improve through continual learning.  </p>