Integrating Machine Learning and Mathematical Optimization for Job Shop
Scheduling
Abstract
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.