An improved method of job shop scheduling using machine learning and mathematical optimization

Abstract

This research is concerned with finding the optimal solution of a job shop scheduling problem (JSSP) in as short time as possible. A JSSP can be formulated as a 0-1 mixed integer programming (0-1 MIP), and it is expected that the optimal schedule can be obtained in a shorter time by predicting a good solution based on data of scheduling performed previously and using the solution as the initial solution for the optimization algorithm. In this concept, it is an important point to predict a solution which satisfy constraints of the 0-1 MIP. This paper provides an improved method based on this concept where the prediction is carried out so that the constraints are always satisfied. Numerical experiments showed that solution time of the proposed method is shorter than that of the previous method, which does not assure the constraints are satisfied, and learning time reduces about half. In addition, it turned out that there is a reason of the shorter solution time other than that the predicted solution always satisfies the constraints. One possible reason is that the number of circular sequences tends to be smaller than the previous method. Further analysis and additional evaluations from this point of view will be performed in a future work.