Improvement of job shop scheduling method based on mathematical optimization and machine learning

Abstract

This research is concerned with finding the optimal solution of a job shop scheduling problem (JSSP) in a shorter time. As a result of recent trends such as Industry 4.0, machine learning has received a lot of attention, and job shop scheduling methods using machine learning techniques have been developed. We have focused on hybridization of machine learning and mathematical optimization. A JSSP can be formulated as a 0-1 mixed integer programming, and it is expected that the optimal solution can be obtained in a shorter time by providing a good initial solution for the optimization algorithm by means of a learner constructed with data of scheduling performed previously. In our method based on this idea, the processing times of all operations are used as input features to predict a good value of each binary variable which represents the precedence relationship between two operations processed on the same machine. However, the information about the operations which are not related to the intended two operations may work as noise in learning and prediction. In this paper, two limitation methods of input features are proposed. In one of the methods, the processing times of only the operations processed on the same machine that the intended operations are processed are input to the learner. In the other methods, the processing times of those operations and their pre/post operations are input. Numerical experiments showed that these methods are effective at least from the point of view of efficient construction of a learner, because the number of nodes in the input and hidden layers can be reduced. From the aspect of better learning and prediction, both of the methods worked well, that is, they could find the optimal solution in a shorter time than the previous method in the cases where the previous method could not achieve good prediction and took a relatively long solution time. However, in the cases where the previous method could solve the problem in a relatively short time, the limitation methods could not predict a good initial solution and took a relatively long solution time. Between the results of the two limitation methods, there were no difference. These results imply that the processing times of the pre/post operations do not strongly affect performance on learning and prediction and that it is important to analyze what makes a difference between the two cases and utilize the proposed methods in the former case.