Correlation of job-shop scheduling problem features with scheduling efficiency

Abstract

In this paper, we conduct a statistical study of the relationship between Job-Shop Scheduling Problem (JSSP) features and optimal makespan. To this end, a set of 380 mostly novel features, each representing a certain problem characteristic, are manually developed for the JSSP. We then establish the correlation of these features with optimal makespan through statistical analysis measures commonly used in machine learning, such as the Pearson Correlation Coefficient, and as a way to verify that the features capture most of the existing correlation, we further use them to develop machine learning models that attempt to predict the optimal makespan without actually solving a given instance. The prediction is done as classification of instances into coarse lower or higher-than-average classes. The results, which constitute cross-validation and test accuracy measures of around 80% on a set of 15,000 randomly generated problem instances, are reported and discussed. We argue that given the obtained correlation information, a human expert can earn insight into the JSSP structure, and consequently design better instances, design better heuristic or hyper-heuristics, design better benchmark instances, and in general make better decisions and perform better-informed trade-offs in various stages of the scheduling process. To support this idea, we also demonstrate how useful the obtained insight can be through a real-world application.