Heuristic control of a constraint-based algorithm for the preemptive job-shop scheduling problem

In the recent years, constraint programming has been applied to a wide variety of academic and industrial non-preemptive scheduling problems, i.e., problems in which activities cannot be interrupted. In comparison, preemptive scheduling problems have received almost no attention from both the Operations Research and the Artificial Intelligence community. Motivated by the needs of a specific application, we engaged in a study of the applicability of constraint programming techniques to preemptive scheduling problems. This paper presents the algorithms we developed and the results we obtained on the preemptive variant of the famous ‘job-shop scheduling problem’. Ten heuristic search strategies, combined with two different constraint propagation techniques, are presented, and compared using two well-known series of job-shop scheduling instances from the literature. The best combination, which relies on ‘limited discrepancy search’ and on ‘edge-finding’ techniques, is shown to provide excellent solutions to the preemptive job-shop scheduling problem. A mean relative distance to the optimal solution of 0.32% is achieved in five minutes, on instances with 10 jobs and 10 machines (100 activities).