A Mixed Closure-CSP Method to Solve Scheduling Problems

Scheduling problems can be seen as a set of temporal metric and disjunctive constraints. So, they can be formulated in terms of CSPs techniques. In the literature, there are CSP-based methods which interleave (sequentially) searching efforts with the application of consistency enforcing mechanisms and variable/ordering heuristics. Thus, the number of backtrackings needed to obtain a solution is reduced. Alternatively, in this paper, we propose a new method that integrates effectively the CSP process into a limited closure process: not interleaving them but as a part of the same process. Such integration allows us to define better informed heuristics. They are used to limit the complete closure process applied, with a maximum number of disjunctions allowed, and so reduce their complexity, while reducing the search space. We can also maintain more time open disjunctive solutions in the CSP process, limiting the number of backtrackings realized, and avoiding to know all problem constraints in advance. Experiments done with flow-shop and job-shop instances show that our approach obtains a feasible solution/optimal solution without needing of backtracking in most of the cases. We also analyze the behaviour of our algorithm when some constraints are known dynamically, obtaining better results than using a pure CSP process.