A mixed closure-CSP method for solving scheduling problems

Scheduling problems can be viewed as a set of temporal metric and disjunctive constraints and so they can be formulated in terms of CSP techniques. In the literature, there are CSP-based methods which sequentially interleave search efforts with the application of consistency enforcing mechanisms and variable/ordering heuristics. Therefore, the number of backtrackings needed to obtain a solution is reduced. In this paper, we propose a new method that effectively integrates the CSP process into a limited closure process: not by interleaving them but rather as a part of the same process. Such an integration allows us to define more informed heuristics. These heuristics are used to limit the complete closure process to a maximum number of disjunctions, thereby reducing its complexity while at the same time reducing the search space. Some open disjunctive solutions can be maintained in the CSP process, limiting the number of backtrackings necessary, and avoiding having to know all the problem constraints in advance. Our experiments with flow-shop and job-shop instances show that this approach obtains a feasible solution/optimal solution without having to use backtracking in most cases. We also analyze the behaviour of our algorithm when some constraints are known dynamically and we demonstrate that it can provide better results than a pure CSP process.