Incremental propagation rules for a precedence graph with optional activities and time windows

Abstract

Constraint-based scheduling is a powerful tool for solving complex real-life scheduling problems thanks to a natural integration of special solving algorithms encoded in so-called global constraints. Global constraints describe subproblems of the scheduling problem, eg, allocation of activities to a disjunctive resource. Filtering algorithms behind these constraints are used to prune the search space by eliminating options that violate the constraint. The filtering algorithms are frequently expressed in the form of propagation rules that react to some change appearing during problem solving, eg, adding a new precedence relation, by proposing a derived restriction, eg, shrinking a time window. These changes can be invoked by other constraints or they can be a result of some search decision. This paper describes new incremental propagation rules integrating propagation of precedence relations and time windows for activities allocated to a disjunctive resource. Moreover, the rules also cover so-called optional activities that may or may not be present in the final schedule.