Incremental Constraint-Posting Algorithms in Interleaved Planning and Scheduling

In this paper we examine a collection of related incremental constraint-posting algorithms for temporal planning and for planning with continuous processes. The basis for these algorithms is an incremental version of the Bellman-Ford single-source shortest-path algorithm for consistency checking Simple Temporal Networks (STNs). We extend an existing incremental algorithm for STNs and then proceed to show how this algorithm plays a key role in temporal planning by a forward-chaining strategy, interleaving action choice with action scheduling. We go on to consider the more complex problem of temporal planning with continuous linear processes and show how the incremental STN algorithm can be integrated with a linear program (LP) solver, to achieve an efficient incremental constraint-posting algorithm for use in a forward-search planner. We demonstrate empirically that the incremental algorithms improve performance in both temporal and temporal and numeric settings.