Saturated Cost Partitioning for Optimal Classical Planning

Abstract

Cost partitioning is a method for admissibly combining a set of admissible heuristic estimators by distributing operator costs among the heuristics. Computing an optimal cost partitioning, i.e., the operator cost distribution that maximizes the heuristic value, is often prohibitively expensive to compute. Saturated cost partitioning is an alternative that is much faster to compute and has been shown to yield high-quality heuristics. However, its greedy nature makes it highly susceptible to the order in which the heuristics are considered. We propose a greedy algorithm to generate orders and show how to use hill-climbing search to optimize a given order. Combining both techniques leads to significantly better heuristic estimates than using the best random order that is generated in the same time. Since there is often no single order that gives good guidance on the whole state space, we use the maximum of multiple orders as a heuristic that is significantly better informed than any single-order heuristic, especially when we actively search for a set of diverse orders.

Merge-and-Shrink: A Compositional Theory of Transformations of Factored Transition Systems

“…Note that the second result is only a sufficient condition, not a necessary condition, as reducing the cost of a label does not necessarily increase the max-factor heuristic. It is easy to see that label reduction preserves all local heuristic values in a given factor iff no costs are reduced below their saturated costs, as discussed in the work on saturated cost partitioning (Seipp, Keller, & Helmert, 2020).…”

Pattern Selection for Optimal Classical Planning with Saturated Cost Partitioning

“…More concretely, for a given pattern collection C, we start with an empty family of saturated cost partitioning heuristics F and a setŜ of 1000 sample states obtained with random walks [Haslum et al, 2007]. Then we iteratively sample a new state s and compute a greedy order ω of C that works well for s [Seipp, 2017]. If h SCP ω has a higher heuristic estimate for any state s ∈Ŝ than all heuristics in F , we add h SCP ω to F .…”

“…Instead of discarding the computed pattern sequences when SYS-SCP finishes, we can turn each pattern sequence σ into a full pattern order by randomly appending all SYS-SCP patterns missing from σ to σ and pass the resulting order to the diversification procedure. Feeding the diversification exclusively with such orders leads to solving 1130 tasks, while using only greedy orders for sample states [Seipp, 2017] solves 1156 tasks. We obtain the best results by diversifying both types of orders, solving 1168 tasks, and we use this variant in all other experiments.…”

Refining Abstraction Heuristics during Real-Time Planning

“…We use Cartesian abstraction here as it allows fine-grained state partitions (in difference to pattern databases) yet supports effective refinement operations (in difference to mergeand-shrink abstraction). Furthermore, Cartesian abstractions can provide state-of-the-art performance when using not one but an ensemble of abstractions, made additive through cost partitioning (Katz and Domshlak 2008;Seipp and Helmert 2014;Seipp 2017) where the cost of each action is distributed across abstractions.…”

“…Where relevant, we discuss these questions for Cartesian abstraction, which assumes a representation of the state space in terms of state variables, and restricts blocks to be cross-products of statevariable domain subsets (Ball, Podelski, and Rajamani 2001;Seipp and Helmert 2013). Cartesian abstraction allows finegrained state partitions yet supports effective refinement operations, and it underlies the current state of the art in using abstractions to design heuristic functions in planning (Seipp and Helmert 2014;Seipp 2017;Seipp and Helmert 2018).…”