Merge-and-shrink is a general framework for creating abstraction heuristics. In this paper we present two new variations of merge-and-shrink: MS-lite and DM-HQ. MS-lite is an extremely fast merge-and-shrink that maintains only the smallest abstractions that preserve local heuristic information. MS-lite has complementary strength over other merge-and-shrink methods due to its efficiency. In addition, we show that MS-lite has little dependence on merging strategies and its eager shrinking strategy can lead to better heuristics for some planning tasks. DM-HQ features a merging criterion that utilizes information about heuristic quality to make the merging decisions. Our experiments show that combining DM-HQ and MS-lite dramatically outperforms the current state-of-the-art merge-and-shrink method by solving 75 more tasks on an International Planning Competition (IPC) benchmark set of 1499 tasks.

In many planning applications, actions can have highly diverse costs. Recent studies focus on the effects of diverse action costs on search algorithms, but not on their effects on domain-independent heuristics. In this paper, we demonstrate there are negative impacts of action cost diversity on merge-and-shrink (M&S), a successful abstraction method for producing high-quality heuristics for planning problems. We propose a new cost partitioning method to address the negative effects of diverse action costs on M&S. We investigate nonunit cost IPC domains, especially those for which diverse action costs have severe negative effects on the quality of the M&S heuristic. Our experiments demonstrate that in these domains, an additive set of M&S heuristics using the new cost partitioning method produces much more informative and effective heuristics than creating a single M&S heuristic which directly encodes diverse costs.

Merge-and-shrink is a general method for deriving accurate abstraction heuristics.We present two novel nonlinear merging strategies, UMC and MIASM, based on variable interaction. The principle underlying our methods is to merge strongly interacting variables early on. UMC measures variable interaction by weighted causal graph edges, and MIASM measures variable interaction in terms of the number of necessary states in the abstract space defined by the variables. The methods partition variables into clusters in which the variable interactions are strong, and merge variables within each cluster before merging the clusters. Experiment results show that our merging strategies outperform existing merging strategies in general and can produce heuristics that give perfect guidance for solving tasks that previous methods cannot even solve.

Diverse action costs are an essential feature of many real-world planning applications. Some recent studies have shown that diversity of action costs makes planning more difficult, and that searching using unit action costs can outperform searching the same domain with diverse action costs. In this paper, we provide experimental evidence and theoretical analysis showing that search can also benefit from action cost diversity. We show that on several IPC problems cost diversity has a positive effect (reduces search effort). We then present a theoretical analysis establishing that these positive cases are not accidental. Our main result is a "No Free Lunch" theorem showing that any negative effects of cost diversity are always perfectly counterbalanced by positive effects. Our theoretical analysis also shows that it is advantageous to have a strongly concentrated distribution of solution costs. In many domains, unit costs will give rise to a more concentrated distribution than diverse costs, but we give an example typifying domains in which the opposite is the case.

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