Non-Linear Merging Strategies for Merge-and-Shrink Based on Variable Interactions

Abstract

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.

Merge-and-Shrink Heuristics for Classical Planning: Efficient Implementation and Partial Abstractions

“…In the first experiment, we can only use the merge strategies that were available already in the previous implementation. This includes two representatives of simple linear strategies, causal graph goal level (CGGL) (Helmert, Haslum, and Hoffmann 2007) and reverse level (RL) (Nissim, Hoffmann, and Helmert 2011), as well as the non-linear merge strategies DFP (Dräger, Finkbeiner, and Podelski 2009;Sievers, Wehrle, and Helmert 2014) and maximum intermediate abstraction size minimizing (MIASM) (Fan, Müller, and Holte 2014), the latter using DFP as fallback mechanism (MIASMdfp or Mdfp for short). In the second experiment, we also use the most recent, state-of-the-art non-linear merge strategies score-based MIASM (sbM), also called DYN-MIASM, and the strategy based on strongly connected components of the causal graph (Sievers, Wehrle, and Helmert 2016), which uses DFP for internal merging (SCCdfp).…”