Scorpion

ion Heuristics Depending on whether or not a given task contains conditional effects, we use a different set of abstraction heuristics. Tasks Without Conditional Effects For tasks without conditional effects we use the combination of the following heuristics: • Cartesian abstraction heuristics (CART): We consider Cartesian abstractions of the landmark and goal task decompositions (Seipp and Helmert 2018). We limit the total number of non-looping transitions in all abstractions underlying the Cartesian heuristics by one million. • pattern databases found by hill climbing (HC): We use the algorithm by Haslum et al. (2007) for searching via hill climbing in the space of pattern collections. We limit the time for hill climbing by 100 seconds. • pattern databases for systematic patterns (SYS): We use a procedure that generates all interesting patterns up to size 2 (Pommerening, Röger, and Helmert 2013). Tasks With Conditional Effects For tasks with conditional effects we compute pattern database heuristics for systematically generated patterns of sizes 1, 2 and 3 (Pommerening, Röger, and Helmert 2013). Since generating these heuristics can take very long for some We chose the name “Scorpion” since it contains the letters s(aturated) c(ost) p(artitioning) in this order. tasks, we limit the time for generating PDB heuristics by 300 seconds. Saturated Cost Partitioning We combine the information contained in the component heuristics with saturated cost partitioning (Seipp and Helmert 2018). Given an ordered collection of heuristics, saturated cost partitioning iteratively assigns each heuristic h only the costs that h needs for justifying its estimates and saves the remaining costs for subsequent heuristics. Distributing the operator costs among the component heuristics in this way makes the sum of the individual heuristic values admissible. The quality of the resulting saturated cost partitioning heuristic strongly depends on the order in which the component heuristics are considered (Seipp, Keller, and Helmert 2017). Additionally, we can obtain much stronger heuristics by maximizing over multiple saturated cost partitioning heuristics computed for different orders instead of using a single saturated cost partitioning heuristic (Seipp, Keller, and Helmert 2017). We therefore iteratively sample a state (using the sampling algorithm by Haslum et al. 2007), use a greedy algorithm for finding an initial order for the state (more concretely, we use the static greedy ordering algorithm with the q h stolen scoring function) and afterwards optimize the order with simple hill climbing in the space of orders for at most two seconds (Seipp 2018). If the the saturated cost partitioning heuristic computed for the resulting optimized greedy order yields a higher estimate for one of a set of 1000 sample states than all previously added orders, we add the order to our set of orders. We limit the time for finding orders in this way to 200 seconds. Operator Pruning Techniques We employ two operator pruning techniques: • strong stubborn sets: We use the variant that instantiates strong stubborn sets for classical planning in a straight-forward way (Alkhazraji et al. 2012; Wehrle and Helmert 2014). We compute the interference relation “on demand” during the search and switch off pruning completely in case the fraction of pruned successor states is less than 20% of the total successor states after 1000 expansions.