Contents

This page describes the various merge strategies supported by the planner.

## Merge strategy DFP

This merge strategy implements the algorithm originally described in the paper "Directed model checking with distance-preserving abstractions" by Draeger, Finkbeiner and Podelski (SPIN 2006), adapted to planning in the following paper:

Silvan Sievers, Martin Wehrle and Malte Helmert.

Generalized Label Reduction for Merge-and-Shrink Heuristics.

In*Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI 2014)*, pp. 2358-2366. AAAI Press, 2014.

Using this command line option is deprecated, please use the equivalent configurations

merge_strategy=merge_stateless(merge_selector=score_based_filtering(scoring_functions=[goal_relevance,dfp,total_order(<order_option>))]))

if specifying tie-breaking order criteria, or

merge_strategy=merge_stateless(merge_selector=score_based_filtering(scoring_functions=[goal_relevance,dfp,single_random()]))

if using full random tie-breaking.

merge_dfp(atomic_ts_order=reverse_level, product_ts_order=new_to_old, atomic_before_product=false, random_seed=-1, randomized_order=false)

*atomic_ts_order*({reverse_level, level, random}): The order in which atomic transition systems are considered when considering pairs of potential merges.`reverse_level`: the variable order of Fast Downward`level`: opposite of reverse_level`random`: a randomized order

*product_ts_order*({old_to_new, new_to_old, random}): The order in which product transition systems are considered when considering pairs of potential merges.`old_to_new`: consider composite transition systems from most recent to oldest, that is in decreasing index order`new_to_old`: opposite of old_to_new`random`: a randomized order

*atomic_before_product*(bool): Consider atomic transition systems before composite ones iff true.*random_seed*(int [-1, infinity]): Set to -1 (default) to use the global random number generator. Set to any other value to use a local random number generator with the given seed.*randomized_order*(bool): If true, use a 'globally' randomized order, i.e. all transition systems are considered in an arbitrary order. This renders all other ordering options void.

## Linear merge strategies

These merge strategies implement several linear merge orders, which are described in the paper:

Malte Helmert, Patrik Haslum and Joerg Hoffmann.

Flexible Abstraction Heuristics for Optimal Sequential Planning.

In*Proceedings of the Seventeenth International Conference on Automated Planning and Scheduling (ICAPS 2007)*, pp. 176-183. AAAI Press, 2007.

Using this command line option is deprecated, please use the equivalent configuration

merge_strategy=merge_precomputed(merge_tree=linear(<variable_order>))

merge_linear(random_seed=-1, update_option=use_random, variable_order=CG_GOAL_LEVEL)

*random_seed*(int [-1, infinity]): Set to -1 (default) to use the global random number generator. Set to any other value to use a local random number generator with the given seed.*update_option*({use_first, use_second, use_random}): When the merge tree is used within another merge strategy, how should it be updated when a merge different to a merge from the tree is performed: choose among use_first, use_second, and use_random to choose which node of the tree should survive and represent the new merged index. Specify use_first (use_second) to let the node represententing the index that would have been merged earlier (later) survive. use_random chooses a random node.*variable_order*({CG_GOAL_LEVEL, CG_GOAL_RANDOM, GOAL_CG_LEVEL, RANDOM, LEVEL, REVERSE_LEVEL}): the order in which atomic transition systems are merged

## Precomputed merge strategy

This merge strategy has a precomputed merge tree. Note that this merge strategy does not take into account the current state of the factored transition system. This also means that this merge strategy relies on the factored transition system being synchronized with this merge tree, i.e. all merges are performed exactly as given by the merge tree.

merge_precomputed(merge_tree)

*merge_tree*(MergeTree): The precomputed merge tree

## Merge strategy SSCs

This merge strategy implements the algorithm described in the paper

Silvan Sievers, Martin Wehrle and Malte Helmert.

An Analysis of Merge Strategies for Merge-and-Shrink Heuristics.

In*Proceedings of the 26th International Conference on Planning and Scheduling (ICAPS 2016)*, pp. 2358-2366. AAAI Press, 2016.

In a nutshell, it computes the maximal SCCs of the causal graph, obtaining a partitioning of the task's variables. Every such partition is then merged individually, using the specified fallback merge strategy, considering the SCCs in a configurable order. Afterwards, all resulting composite abstractions are merged to form the final abstraction, again using the specified fallback merge strategy and the configurable order of the SCCs.

merge_sccs(order_of_sccs=topological, merge_tree=<none>, merge_selector=<none>)

*order_of_sccs*({topological, reverse_topological, decreasing, increasing}): choose an ordering of the SCCs: topological/reverse_topological or decreasing/increasing in the size of the SCCs. The former two options refer to the directed graph where each obtained SCC is a 'supervertex'. For the latter two options, the tie-breaking is to use the topological order according to that same graph of SCC supervertices.*merge_tree*(MergeTree): the fallback merge strategy to use if a precomputed strategy should be used.*merge_selector*(MergeSelector): the fallback merge strategy to use if a stateless strategy should be used.

## Stateless merge strategy

This merge strategy has a merge selector, which computes the next merge only depending on the current state of the factored transition system, not requiring any additional information.

merge_stateless(merge_selector)

*merge_selector*(MergeSelector): The merge selector to be used.