Contents

- Additive heuristic
- Potential heuristic optimized for all states
- Blind heuristic
- Context-enhanced additive heuristic
- Additive CEGAR heuristic
- Causal graph heuristic
- Diverse potential heuristics
- FF heuristic
- Goal count heuristic
- h^m heuristic
- Max heuristic
- Potential heuristic optimized for initial state
- Landmark-count heuristic
- Landmark-cut heuristic
- Max evaluator
- Merge-and-shrink heuristic
- Operator counting heuristic
- Sample-based potential heuristics

- Basic Evaluators
- Pattern Database Heuristics

An evaluator specification is either a newly created evaluator instance or an evaluator that has been defined previously. This page describes how one can specify a new evaluator instance. For re-using evaluators, see Evaluator Predefinitions.

If the evaluator is a heuristic, definitions of *properties* in the descriptions below:

**admissible:**h(s) <= h*(s) for all states s**consistent:**h(s) <= c(s, s') + h(s') for all states s connected to states s' by an action with cost c(s, s')**safe:**h(s) = infinity is only true for states with h*(s) = infinity**preferred operators:**this heuristic identifies preferred operators

## Additive heuristic

add(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported (in the sense that the planner won't complain -- handling of axioms might be very stupid and even render the heuristic unsafe)

Properties:

**admissible:**no**consistent:**no**safe:**yes for tasks without axioms**preferred operators:**yes

## Potential heuristic optimized for all states

The algorithm is based on

Jendrik Seipp, Florian Pommerening and Malte Helmert.

New Optimization Functions for Potential Heuristics.

In*Proceedings of the 25th International Conference on Automated Planning and Scheduling (ICAPS 2015)*, pp. 193-201. AAAI Press 2015.

all_states_potential(max_potential=1e8, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true)

*max_potential*(double [0.0, infinity]): Bound potentials by this number*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Blind heuristic

Returns cost of cheapest action for non-goal states, 0 for goal states

blind(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Context-enhanced additive heuristic

cea(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported (in the sense that the planner won't complain -- handling of axioms might be very stupid and even render the heuristic unsafe)

Properties:

**admissible:**no**consistent:**no**safe:**no**preferred operators:**yes

## Additive CEGAR heuristic

See the paper introducing Counterexample-guided Abstraction Refinement (CEGAR) for classical planning:

Jendrik Seipp and Malte Helmert.

Counterexample-guided Cartesian Abstraction Refinement.

In*Proceedings of the 23rd International Conference on Automated Planning and Scheduling (ICAPS 2013)*, pp. 347-351. AAAI Press 2013.

and the paper showing how to make the abstractions additive:

Jendrik Seipp and Malte Helmert.

Diverse and Additive Cartesian Abstraction Heuristics.

In*Proceedings of the 24th International Conference on Automated Planning and Scheduling (ICAPS 2014)*, pp. 289-297. AAAI Press 2014.

cegar(subtasks=[landmarks(),goals()], max_states=infinity, max_transitions=1000000, max_time=infinity, pick=MAX_REFINED, use_general_costs=true, transform=no_transform(), cache_estimates=true, random_seed=-1)

*subtasks*(list of SubtaskGenerator): subtask generators*max_states*(int [1, infinity]): maximum sum of abstract states over all abstractions*max_transitions*(int [0, infinity]): maximum sum of real transitions (excluding self-loops) over all abstractions*max_time*(double [0.0, infinity]): maximum time in seconds for building abstractions*pick*({RANDOM, MIN_UNWANTED, MAX_UNWANTED, MIN_REFINED, MAX_REFINED, MIN_HADD, MAX_HADD}): split-selection strategy*use_general_costs*(bool): allow negative costs in cost partitioning*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates*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.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Causal graph heuristic

cg(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported (in the sense that the planner won't complain -- handling of axioms might be very stupid and even render the heuristic unsafe)

Properties:

**admissible:**no**consistent:**no**safe:**no**preferred operators:**yes

## Diverse potential heuristics

The algorithm is based on

Jendrik Seipp, Florian Pommerening and Malte Helmert.

New Optimization Functions for Potential Heuristics.

In*Proceedings of the 25th International Conference on Automated Planning and Scheduling (ICAPS 2015)*, pp. 193-201. AAAI Press 2015.

diverse_potentials(num_samples=1000, max_num_heuristics=infinity, max_potential=1e8, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true, random_seed=-1)

*num_samples*(int [0, infinity]): Number of states to sample*max_num_heuristics*(int [0, infinity]): maximum number of potential heuristics*max_potential*(double [0.0, infinity]): Bound potentials by this number*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates*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.

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## FF heuristic

ff(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported (in the sense that the planner won't complain -- handling of axioms might be very stupid and even render the heuristic unsafe)

Properties:

**admissible:**no**consistent:**no**safe:**yes for tasks without axioms**preferred operators:**yes

## Goal count heuristic

goalcount(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**ignored by design**conditional effects:**supported**axioms:**supported

Properties:

**admissible:**no**consistent:**no**safe:**yes**preferred operators:**no

## h^m heuristic

hm(m=2, transform=no_transform(), cache_estimates=true)

*m*(int [1, infinity]): subset size*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**ignored**axioms:**ignored

Properties:

**admissible:**yes for tasks without conditional effects or axioms**consistent:**yes for tasks without conditional effects or axioms**safe:**yes for tasks without conditional effects or axioms**preferred operators:**no

## Max heuristic

hmax(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**supported**axioms:**supported (in the sense that the planner won't complain -- handling of axioms might be very stupid and even render the heuristic unsafe)

Properties:

**admissible:**yes for tasks without axioms**consistent:**yes for tasks without axioms**safe:**yes for tasks without axioms**preferred operators:**no

## Potential heuristic optimized for initial state

The algorithm is based on

Jendrik Seipp, Florian Pommerening and Malte Helmert.

New Optimization Functions for Potential Heuristics.

In*Proceedings of the 25th International Conference on Automated Planning and Scheduling (ICAPS 2015)*, pp. 193-201. AAAI Press 2015.

initial_state_potential(max_potential=1e8, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true)

*max_potential*(double [0.0, infinity]): Bound potentials by this number*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Landmark-count heuristic

For the inadmissible variant see the papers

Silvia Richter, Malte Helmert and Matthias Westphal.

Landmarks Revisited.

In*Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI 2008)*, pp. 975-982. AAAI Press 2008.

and

Silvia Richter and Matthias Westphal.

The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks.

In*Journal of Artificial Intelligence Research 39*, pp. 127-177. AAAI Press 2010.

For the admissible variant see the papers

Erez Karpas and Carmel Domshlak.

Cost-Optimal Planning with Landmarks.

In*Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009)*, pp. 1728-1733. AAAI Press 2009.

and

Emil Keyder and Silvia Richter and Malte Helmert.

Sound and Complete Landmarks for And/Or Graphs.

In*Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010)*, pp. 335-340. IOS Press 2010.

lmcount(lm_factory, admissible=false, optimal=false, pref=false, alm=true, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true)

*lm_factory*(LandmarkFactory): the set of landmarks to use for this heuristic. The set of landmarks can be specified here, or predefined (see LandmarkFactory).*admissible*(bool): get admissible estimate*optimal*(bool): use optimal (LP-based) cost sharing (only makes sense with`admissible=true`)*pref*(bool): identify preferred operators (see Using preferred operators with the lmcount heuristic)*alm*(bool): use action landmarks*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

**Optimal search:** When using landmarks for optimal search (`admissible=true`), you probably also want to add this heuristic as a lazy_evaluator in the A* algorithm to improve heuristic estimates.

**Note:** To use `optimal=true`, you must build the planner with LP support. See LPBuildInstructions.

**Differences to the literature:** This heuristic differs from the description in the literature (see references above) in the set of preferred operators computed. The original implementation described in the literature computes two kinds of preferred operators:

- If there is an applicable operator that reaches a landmark, all such operators are preferred.
- If no such operators exist, perform an FF-style relaxed exploration towards the nearest landmarks (according to the landmark orderings) and use the preferred operators of this exploration.

Our implementation of the heuristic only considers preferred operators of the first type and does not include the second type. The rationale for this change is that it reduces code complexity and helps more cleanly separate landmark-based and FF-based computations in LAMA-like planner configurations. In our experiments, only considering preferred operators of the first type reduces performance when using the heuristic and its preferred operators in isolation but improves performance when using this heuristic in conjunction with the FF heuristic, as in LAMA-like planner configurations.

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional_effects:**supported if the LandmarkFactory supports them; otherwise ignored with`admissible=false`and not allowed with`admissible=true`**axioms:**ignored with`admissible=false`; not allowed with`admissible=true`

Properties:

**admissible:**yes if`admissible=true`**consistent:**complicated; needs further thought**safe:**yes except on tasks with axioms or on tasks with conditional effects when using a LandmarkFactory not supporting them**preferred operators:**yes (if enabled; see`pref`option)

## Landmark-cut heuristic

lmcut(transform=no_transform(), cache_estimates=true)

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**no**safe:**yes**preferred operators:**no

## Max evaluator

Calculates the maximum of the sub-evaluators.

max(evals)

*evals*(list of Evaluator): at least one evaluator

## Merge-and-shrink heuristic

This heuristic implements the algorithm described 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.

For a more exhaustive description of merge-and-shrink, see the journal paper

Malte Helmert, Patrik Haslum, Joerg Hoffmann and Raz Nissim.

Merge-and-Shrink Abstraction: A Method for Generating Lower Bounds in Factored State Spaces.

In*Journal of the ACM 61 (3)*, pp. 16:1-63. 2014.

Please note that the journal paper describes the "old" theory of label reduction, which has been superseded by the above conference paper and is no longer implemented in Fast Downward.

The following paper describes how to improve the DFP merge strategy with tie-breaking, and presents two new merge strategies (dyn-MIASM and SCC-DFP):

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 Automated Planning and Scheduling (ICAPS 2016)*, pp. 294-298. AAAI Press 2016.

merge_and_shrink(merge_strategy, shrink_strategy, label_reduction=<none>, prune_unreachable_states=true, prune_irrelevant_states=true, max_states=-1, max_states_before_merge=-1, threshold_before_merge=-1, transform=no_transform(), cache_estimates=true, verbosity=verbose)

*merge_strategy*(MergeStrategy): See detailed documentation for merge strategies. We currently recommend SCC-DFP, which can be achieved using`merge_strategy=merge_sccs(order_of_sccs=topological,merge_selector=score_based_filtering(scoring_functions=[goal_relevance,dfp,total_order]))`*shrink_strategy*(ShrinkStrategy): See detailed documentation for shrink strategies. We currently recommend non-greedy shrink_bisimulation, which can be achieved using`shrink_strategy=shrink_bisimulation(greedy=false)`*label_reduction*(LabelReduction): See detailed documentation for labels. There is currently only one 'option' to use label_reduction, which is`label_reduction=exact`Also note the interaction with shrink strategies.*prune_unreachable_states*(bool): If true, prune abstract states unreachable from the initial state.*prune_irrelevant_states*(bool): If true, prune abstract states from which no goal state can be reached.*max_states*(int [-1, infinity]): maximum transition system size allowed at any time point.*max_states_before_merge*(int [-1, infinity]): maximum transition system size allowed for two transition systems before being merged to form the synchronized product.*threshold_before_merge*(int [-1, infinity]): If a transition system, before being merged, surpasses this soft transition system size limit, the shrink strategy is called to possibly shrink the transition system.*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates*verbosity*({silent, normal, verbose}): Option to specify the level of verbosity.`silent`: silent: no output during construction, only starting and final statistics`normal`: normal: basic output during construction, starting and final statistics`verbose`: verbose: full output during construction, starting and final statistics

**Note:** Conditional effects are supported directly. Note, however, that for tasks that are not factored (in the sense of the JACM 2014 merge-and-shrink paper), the atomic transition systems on which merge-and-shrink heuristics are based are nondeterministic, which can lead to poor heuristics even when only perfect shrinking is performed.

**Note:** When pruning unreachable states, admissibility and consistency is only guaranteed for reachable states and transitions between reachable states. While this does not impact regular A* search which will never encounter any unreachable state, it impacts techniques like symmetry-based pruning: a reachable state which is mapped to an unreachable symmetric state (which hence is pruned) would falsely be considered a dead-end and also be pruned, thus violating optimality of the search.

**Note:** A currently recommended good configuration uses bisimulation based shrinking, the merge strategy SCC-DFP, and the appropriate label reduction setting (max_states has been altered to be between 10000 and 200000 in the literature):

merge_and_shrink(shrink_strategy=shrink_bisimulation(greedy=false),merge_strategy=merge_sccs(order_of_sccs=topological,merge_selector=score_based_filtering(scoring_functions=[goal_relevance,dfp,total_order])),label_reduction=exact(before_shrinking=true,before_merging=false),max_states=50000,threshold_before_merge=1)

Note that for versions of Fast Downward prior to 2016-08-19, the syntax differs. See the recommendation in the file merge_and_shrink_heuristic.cc for an example configuration.

Language features supported:

**action costs:**supported**conditional effects:**supported (but see note)**axioms:**not supported

Properties:

**admissible:**yes (but see note)**consistent:**yes (but see note)**safe:**yes**preferred operators:**no

## Operator counting heuristic

An operator counting heuristic computes a linear program (LP) in each state. The LP has one variable Count_o for each operator o that represents how often the operator is used in a plan. Operator counting constraints are linear constraints over these varaibles that are guaranteed to have a solution with Count_o = occurrences(o, pi) for every plan pi. Minimizing the total cost of operators subject to some operator counting constraints is an admissible heuristic. For details, see

Florian Pommerening, Gabriele Roeger, Malte Helmert and Blai Bonet.

LP-based Heuristics for Cost-optimal Planning.

In*Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling (ICAPS 2014)*, pp. 226-234. AAAI Press 2014.

operatorcounting(constraint_generators, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true)

*constraint_generators*(list of ConstraintGenerator): methods that generate constraints over operator counting variables*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional effects:**not supported (the heuristic supports them in theory, but none of the currently implemented constraint generators do)**axioms:**not supported (the heuristic supports them in theory, but none of the currently implemented constraint generators do)

Properties:

**admissible:**yes**consistent:**yes, if all constraint generators represent consistent heuristics**safe:**yes**preferred operators:**no

## Sample-based potential heuristics

Maximum over multiple potential heuristics optimized for samples. The algorithm is based on

New Optimization Functions for Potential Heuristics.

In*Proceedings of the 25th International Conference on Automated Planning and Scheduling (ICAPS 2015)*, pp. 193-201. AAAI Press 2015.

sample_based_potentials(num_heuristics=1, num_samples=1000, max_potential=1e8, lpsolver=CPLEX, transform=no_transform(), cache_estimates=true, random_seed=-1)

*num_heuristics*(int [0, infinity]): number of potential heuristics*num_samples*(int [0, infinity]): Number of states to sample*max_potential*(double [0.0, infinity]): Bound potentials by this number*lpsolver*({CLP, CPLEX, GUROBI}): external solver that should be used to solve linear programs`CLP`: default LP solver shipped with the COIN library`CPLEX`: commercial solver by IBM`GUROBI`: commercial solver

*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates*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.

**Note:** to use an LP solver, you must build the planner with LP support. See LPBuildInstructions.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

# Basic Evaluators

## Constant evaluator

Returns a constant value.

const(value=1)

*value*(int [0, infinity]): the constant value

## g-value evaluator

Returns the g-value (path cost) of the search node.

g()

## Preference evaluator

Returns 0 if preferred is true and 1 otherwise.

pref()

## Sum evaluator

Calculates the sum of the sub-evaluators.

sum(evals)

*evals*(list of Evaluator): at least one evaluator

## Weighted evaluator

Multiplies the value of the evaluator with the given weight.

weight(eval, weight)

*eval*(Evaluator): evaluator*weight*(int): weight

# Pattern Database Heuristics

## Canonical PDB

The canonical pattern database heuristic is calculated as follows. For a given pattern collection C, the value of the canonical heuristic function is the maximum over all maximal additive subsets A in C, where the value for one subset S in A is the sum of the heuristic values for all patterns in S for a given state.

cpdbs(patterns=systematic(1), max_time_dominance_pruning=infinity, transform=no_transform(), cache_estimates=true)

*patterns*(PatternCollectionGenerator): pattern generation method*max_time_dominance_pruning*(double [0.0, infinity]): The maximum time in seconds spent on dominance pruning. Using 0.0 turns off dominance pruning. Dominance pruning excludes patterns and additive subsets that will never contribute to the heuristic value because there are dominating subsets in the collection.*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## iPDB

This pattern generation method is an adaption of the algorithm described in the following paper:

Patrik Haslum, Adi Botea, Malte Helmert, Blai Bonet and Sven Koenig.

Domain-Independent Construction of Pattern Database Heuristics for Cost-Optimal Planning.

In*Proceedings of the 22nd AAAI Conference on Artificial Intelligence (AAAI 2007)*, pp. 1007-1012. AAAI Press 2007.

For implementation notes, see:

Silvan Sievers, Manuela Ortlieb and Malte Helmert.

Efficient Implementation of Pattern Database Heuristics for Classical Planning.

In*Proceedings of the Fifth Annual Symposium on Combinatorial Search (SoCS 2012)*, pp. 105-111. AAAI Press 2012.

ipdb(pdb_max_size=2000000, collection_max_size=20000000, num_samples=1000, min_improvement=10, max_time=infinity, random_seed=-1, max_time_dominance_pruning=infinity, transform=no_transform(), cache_estimates=true)

*pdb_max_size*(int [1, infinity]): maximal number of states per pattern database*collection_max_size*(int [1, infinity]): maximal number of states in the pattern collection*num_samples*(int [1, infinity]): number of samples (random states) on which to evaluate each candidate pattern collection*min_improvement*(int [1, infinity]): minimum number of samples on which a candidate pattern collection must improve on the current one to be considered as the next pattern collection*max_time*(double [0.0, infinity]): maximum time in seconds for improving the initial pattern collection via hill climbing. If set to 0, no hill climbing is performed at all. Note that this limit only affects hill climbing. Use max_time_dominance_pruning to limit the time spent for pruning dominated patterns.*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.*max_time_dominance_pruning*(double [0.0, infinity]): The maximum time in seconds spent on dominance pruning. Using 0.0 turns off dominance pruning. Dominance pruning excludes patterns and additive subsets that will never contribute to the heuristic value because there are dominating subsets in the collection.*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

**Note:** The pattern collection created by the algorithm will always contain all patterns consisting of a single goal variable, even if this violates the pdb_max_size or collection_max_size limits.

**Note:** This pattern generation method uses the canonical pattern collection heuristic.

### Implementation Notes

The following will very briefly describe the algorithm and explain the differences between the original implementation from 2007 and the new one in Fast Downward.

The aim of the algorithm is to output a pattern collection for which the Canonical PDB yields the best heuristic estimates.

The algorithm is basically a local search (hill climbing) which searches the "pattern neighbourhood" (starting initially with a pattern for each goal variable) for improving the pattern collection. This is done as described in the section "pattern construction as search" in the paper, except for the corrected search neighbourhood discussed below. For evaluating the neighbourhood, the "counting approximation" as introduced in the paper was implemented. An important difference however consists in the fact that this implementation computes all pattern databases for each candidate pattern rather than using A* search to compute the heuristic values only for the sample states for each pattern.

Also the logic for sampling the search space differs a bit from the original implementation. The original implementation uses a random walk of a length which is binomially distributed with the mean at the estimated solution depth (estimation is done with the current pattern collection heuristic). In the Fast Downward implementation, also a random walk is used, where the length is the estimation of the number of solution steps, which is calculated by dividing the current heuristic estimate for the initial state by the average operator costs of the planning task (calculated only once and not updated during sampling!) to take non-unit cost problems into account. This yields a random walk of an expected lenght of np = 2 * estimated number of solution steps. If the random walk gets stuck, it is being restarted from the initial state, exactly as described in the original paper.

The section "avoiding redundant evaluations" describes how the search neighbourhood of patterns can be restricted to variables that are relevant to the variables already included in the pattern by analyzing causal graphs. There is a mistake in the paper that leads to some relevant neighbouring patterns being ignored. See the errata for details. This mistake has been addressed in this implementation. The second approach described in the paper (statistical confidence interval) is not applicable to this implementation, as it doesn't use A* search but constructs the entire pattern databases for all candidate patterns anyway. The search is ended if there is no more improvement (or the improvement is smaller than the minimal improvement which can be set as an option), however there is no limit of iterations of the local search. This is similar to the techniques used in the original implementation as described in the paper.

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Pattern database heuristic

TODO

pdb(pattern=greedy(), transform=no_transform(), cache_estimates=true)

*pattern*(PatternGenerator): pattern generation method*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no

## Zero-One PDB

The zero/one pattern database heuristic is simply the sum of the heuristic values of all patterns in the pattern collection. In contrast to the canonical pattern database heuristic, there is no need to check for additive subsets, because the additivity of the patterns is guaranteed by action cost partitioning. This heuristic uses the most simple form of action cost partitioning, i.e. if an operator affects more than one pattern in the collection, its costs are entirely taken into account for one pattern (the first one which it affects) and set to zero for all other affected patterns.

zopdbs(patterns=systematic(1), transform=no_transform(), cache_estimates=true)

*patterns*(PatternCollectionGenerator): pattern generation method*transform*(AbstractTask): Optional task transformation for the heuristic. Currently, adapt_costs() and no_transform() are available.*cache_estimates*(bool): cache heuristic estimates

Language features supported:

**action costs:**supported**conditional effects:**not supported**axioms:**not supported

Properties:

**admissible:**yes**consistent:**yes**safe:**yes**preferred operators:**no