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• Heuristic

A heuristic specification is either a newly created heuristic instance or a heuristic that has been defined previously. This page describes how one can specify a new heuristic instance. For re-using heuristics, see Heuristic Predefinitions.

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(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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

Blind heuristic

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

blind(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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

Causal graph heuristic

cg(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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

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(cost_type=NORMAL, patterns=None, combo=false, max_states=1000000)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

• patterns (list of list of int): list of patterns (which are lists of variable numbers of the planning task) Default: each goal variable is used as a single-variable pattern in the collection.

• combo (bool): use the combo strategy

• max_states (int): maximum abstraction size for combo strategy

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

See also Synergy.

ff(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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

Genetic Algorithm PDB

The following paper describes the automated creation of pattern databases with a genetic algorithm. Pattern collections are initially created with a bin-packing algorithm. The genetic algorithm is used to optimize the pattern collections with an objective function that estimates the mean heuristic value of the the pattern collections. Pattern collections with higher mean heuristic estimates are more likely selected for the next generation.

• Stefan Edelkamp
  Automated Creation of Pattern Database Search Heuristics.
  In Proceedings of the 4th Workshop on Model Checking and Artificial Intelligence (MoChArt 2006), pp. 35-50, 2007.

gapdb(pdb_max_size=50000, num_collections=5, num_episodes=30, mutation_probability=0.01, disjoint=false, cost_type=NORMAL)

• pdb_max_size (int): maximal number of states per pattern database

• num_collections (int): number of pattern collections to maintain in the genetic algorithm (population size)

• num_episodes (int): number of episodes for the genetic algorithm

• mutation_probability (double): probability between 0 and 1 for flipping a bit in the genetic algorithm

• disjoint (bool): consider a pattern collection invalid (giving it very low fitness) if its patterns are not disjoint

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

Note: This pattern generation method uses the zero/one pattern database heuristic.

Implementation Notes

The standard genetic algorithm procedure as described in the paper is implemented in Fast Downward. The implementation is close to the paper.

• Initialization
  In Fast Downward bin-packing with the next-fit strategy is used. A bin corresponds to a pattern which contains variables up to pdb_max_size. With this method each variable occurs exactly in one pattern of a collection. There are num_collections collections created.

• Mutation
  With probability mutation_probability a bit is flipped meaning that either a variable is added to a pattern or deleted from a pattern.

• Recombination
  Recombination isn't implemented in Fast Downward. In the paper recombination is described but not used.

• Evaluation
  For each pattern collection the mean heuristic value is computed. For a single pattern database the mean heuristic value is the sum of all pattern database entries divided through the number of entries. Entries with infinite heuristic values are ignored in this calculation. The sum of these individual mean heuristic values yield the mean heuristic value of the collection.

• Selection
  The higher the mean heuristic value of a pattern collection is, the more likely this pattern collection should be selected for the next generation. Therefore the mean heuristic values are normalized and converted into probabilities and Roulette Wheel Selection is used.

Language features supported:

• action costs: supported

• conditional_effects: not supported

• axioms: not supported

Properties:

• admissible: yes

• consistent: yes

• safe: yes

• preferred operators: no

Goal count heuristic

goalcount(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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, cost_type=NORMAL)

• m (int): subset size

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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

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 also this paper:

• 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, cost_type=NORMAL)

• pdb_max_size (int): maximal number of states per pattern database

• collection_max_size (int): maximal number of states in the pattern collection

• num_samples (int): number of samples (random states) on which to evaluate each candidate pattern collection

• min_improvement (int): minimum number of samples on which a candidate pattern collection must improve on the current one to be considered as the next pattern collection

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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 exactly as described in the section "pattern construction as search" in the paper. 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 somewhat relevant to the variables already included in the pattern by analyzing causal graphs. This is also implemented in Fast Downward. 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), how ever 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

Landmark-count heuristic

See also Synergy

lmcount(lm_graph, admissible=false, optimal=false, pref=false, alm=true, cost_type=NORMAL)

• lm_graph (LandmarkGraph): the set of landmarks to use for this heuristic. The set of landmarks can be specified here, or predefined (see LandmarkGraph).

• 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

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

Note: to use optimal=true, you must build the planner with USE_LP=1. See LPBuildInstructions.

Optimal search: when using landmarks for optimal search (admissible=true), you probably also want to enable the mpd option of the A* algorithm to improve heuristic estimates

cost_type parameter: only used when admissible=true (see LandmarkGraph)

Language features supported:

• action costs: supported

• conditional_effects: supported if admissible=false

• axioms: supported if admissible=false (but may behave stupidly and lead to an unsafe heuristic)

Properties:

• admissible: yes if admissible=true and there are neither conditional effects nor axioms

• consistent: no

• safe: yes (except maybe on tasks with axioms or when using admissible=true on tasks with conditional effects)

• preferred operators: yes (if enabled; see pref option)

Landmark-cut heuristic

lmcut(cost_type=NORMAL)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

Language features supported:

• action costs: supported

• conditional_effects: not supported

• axioms: not supported

Properties:

• admissible: yes

• consistent: no

• safe: yes

• preferred operators: no

Merge-and-shrink heuristic

Note: The parameter space and syntax for the merge-and-shrink heuristic has changed significantly in August 2011.

merge_and_shrink(merge_strategy=MERGE_LINEAR_CG_GOAL_LEVEL, shrink_strategy=shrink_fh(max_states=50000, max_states_before_merge=50000, shrink_f=high, shrink_h=low), reduce_labels=true, expensive_statistics=false, cost_type=NORMAL)

• merge_strategy ({MERGE_LINEAR_CG_GOAL_LEVEL, MERGE_LINEAR_CG_GOAL_RANDOM, MERGE_LINEAR_GOAL_CG_LEVEL, MERGE_LINEAR_RANDOM, MERGE_DFP, MERGE_LINEAR_LEVEL, MERGE_LINEAR_REVERSE_LEVEL}): merge strategy

• shrink_strategy (ShrinkStrategy): shrink strategy; try one of the following:

shrink_fh(max_states=N)

• f-preserving abstractions from the Helmert/Haslum/Hoffmann ICAPS 2007 paper (called HHH in the IJCAI 2011 paper by Nissim, Hoffmann and Helmert). Here, N is a numerical parameter for which sensible values include 1000, 10000, 50000, 100000 and 200000. Combine this with the default merge strategy MERGE_LINEAR_CG_GOAL_LEVEL to match the heuristic in the paper.

shrink_bisimulation(max_states=infinity, threshold=1, greedy=true, initialize_by_h=false, group_by_h=false)

• Greedy bisimulation without size bound (called M&S-gop in the IJCAI 2011 paper by Nissim, Hoffmann and Helmert). Combine this with the merge strategy MERGE_LINEAR_REVERSE_LEVEL to match the heuristic in the paper.

shrink_bisimulation(max_states=N, greedy=false, initialize_by_h=true, group_by_h=true)

• Exact bisimulation with a size limit (called DFP-bop in the IJCAI 2011 paper by Nissim, Hoffmann and Helmert), where N is a numerical parameter for which sensible values include 1000, 10000, 50000, 100000 and 200000. Combine this with the merge strategy MERGE_LINEAR_REVERSE_LEVEL to match the heuristic in the paper.

• reduce_labels (bool): enable label reduction. Note: it is hard to fathom a scenario where label reduction is a bad idea. The overhead should be low and the gains in time and memory can be massive. So unless you really know what you're doing, don't set this to false. (The point of this option is to perform controlled experiments on how useful label reduction is exactly.)

• expensive_statistics (bool): show statistics on "unique unlabeled edges" (WARNING: these are *very* slow, i.e. too expensive to show by default (in terms of time and memory). When this is used, the planner prints a big warning on stderr with information on the performance impact. Don't use when benchmarking!)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

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(cost_type=NORMAL, max_states=1000000, pattern=None)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

• max_states (int): maximal number of abstract states in the pattern database

• pattern (list of int): list of variable numbers of the planning task that should be used as pattern. Default: the variables are selected automatically based on a simple greedy strategy.

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(cost_type=NORMAL, patterns=None, combo=false, max_states=1000000)

• cost_type ({NORMAL, ONE, PLUSONE}): Operator cost adjustment type. No matter what this setting is, axioms will always be considered as actions of cost 0 by the heuristics that treat axioms as actions.

  • NORMAL: all actions are accounted for with their real cost

  • ONE: all actions are accounted for as unit cost

  • PLUSONE: all actions are accounted for as their real cost + 1 (except if all actions have original cost 1, in which case cost 1 is used). This is the behaviour known for the heuristics of the LAMA planner. This is intended to be used by the heuristics, not search engines, but is supported for both.

• patterns (list of list of int): list of patterns (which are lists of variable numbers of the planning task) Default: each goal variable is used as a single-variable pattern in the collection.

• combo (bool): use the combo strategy

• max_states (int): maximum abstraction size for combo strategy

Language features supported:

• action costs: supported

• conditional_effects: not supported

• axioms: not supported

Properties:

• admissible: yes

• consistent: yes

• safe: yes

• preferred operators: no

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