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== Delete relaxation constraints ==

Operator-counting constraints based on the delete relaxation. By default the constraints encode an easy-to-compute relaxation of h^+^. With the right settings, these constraints can be used to compute the optimal delete-relaxation heuristic h^+^ (see example below). For details, see

 * Tatsuya Imai and Alex Fukunaga.<<BR>>
 [[https://www.jair.org/index.php/jair/article/download/10972/26119/|On a practical, integer-linear programming model for delete-freetasks and its use as a heuristic for cost-optimal planning]].<<BR>>
 ''Journal of Artificial Intelligence Research'' 54:631-677. 2015.

{{{
delete_relaxation_constraints(use_time_vars=false, use_integer_vars=false)
}}}

 * ''use_time_vars'' (bool): use variables for time steps. With these additional variables the constraints enforce an order between the selected operators. Leaving this off (default) corresponds to the time relaxation by Imai and Fukunaga. Switching it on, can increase the heuristic value but will increase the size of the constraints which has a strong impact on runtime. Constraints involving time variables use a big-M encoding, so they are more useful if used with integer variables.
 * ''use_integer_vars'' (bool): restrict auxiliary variables to integer values. These variables encode whether operators are used, facts are reached, which operator first achieves which fact, and in which order the operators are used. Restricting them to integers generally improves the heuristic value at the cost of increased runtime.
'''Example:''' To compute the optimal delete-relaxation heuristic h^+^, use
{{{
operatorcounting([delete_relaxation_constraints(use_time_vars=true, use_integer_vars=true)], use_integer_operator_counts=true))
}}}
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Computes a set of landmarks in each state using the LM-cut method. For each landmark L the constraint sum_{o in L} Count_o >= 1 is added to the operator counting LP temporarily. After the heuristic value for the state is computed, all temporary constraints are removed again. For details, see
 * Florian Pommerening, Gabriele Röger, Malte Helmert and Blai Bonet.<<BR>>
Computes a set of landmarks in each state using the LM-cut method. For each landmark L the constraint sum_{o in L} Count_o >= 1 is added to the operator-counting LP temporarily. After the heuristic value for the state is computed, all temporary constraints are removed again. For details, see

* Florian Pommerening, Gabriele Roeger, Malte Helmert and Blai Bonet.<<BR>>
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 In ''Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling (ICAPS 2014)'', pp. 226-234. AAAI Press 2014.  In ''Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling (ICAPS 2014)'', pp. 226-234. AAAI Press, 2014.
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 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 22682274. 2013.  In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2268-2274. AAAI Press, 2013.
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== Posthoc optimization constraints for iPDB patterns == == Posthoc optimization constraints ==
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A pattern collection is discovered, using iPDB hillclimbing (see [Doc/[[Doc/Heuristic#iPDB|iPDB]]]).The generator will compute a PDB for each pattern and add the constraint h(s) <= sum_{o in relevant(h)} Count_o. For details, see
 * Florian Pommerening, Gabriele Röger and Malte Helmert.<<BR>>
The generator will compute a PDB for each pattern and add the constraint h(s) <= sum_{o in relevant(h)} Count_o. For details, see

* Florian Pommerening, Gabriele Roeger and Malte Helmert.<<BR>>
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 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2357-2364. 2013.  In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2357-2364. AAAI Press, 2013.
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pho_constraints_ipdb(pdb_max_size=2000000, collection_max_size=20000000, num_samples=1000, min_improvement=10, max_time=infinity) pho_constraints(patterns=systematic(2))
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 * ''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.
== Posthoc optimization constraints for manually specified patterns ==
The generator will compute a PDB for each pattern and add the constraint h(s) <= sum_{o in relevant(h)} Count_o. For details, see
 * Florian Pommerening, Gabriele Röger and Malte Helmert.<<BR>>
 [[http://ijcai.org/papers13/Papers/IJCAI13-347.pdf|Getting the Most Out of Pattern Databases for Classical Planning]].<<BR>>
 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2357-2364. 2013.
 * ''patterns'' ([[Doc/PatternCollectionGenerator|PatternCollectionGenerator]]): pattern generation method
== State equation constraints ==
For each fact, a permanent constraint is added that considers the net change of the fact, i.e., the total number of times the fact is added minus the total number of times is removed. The bounds of each constraint depend on the current state and the goal state and are updated in each state. For details, see

 * Menkes van den Briel, J. Benton, Subbarao Kambhampati and Thomas Vossen.<<BR>>
 [[http://link.springer.com/chapter/10.1007/978-3-540-74970-7_46|An LP-based heuristic for optimal planning]].<<BR>>
 In ''Proceedings of the Thirteenth International Conference on Principles and Practice of Constraint Programming (CP 2007)'', pp. 651-665. Springer-Verlag, 2007.

 * Blai Bonet.<<BR>>
 [[http://ijcai.org/papers13/Papers/IJCAI13-335.pdf|An admissible heuristic for SAS+ planning obtained from the state equation]].<<BR>>
 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2268-2274. AAAI Press, 2013.

 * Florian Pommerening, Gabriele Roeger, Malte Helmert and Blai Bonet.<<BR>>
 [[http://www.aaai.org/ocs/index.php/ICAPS/ICAPS14/paper/view/7892/8031|LP-based Heuristics for Cost-optimal Planning]].<<BR>>
 In ''Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling (ICAPS 2014)'', pp. 226-234. AAAI Press, 2014.
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pho_constraints_manual(patterns=<none>, combo=false, max_states=1000000) state_equation_constraints(verbosity=normal)
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 * ''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 [1, infinity]): maximum abstraction size for combo strategy
== Posthoc optimization constraints for systematically generated patterns ==
All (interesting) patterns with up to pattern_max_size variables are generated. The generator will compute a PDB for each pattern and add the constraint h(s) <= sum_{o in relevant(h)} Count_o. For details, see
 * Florian Pommerening, Gabriele Röger and Malte Helmert.<<BR>>
 [[http://ijcai.org/papers13/Papers/IJCAI13-347.pdf|Getting the Most Out of Pattern Databases for Classical Planning]].<<BR>>
 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2357-2364. 2013.
 * ''verbosity'' ({silent, normal, verbose, debug}): Option to specify the verbosity level.
  * {{{silent}}}: only the most basic output
  * {{{normal}}}: relevant information to monitor progress
  * {{{verbose}}}: full output
  * {{{debug}}}: like verbose with additional debug output
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{{{
pho_constraints_systematic(pattern_max_size=1, only_interesting_patterns=true)
}}}

 * ''pattern_max_size'' (int): max number of variables per pattern
 * ''only_interesting_patterns'' (bool): Only consider the union of two disjoint patterns if the union has more information than the individual patterns.
== State equation constraints ==
For each fact, a permanent constraint is added that considers the net change of the fact, i.e., the total number of times the fact is added minus the total number of times is removed. The bounds of each constraint depend on the current state and the goal state and are updated in each state. For details, see
 * Menkes van den Briel, J. Benton, Subbarao Kambhampati and Thomas Vossen.<<BR>>
 [[http://link.springer.com/chapter/10.1007/978-3-540-74970-7_46|An LP-based heuristic for optimal planning]].<<BR>>
 In ''Proceedings of the Thirteenth International Conference on Principles and Practice of Constraint Programming (CP 2007)'', pp. 651–665. 2007.
 * Blai Bonet.<<BR>>
 [[http://ijcai.org/papers13/Papers/IJCAI13-335.pdf|An admissible heuristic for SAS+ planning obtained from the state equation]].<<BR>>
 In ''Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI 2013)'', pp. 2268–2274. 2013.
 * Florian Pommerening, Gabriele Röger, Malte Helmert and Blai Bonet.<<BR>>
 [[http://www.aaai.org/ocs/index.php/ICAPS/ICAPS14/paper/view/7892/8031|LP-based Heuristics for Cost-optimal Planning]].<<BR>>
 In ''Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling (ICAPS 2014)'', pp. 226-234. AAAI Press 2014.

{{{
state_equation_constraints()
}}}

/* moin code generated by txt2tags 2.6b (http://txt2tags.sf.net) */
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Delete relaxation constraints

Operator-counting constraints based on the delete relaxation. By default the constraints encode an easy-to-compute relaxation of h+. With the right settings, these constraints can be used to compute the optimal delete-relaxation heuristic h+ (see example below). For details, see

delete_relaxation_constraints(use_time_vars=false, use_integer_vars=false)
  • use_time_vars (bool): use variables for time steps. With these additional variables the constraints enforce an order between the selected operators. Leaving this off (default) corresponds to the time relaxation by Imai and Fukunaga. Switching it on, can increase the heuristic value but will increase the size of the constraints which has a strong impact on runtime. Constraints involving time variables use a big-M encoding, so they are more useful if used with integer variables.

  • use_integer_vars (bool): restrict auxiliary variables to integer values. These variables encode whether operators are used, facts are reached, which operator first achieves which fact, and in which order the operators are used. Restricting them to integers generally improves the heuristic value at the cost of increased runtime.

Example: To compute the optimal delete-relaxation heuristic h+, use

operatorcounting([delete_relaxation_constraints(use_time_vars=true, use_integer_vars=true)], use_integer_operator_counts=true))

LM-cut landmark constraints

Computes a set of landmarks in each state using the LM-cut method. For each landmark L the constraint sum_{o in L} Count_o >= 1 is added to the operator-counting LP temporarily. After the heuristic value for the state is computed, all temporary constraints are removed again. For details, see

lmcut_constraints()

Posthoc optimization constraints

The generator will compute a PDB for each pattern and add the constraint h(s) <= sum_{o in relevant(h)} Count_o. For details, see

pho_constraints(patterns=systematic(2))

State equation constraints

For each fact, a permanent constraint is added that considers the net change of the fact, i.e., the total number of times the fact is added minus the total number of times is removed. The bounds of each constraint depend on the current state and the goal state and are updated in each state. For details, see

state_equation_constraints(verbosity=normal)
  • verbosity ({silent, normal, verbose, debug}): Option to specify the verbosity level.

    • silent: only the most basic output

    • normal: relevant information to monitor progress

    • verbose: full output

    • debug: like verbose with additional debug output

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