Contents

## A* search (eager)

A* is a special case of eager best first search that uses g+h as f-function. We break ties using the evaluator. Closed nodes are re-opened.

astar(eval, mpd=false, pruning=null(), cost_type=NORMAL, bound=infinity, max_time=infinity)

*eval*(ScalarEvaluator): evaluator for h-value*mpd*(bool): use multi-path dependence (LM-A*)*pruning*(PruningMethod): Pruning methods can prune or reorder the set of applicable operators in each state and thereby influence the number and order of successor states that are considered.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**mpd option:** This option is currently only present for the A* algorithm and not for the more general eager search, because the current implementation of multi-path depedence does not support general open lists.

### Equivalent statements using general eager search

--search astar(evaluator)

is equivalent to

--heuristic h=evaluator --search eager(tiebreaking([sum([g(), h]), h], unsafe_pruning=false), reopen_closed=true, f_eval=sum([g(), h]))

## Eager best-first search

eager(open, reopen_closed=false, f_eval=<none>, preferred=[], pruning=null(), cost_type=NORMAL, bound=infinity, max_time=infinity)

*open*(OpenList): open list*reopen_closed*(bool): reopen closed nodes*f_eval*(ScalarEvaluator): set evaluator for jump statistics. (Optional; if no evaluator is used, jump statistics will not be displayed.)*preferred*(list of Heuristic): use preferred operators of these heuristics*pruning*(PruningMethod): Pruning methods can prune or reorder the set of applicable operators in each state and thereby influence the number and order of successor states that are considered.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

## Greedy search (eager)

eager_greedy(evals, preferred=[], boost=0, pruning=null(), cost_type=NORMAL, bound=infinity, max_time=infinity)

*evals*(list of ScalarEvaluator): scalar evaluators*preferred*(list of Heuristic): use preferred operators of these heuristics*boost*(int): boost value for preferred operator open lists*pruning*(PruningMethod): Pruning methods can prune or reorder the set of applicable operators in each state and thereby influence the number and order of successor states that are considered.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**Open list:** In most cases, eager greedy best first search uses an alternation open list with one queue for each evaluator. If preferred operator heuristics are used, it adds an extra queue for each of these evaluators that includes only the nodes that are generated with a preferred operator. If only one evaluator and no preferred operator heuristic is used, the search does not use an alternation open list but a standard open list with only one queue.

**Closed nodes:** Closed node are not re-opened

### Equivalent statements using general eager search

--heuristic h2=eval2 --search eager_greedy([eval1, h2], preferred=h2, boost=100)

is equivalent to

--heuristic h1=eval1 --heuristic h2=eval2 --search eager(alt([single(h1), single(h1, pref_only=true), single(h2), single(h2, pref_only=true)], boost=100), preferred=h2)

--search eager_greedy([eval1, eval2])

is equivalent to

--search eager(alt([single(eval1), single(eval2)]))

--heuristic h1=eval1 --search eager_greedy(h1, preferred=h1)

is equivalent to

--heuristic h1=eval1 --search eager(alt([single(h1), single(h1, pref_only=true)]), preferred=h1)

--search eager_greedy(eval1)

is equivalent to

--search eager(single(eval1))

## Lazy enforced hill-climbing

ehc(h, preferred_usage=PRUNE_BY_PREFERRED, preferred=[], cost_type=NORMAL, bound=infinity, max_time=infinity)

*h*(Heuristic): heuristic*preferred_usage*({PRUNE_BY_PREFERRED, RANK_PREFERRED_FIRST}): preferred operator usage*preferred*(list of Heuristic): use preferred operators of these heuristics*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

## Iterated search

iterated(engine_configs, pass_bound=true, repeat_last=false, continue_on_fail=false, continue_on_solve=true, cost_type=NORMAL, bound=infinity, max_time=infinity)

*engine_configs*(list of ParseTree (this just means the input is parsed at a later point. The real type is probably a search engine.)): list of search engines for each phase*pass_bound*(bool): use bound from previous search. The bound is the real cost of the plan found before, regardless of the cost_type parameter.*repeat_last*(bool): repeat last phase of search*continue_on_fail*(bool): continue search after no solution found*continue_on_solve*(bool): continue search after solution found*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**Note 1:** We don't cache heuristic values between search iterations at the moment. If you perform a LAMA-style iterative search, heuristic values will be computed multiple times.

**Note 2:** The configuration

--search "iterated([lazy_wastar(merge_and_shrink(),w=10), lazy_wastar(merge_and_shrink(),w=5), lazy_wastar(merge_and_shrink(),w=3), lazy_wastar(merge_and_shrink(),w=2), lazy_wastar(merge_and_shrink(),w=1)])"

would perform the preprocessing phase of the merge and shrink heuristic 5 times (once before each iteration).

To avoid this, use heuristic predefinition, which avoids duplicate preprocessing, as follows:

--heuristic "h=merge_and_shrink()" --search "iterated([lazy_wastar(h,w=10), lazy_wastar(h,w=5), lazy_wastar(h,w=3), lazy_wastar(h,w=2), lazy_wastar(h,w=1)])"

**Note 3:** If you reuse the same landmark count heuristic (using heuristic predefinition) between iterations, the path data (that is, landmark status for each visited state) will be saved between iterations.

## Lazy best-first search

lazy(open, reopen_closed=false, preferred=[], randomize_successors=false, preferred_successors_first=false, random_seed=-1, cost_type=NORMAL, bound=infinity, max_time=infinity)

*open*(OpenList): open list*reopen_closed*(bool): reopen closed nodes*preferred*(list of Heuristic): use preferred operators of these heuristics*randomize_successors*(bool): randomize the order in which successors are generated*preferred_successors_first*(bool): consider preferred operators first*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.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**Successor ordering:** When using randomize_successors=true and preferred_successors_first=true, randomization happens before preferred operators are moved to the front.

## Greedy search (lazy)

lazy_greedy(evals, preferred=[], reopen_closed=false, boost=1000, randomize_successors=false, preferred_successors_first=false, random_seed=-1, cost_type=NORMAL, bound=infinity, max_time=infinity)

*evals*(list of ScalarEvaluator): scalar evaluators*preferred*(list of Heuristic): use preferred operators of these heuristics*reopen_closed*(bool): reopen closed nodes*boost*(int): boost value for alternation queues that are restricted to preferred operator nodes*randomize_successors*(bool): randomize the order in which successors are generated*preferred_successors_first*(bool): consider preferred operators first*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.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**Open lists:** In most cases, lazy greedy best first search uses an alternation open list with one queue for each evaluator. If preferred operator heuristics are used, it adds an extra queue for each of these evaluators that includes only the nodes that are generated with a preferred operator. If only one evaluator and no preferred operator heuristic is used, the search does not use an alternation open list but a standard open list with only one queue.

### Equivalent statements using general lazy search

--heuristic h2=eval2 --search lazy_greedy([eval1, h2], preferred=h2, boost=100)

is equivalent to

--heuristic h1=eval1 --heuristic h2=eval2 --search lazy(alt([single(h1), single(h1, pref_only=true), single(h2), single(h2, pref_only=true)], boost=100), preferred=h2)

--search lazy_greedy([eval1, eval2], boost=100)

is equivalent to

--search lazy(alt([single(eval1), single(eval2)], boost=100))

--heuristic h1=eval1 --search lazy_greedy(h1, preferred=h1)

is equivalent to

--heuristic h1=eval1 --search lazy(alt([single(h1), single(h1, pref_only=true)], boost=1000), preferred=h1)

--search lazy_greedy(eval1)

is equivalent to

--search lazy(single(eval1))

**Successor ordering:** When using randomize_successors=true and preferred_successors_first=true, randomization happens before preferred operators are moved to the front.

## (Weighted) A* search (lazy)

Weighted A* is a special case of lazy best first search.

lazy_wastar(evals, preferred=[], reopen_closed=true, boost=1000, w=1, randomize_successors=false, preferred_successors_first=false, random_seed=-1, cost_type=NORMAL, bound=infinity, max_time=infinity)

*evals*(list of ScalarEvaluator): scalar evaluators*preferred*(list of Heuristic): use preferred operators of these heuristics*reopen_closed*(bool): reopen closed nodes*boost*(int): boost value for preferred operator open lists*w*(int): heuristic weight*randomize_successors*(bool): randomize the order in which successors are generated*preferred_successors_first*(bool): consider preferred operators first*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.*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.

*bound*(int): exclusive depth bound on g-values. Cutoffs are always performed according to the real cost, regardless of the cost_type parameter*max_time*(double): maximum time in seconds the search is allowed to run for. The timeout is only checked after each complete search step (usually a node expansion), so the actual runtime can be arbitrarily longer. Therefore, this parameter should not be used for time-limiting experiments. Timed-out searches are treated as failed searches, just like incomplete search algorithms that exhaust their search space.

**Open lists:** In the general case, it uses an alternation open list with one queue for each evaluator h that ranks the nodes by g + w * h. If preferred operator heuristics are used, it adds for each of the evaluators another such queue that only inserts nodes that are generated by preferred operators. In the special case with only one evaluator and no preferred operator heuristics, it uses a single queue that is ranked by g + w * h.

### Equivalent statements using general lazy search

--heuristic h1=eval1 --search lazy_wastar([h1, eval2], w=2, preferred=h1, bound=100, boost=500)

is equivalent to

--heuristic h1=eval1 --heuristic h2=eval2 --search lazy(alt([single(sum([g(), weight(h1, 2)])), single(sum([g(), weight(h1, 2)]), pref_only=true), single(sum([g(), weight(h2, 2)])), single(sum([g(), weight(h2, 2)]), pref_only=true)], boost=500), preferred=h1, reopen_closed=true, bound=100)

--search lazy_wastar([eval1, eval2], w=2, bound=100)

is equivalent to

--search lazy(alt([single(sum([g(), weight(eval1, 2)])), single(sum([g(), weight(eval2, 2)]))], boost=1000), reopen_closed=true, bound=100)

--search lazy_wastar([eval1, eval2], bound=100, boost=0)

is equivalent to

--search lazy(alt([single(sum([g(), eval1])), single(sum([g(), eval2]))]) reopen_closed=true, bound=100)

--search lazy_wastar(eval1, w=2)

is equivalent to

--search lazy(single(sum([g(), weight(eval1, 2)])), reopen_closed=true)

**Successor ordering:** When using randomize_successors=true and preferred_successors_first=true, randomization happens before preferred operators are moved to the front.