The AIPS-98 Planning Competition

22 Pages·2000·0.14 MB·English

by  Derek Long

AI Magazine Volume 21 Number 2 (2000) (© AAAI)
Articles
The AIPS-98
Planning Competition
Edited by Derek Long,
with Henry Kautz and Bart Selman (BLACKBOX team);
Blai Bonet and Hector Geffner (HSP team);
Jana Koehler, Michael Brenner, Joerg Hoffmann,
and Frank Rittinger (IPP team);
Corin R. Anderson, Daniel S. Weld, and David E. Smith (SGP team);
and Maria Fox and Derek Long (STAN team)
(cid:2) In 1998, the international planning community such as the Message Understanding Competi-
was invited to take part in the first planning com- tion (MUC) series, sponsored by the Defense
petition, hosted by the Artificial Intelligence Plan- Advanced Research Projects Agency (DARPA);
ning Systems Conference, to provide a new impe- the Text Retrieval Competition (TREC) series,
tus for empirical evaluation and direct comparison sponsored by National Institute of Standards
of automatic domain-independent planning sys- and Technology and DARPA; and the Turing
tems. This article describes the systems that com-
Competition. These competitions have stimu-
peted in the event, examines the results, and con-
lated work, but they also represent a serious
siders some of the implications for the future of
investment in effort for the competition orga-
the field.
nizers and competitors. It is a formidable task
to create a collection of tasks that is realistically
within the reach of the existing technology
The International Artificial Intelligence
and that represents an adequate challenge and
Planning Systems Conference (AIPS-98),
points the way for the field to develop. Admin-
held at Carnegie Mellon University in
istrative problems represent a huge overhead to
Pittsburgh in June 1998, played host to the first
this task: A common language must be devel-
world planning competition. Competitors
oped that allows problems to be specified and
were invited to come and compete on a collec-
results evaluated, scoring mechanisms must be
tion of domains and associated problems, sight
determined, and the environment must be
unseen, using whatever planning technology
selected and competitors forewarned. Tribute
they wanted. Tracks were offered for STRIPS, ADL, should be paid to Drew McDermott for the role
and HTNplanning, but in the event, only STRIPS he played in almost single-handedly executing
and ADLwere entered. Indeed, ADLsaw only two all these tasks, with support from the competi-
competitors: IPP (Koehler et al. 1997) and SGP tion committee.
(Anderson and Weld 1998). IPPgave a convinc- For the competitors, the competition repre-
ingly superior performance over SGP, the only sents a challenge to the robustness of their
Lisp-based planner in the competition, in a software, and demands work in meeting the
single round playoff. The STRIPStrack originally specifications for both input and output for-
attracted some 9 or 10 declarations of intent to mats, while they continue to develop and
take part. This article gives an account of the enhance the basic functions of their systems.
competition as seen by the competitors who The development of PDDL (McDermott and
actually arrived in Pittsburgh and took part in AIPS 1998) as the common language for the
the two tracks. competition problem specifications was an
Competitions as a way to evaluate and pro- important step in the progress of the competi-
mote progress in various fields have precedents, tion. A challenge to the competitors was to
Copyright © 2000, American Association for Artificial Intelligence. All rights reserved. 0738-4602-2000 / $2.00 SUMMER 2000 13
Articles
adapt to the many minor changes in this lan- domains that planners can realistically be
guage as it steadily stabilized. Another impor- expected to handle. All the planners in the
tant problem was anticipating the demands of competition were solving some instances of
the competition domains. All the planners that problems in times measured in milliseconds,
eventually competed are domain-independent including nontrivial instances. Second, the col-
planners that require little or no manual guid- lection of planners that are sufficiently robust
ance in selecting run-time behavior; however, for release into the general research communi-
the performance of all the planners can be ty, requiring no additional special-purpose
affected dramatically by the design of the domain encoding beyond STRIPS or ADL, and
encoding of the domain and problem specifica- that can tackle significant instances in reason-
tions. The criteria by which success was to be able time is still small. The qualifications are
judged were also volatile: Trade-offs between important, however, because there are clearly
…
the planning time and the optimality of the many more planners being actively worked on
the collection plan produced were a controversial balancing that are either still insufficiently robust to be
act. Optimality was measured purely by the entered into a competition event or require too
of planners
number of steps in the plan for the STRIPStrack; much careful encoding of their domains to be
that are so, planners producing optimal parallel plans able to compete automatically across large
might well find themselves significantly out- numbers of problems, sight unseen. It is hoped
sufficiently
performed by planners concentrating on that this situation changes as the competition
robust for sequential plan optimality. Furthermore, the is repeated in future years, with a widening of
release into selection of domains to be used in the compe- the field and a broadening of the range of tech-
tition was hard. All the competitors had some nology being exposed. This latter point is par-
the general
collection of favored domains that showcased ticularly poignant because at AIPS-98, three of
research the characteristics of their planners. In princi- the five planners involved were directly built
ple, all competitors had the opportunity to on GRAPHPLAN (Blum and Furst 1997) (IPP, SGP,
community,
propose domains for use, but the constraints and STAN), one exploited GRAPHPLANtechnology
requiring no on the time available for the competition made (BLACKBOX), and only one was independent of
additional it impossible to use all of them. GRAPHPLANin every way (HSP). The role of GRAPH-
These various challenges thinned the field so PLAN in shaping the domain-independent–
special- that the competition eventually hosted four planning research field at the time of the com-
purpose STRIPS planners and two ADL planners (IPP took petition is so significant that a short summary
part in both tracks). It was apparent that sever- of the features of the system is included in this
domain
al others would liked to have participated but section.
encoding were unable to meet the input and output cri- Interestingly, all five planners used a full
teria within the time scales that were imposed instantiation of actions as a prelude to search,
beyond STRIPS by the organization of the competition. explaining in part the difficulties all the plan-
or ADL, and This article presents the competitors’ impres- ners experienced with problems that involved
sions of the competition and a summary of the huge numbers of ground-operator instances.
that can
planning technology with which they compet- This point is discussed further in the next sec-
tackle ed. The Competing Planners includes a series tion. It is unfortunate that no constraint-post-
significant of short subsections that highlight features of ing planner, avoiding the initial grounding of
the individual planners that took part and action schemas, took part to compare perfor-
instances in briefly explores the issues that have led to the mance. Some informal experiments withPRODI-
reasonable differences in the systems that competed. GY(Fink and Veloso 1996) during the competi-
Review of Results examines the results of the tion suggested that it might have performed
time is still
competition, analyzing the issues they raise significantly better than the other planners in
small. and pointing out some of the questions that some domains, but it was completely outper-
they leave unanswered. Finally, The Future formed in others. This pattern hints at one of
considers the future of the competition and the the most interesting issues that the competi-
role it might play in pushing forward planning tion raised (discussed in more detail in the next
research. section): Different planning technologies,
despite being domain independent, are actual-
The Competing Planners ly highly sensitive to both domain and prob-
lem instance in determining actual perfor-
The competition highlighted several facets of mance.
the current state of the planning research field. This section proceeds with a summary of
First, even within the last couple of years, the GRAPHPLANbefore proceeding with an examina-
technology has advanced dramatically in terms tion of each of the competing systems in turn.
of the size of problems in standard benchmark The organization of this sequence reflects the
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Articles
relationship between each system and GRAPH- actions are considered mutually exclusive if the
PLAN. IPP, SGP, and STAN are essentially exten- negative effects of one intersects with the pre-
sions of GRAPHPLAN, each exploring different conditions or positive effects of the other or if
directions. BLACKBOX exploits the core GRAPH- they have mutually exclusive preconditions.
PLANdata structure but carries out its search for Facts are mutually exclusive if all pairs of
a plan in an entirely different way. Finally, HSP actions that achieve the two facts are them-
is an entirely different approach to planning. selves mutually exclusive. The graph is seeded
with an initial layer representing the facts true
GRAPHPLAN in the initial state. The graph is constructed
GRAPHPLANis an exceptionally influential plan- until a layer of facts includes all the plan goals
ning system devised by Blum and Furst (1997). as a collection of nonpairwise mutually exclu-
Since it was first developed, there have been sive nodes in a layer.
several insightful papers that seek to explore its Search is goal directed, starting with the last
relationship with other planning approaches layer of the graph. The goals are identified in
and with constraint solving (Kambhampati the final layer, and a collection of nonpairwise
1999; Kambhampati, Lambrecht, and Parker mutually exclusive actions in the preceding
1997). There has also been considerable activi- action layer is found that includes all the goals
ty devoted to extending and improving the as positive effects. The preconditions of these
underlying algorithms. actions are then used as the seed for a recursive
GRAPHPLAN constructs plans in three phases: search from the immediately preceding layer of
First, the action schemas are fully instantiated facts. The process successfully identifies a plan
to identify the complete set of ground actions if the search reaches a collection of facts in the
for the planning problem. Second, a funda- initial layer. It should be noted that because
mental data structure, called the plan graph, is more than one action can be used in a given The key to
constructed. Third, the plan graph is searched layer of the graph, the plan can include parallel
understanding
in an attempt to identify a plan structure with- actions. Therefore, GRAPHPLANproduces parallel-
in it. If this process fails, the graph is extended, optimal plans that are not always sequentially GRAPHPLAN
and a new search is initiated. This process iter- optimal. If the search fails to produce a plan
then is to
ates until a plan is found, or certain terminat- (including the recursively initiated searches in
ing conditions are encountered, proving that preceding layers), the collection of goals that understand
there is no plan. The interleaved graph-con- cannot be solved is recorded as unsolvable at the
struction and -search processes amount to an the corresponding layer. During subsequent
plan-graph
iterated depth-first search for a plan, ensuring searches, goals are checked against previously
a systematic search guaranteed to find the recorded unsolvable sets, and if they contain data
shortest plan structure. such a set as a subset, then no search is initiat-
structure.
The key to understanding GRAPHPLANthen is ed, but a failure is reported immediately. This
to understand the plan-graph data structure. approach can save a huge amount of wasted
This structure is built as a series of layers of search.
nodes. Nodes in alternate layers represent If the search fails to find a plan for a top-level
ground facts and ground actions. Arcs are cre- goal set, then the graph is extended by another
ated between nodes that represent important action and fact layer, and the search recom-
relationships. Fact nodes are connected to mences. It has been proved (Blum and Furst
action nodes in the immediately succeeding 1997) that certain signals in the data structure
layer when they represent preconditions of the will infallibly demonstrate a problem to be
actions. Actions are connected to the facts in unsolvable, so that the algorithm is not only
the immediately succeeding layer that they sound and complete but also terminating.
achieve as positive effects. They are also con- GRAPHPLANhas had a dramatic impact on the
nected (by differently labeled edges) to their planning community, effectively displacing
negative effects (facts they delete). GRAPHPLAN the earlier nonlinear planning technology as
also inserts special actions, called noops,at each the foundation of fast and effective planners.
action layer, which have the role of causing Nevertheless, it suffers from significant prob-
facts at the preceding layer to persist into the lems. The need to instantiate actions, the stor-
next layer. Using a noop to achieve a goal is age of the plan graph itself, and the records of
equivalent to achieving the goal early and unsolvable goal sets together represent a formi-
allowing it to persist while other actions occur. dable demand on memory. It is not uncom-
Finally, and most significantly, pairs of actions mon to require over 100 megabytes of random-
in the same layer, and pairs of facts in the same access memory (RAM) to solve significant
layer, are connected if they are mutually incon- problems, and memory constraints represent
sistent (or mutually exclusive—”mutex”). Two one of the barriers to solving much larger plan-
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PDDL first-order formulas into the disjunctive
normal form required by IPPbut, in contrast to
domain problem that approach, does not expand out condition-
al action effects. Instead, IPP uses a special
extension of the GRAPHPLANmachinery to han-
dle conditional effects directly. In addition, IPP
represented a first complete reimplementation
PDDL parser of GRAPHPLAN and incorporated many major
PDDL preprocessing improvements in the underlying data struc-
tures. These efforts give IPPa dramatically better
time and space performance than the original
GRAPHPLAN implementation. A particular im-
provement is that IPPexploits a new data struc-
ture to support the recording of goal sets for
RIFO meta strategy
which search has failed (Hoffmann and
Koehler 1999). This data structure makes it pos-
sible for a full subset test to be used efficiently
when checking to see if a new goal set includes
IPP 3.3
a subset already recorded as unsolvable, allow-
ing IPP to make more effective use of these
records.
A further innovation introduced in the IPP
system is the use of a filter to remove facts and
actions from the plan graph that are consid-
PDDL output ered irrelevant to the planning problem. This
process has the potential to improve the per-
formance of the planning system dramatically,
reducing both storage requirements and search
time. This system, RIFO (Nebel, Dimopoulos,
and Koehler 1997), is heuristic and can be con-
plan
trolled to prune the graph more or less aggres-
sively. The competition version of IPP intro-
duces a control harness that uses various
parameters measured from the domain and
Figure 1. IPPArchitecture. problem instance to determine how aggressive-
ly to apply the RIFOmechanism.
ning problems with this technology. Further, The RIFO Metastrategy The competition
the backward search through ground actions version of IPP exploits a metastrategy,
“wrapped” around the planner (figure 1), that
forces the planner to make decisions about
is activated when two threshold parameters—
parts of a plan long before the information is
(1) the number of objects and (2) the number
available to determine how to make the deci-
of ground actions—are exceeded by a planning
sion intelligently. These issues, among others,
problem. These parameters can be set by hand
remain to be resolved if GRAPHPLAN is to have
or can be preset. The strategy configures the
longevity as a planning solution.
RIFOsubsystem within IPP.
IPP RIFOwas developed to cope with the problem
of irrelevant information in plan graphs. Usu-
The IPP (1998) planning system extends the ally, when building a plan graph, a GRAPHPLAN-
GRAPHPLANsystem in several significant ways. In based planner will add a great many facts and
particular, IPP was developed to demonstrate actions that are totally irrelevant to solving the
the extension of the GRAPHPLAN approach to planning problem at hand. By building a tree
allow it to handle a larger subset of ADL (Ped- of possible actions backwards from the goal set,
nault 1989). These extensions include the use ignoring negative effects of actions, RIFO can
of negative preconditions and conditional identify what information is or might be rele-
effects, allowing IPPto enter the ADLtrack of the vant to a problem. This identification allows
competition. To help in handling the ADL the system to exclude irrelevant information.
extensions in PDDL, IPP uses a preprocessing The pruning can be applied at various degrees
phase based on the proposal first documented of strength but at the price of increasing danger
by Gazen and Knoblock (1997) that translates of incompleteness: Overaggressive pruning can
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lead to too many actions being ruled out, mak- achieve this objective because of an additional
ing the planning problem unsolvable. The feature of IPP: the exploitation of inertia, or
metastrategy runs RIFO on the problem input unchanging facts in the domain, to carry out
using the strongest reduction heuristic, which constant folding among the grounded actions
selects a minimal set of relevant initial facts and reduce them to simpler forms. This process
and objects and keeps only those ground represents an important element of the collec-
actions that were used in the tree of actions tion of techniques being developed to control
built from the goals to the initial state. The the size of the plan graph for GRAPHPLAN-based
remainder of the initial state facts, objects (and approaches to planning.
facts and actions including them), and other
actions are pruned from the graph to yield a SGP
reduced problem to be exposed to search. SENSORY GRAPHPLAN (SGP) is a sound, complete
If IPP determines the reduced problem to be planner also built following GRAPHPLAN. SGP
unsolvable, which it usually does quickly, includes support for conditional effects, uni-
because of the effective termination test inher- versal and existential quantification, uncer-
ent to GRAPHPLAN, the search space is enlarged by tainty, and sensing actions. SGP only entered
applying RIFO again using a weaker pruning the ADL track of the competition to demon-
heuristic, restoring all the previously excluded strate these extensions to the underlying
actions that use objects that are newly judged GRAPHPLANmachinery. SGPwas the only planner
to be potentially relevant. If IPP still cannot written in Lisp to enter the competition and,
solve the problem, the original search space is despite the performance limitations from the
fully restored to retain completeness of the language, competed well.
planner, in the worst case leading to some over- SGPhas a number of features that set it apart
head if both RIFOheuristics turn a solvable plan- from the other GRAPHPLAN-based planners. These
ning problem into an unsolvable one or if a unique features, described in the following sub-
completely unsolvable problem is investigated. sections, are factored expansion for handling
Handling of Conditional Effects in IPP conditional effects and the ability to handle
Probably the most important ADL extension uncertainty and sensing actions. SGP is written
in well-documented Lisp code and can be down-
handled by IPPis the use of conditional effects.
Gazen and Knoblock (1997) observe that all loaded from the SGP home page (SGP 1998). SGP
continues to be supported by the University of
the other commonly handled ADL extensions
Washington, with new bug fixes and new releas-
can be converted into STRIPSin reasonable time
es being produced as appropriate.
but that conditional effects lead to a potential-
ly crippling combinatorial cost if an attempt is Factored Expansion of Conditional
made to deal with them in this way. Effects Many of the expressive features of ADL
IPP represents conditional effects directly in are easy to implement in GRAPHPLAN, but han-
planning graphs and also propagates mutual dling conditional effects is surprisingly tricky.
exclusion relationships between facts occur- Conditional effects allow the description of a
ring in conditional effects and their effect con- single action with context-dependent effects.
ditions. However, it does not extend the notion The basic idea is simple: A special when clause
of mutual exclusion between actions, as is introduced into the syntax of action effects.
defined in GRAPHPLAN. This fact contrasts with When takes two arguments: (1) an antecedent
the approach taken in SGP, discussed later, and (2) a consequent. Execution of the action
where a propagation of mutual exclusion rela- will have the consequent’s effect just in case
tions over actions is proposed. that the antecedent is true immediately before
Actions with conditional effects are still execution (much like the preconditions of the
treated as atomic units in IPP, but SGP creates action determine if execution itself is legal),
components similar to GRAPHPLAN’s STRIPS which is exactly why handling actions with
actions that represent each conditional effect conditional effects is tricky: The outcomes of
in the graph. Thus, there is the possibility of the actions depend on the state of the world
marking component nodes as exclusive as well when the action is executed.
as, it is claimed, a performance benefit. A Factored expansion was first described in
detailed discussion of the relative merits of the Anderson and Weld (1998), where it was com-
two approaches is beyond the scope of this arti- pared to full expansion (Gazen and Knoblock
cle but remains an interesting area of debate in 1997) and the conditional-effects handling
the GRAPHPLANcommunity. method of IPP. The idea behind factored expan-
Interestingly, the movie domain, which was sion is twofold: First, all actions that contain
designed to explore the differences in the conditional effects are factored into compo-
approaches to conditional effects, failed to nents, with a single effect (conditional or
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unconditional) in each component. Each com- edge of the world at plan time and assume that
ponent can then be treated, more or less, just the outcome of actions is certain. Although
like a STRIPS action. Second, when the compo- this assumption simplifies the planning
nents are being examined for graph expansion process, it is an unrealistic one. SGPrelaxes the
and backtracking search, the interaction assumption that the agent knows the state of
between components from the same action is the entire world a priori.
considered. In particular, there is the new con- The first step in relaxing this assumption is
cept of component induction: Component C to allow the initial state to include propositions
n
induces C at level i if it is impossible to execute whose truth values are uncertain (either true or
k
Cnwithout executing Ck. false). Internally, SGP represents this sort of
Component induction leads to changes in uncertainty by keeping track of each possible
both the GRAPHPLANmutual-exclusion rules and world. For example, if both propositions Pand
in the backtracking search for a solution. The Q are uncertain, then there are four possible
change to the mutual-exclusion rules is the worlds: (1) Pand Q, (2) Pand not Q,(3) notP
addition of a new rule that can identify more and Q, and (4) not Pand not Q. For each possi-
mutual-exclusion relations: Two components ble world, SGPbuilds and maintains a separate
C and C at level i are mutually exclusive if planning graph. This task is complicated by the
n m
there exists a third componentC that is mutu- fact that because of conditional effects, the out-
k
ally exclusive with C , and C is induced by C come of an action might be different depend-
m k n
at level i. The change to the backtracking ing on the world it is executed in. It should be
search requires that when a component is noted here that SGPmakes the assumption that
selected to establish a goal, all other compo- an uncertain proposition might be true or false
nents from the same action instance must also but does not make any assumptions about
be considered. probabilities (SGP simply records that a propo-
An example of a domain where the factored sition is uncertain and does not associate a
expansion approach shows its strength is the numeric weight with each possibility).
movie domain. The goal of the movie domain The second step in relaxing the complete
is to collect snacks and then watch a movie. knowledge assumption is to limit the agent’s
Before the movie can be “watched,” the movie observational powers to explicit sensing actions.
must be rewound, and the video cassette Sensing actionsare actions in the domain whose
recorder’s (VCR) counter must be set to zero. effects include a special sense statement. Sense
Consider what the planning graph looks like statements are used to let the agent query the
after one level has been built: The VCR’s world for the truth value of a proposition. Based
counter can be reset, the tape can be rewound, on the sensed truth value, the agent can then
and snacks can be fetched. The key thing, how- refine the subset of possible worlds it is in (for
ever, is that the actions to rewind the movie example, if a proposition Pis sensed to be true,
and to reset the VCR’s counter are mutually then the agent knows that it is in one of the pos-
exclusive only if their conditional effects are sible worlds in which Pis true).
considered. The IPPmethod of handling condi- Given the set of planning graphs (one for
tional effects does not find this mutual-exclu- each possible world) and the set of actions,
sion relationship, and thus, IPP must perform including sensing actions, SGPbuilds a plan that
an exhaustive search of the planning graph to will achieve the goals in all possible worlds. To
determine that no plan yet exists. guarantee success in each possible world, the
SGP, however, can identify the induced plan can include actions that are to be executed
mutual-exclusion relationship between the only in some of the possible worlds. Thus, the
two actions. Thus, SGPimmediately knows that plan might have branch points contingent on
no plan yet exists and can thus proceed to the the consequences of sensory actions. The plan
next planning graph level. is a directed acyclic graph, with the possibility
Uncertainty and Sensing Actions The of branches rejoining with each other. The con-
second novel feature in SGPis its ability to deal tingencies in the plan are based on which pos-
with uncertainty and sensing actions (this sible world the agent is in at plan-execution
work is detailed in Smith and Weld [1998a] and time. To resolve which possible world the agent
Weld, Anderson, and Smith [1998]). Although is in, the results of the sensing actions are used.
this part of SGP was not used at the AIPS-98 An important feature of SGPis that the planner
planning contest, it is discussed here in some determines exactly which sensing actions need
detail because it was the main motivation for to be taken to resolve the uncertainty. There are
work on SGP and is the characteristic that dis- two important outcomes here: First, the plan-
tinguishes SGPfrom the other planners. ner does not assume that the agent has full
Classical planners assume complete knowl- observational power. Instead, SGP allows only
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the terms sensed by the sensing actions to be STAN also identifies some goal sets as
used in resolving uncertainty. Second, the unachievable when they exceed certain
agent does not have to resolve exactly which resource limitations imposed by the domain.
possible world it is in but, rather, which of a set Resources include numbers of objects in certain
of possible worlds it is in. This distinction is configurations, the rate at which certain objects
important because with SGP, the agent need not can be put into key configurations during the
necessarily resolve all the uncertainty but sim- plan execution, and other factors as well as the
ply “enough.” physical resources available to the planning
agent (such as grippers, fuel, and containers).
STAN Limits on the availability of abstract resources,
STAN(state-analyzing planner) (1998) is a third such as the rate at which objects can be config-
system based on GRAPHPLAN that extends its ured, arise from the limits imposed by the phys-
planning technology in several ways: First, a ical resources of the agent and are expressed, for
more sophisticated data structure is used to example, in terms of constraints on the number
store the graph and aid in its construction than of plan-graph levels that must have been built
was used in earlier versions of GRAPHPLAN. Sec- before a certain goal configuration can be
ond, more analysis is carried out on the graph achieved. The resource analysis performed by
and the problem it encodes to reduce search STANcan dramatically reduce search, by identi-
branches, including goal-ordering analysis, fying the minimum number of graph layers
symmetry analysis, and resource analysis. that must be built, in some domains including
Third, a wave front is exploited at the fix point the traveling salesman problem discussed later.
of the plan graph to avoid unnecessary addi- Finally, STANexploits structural features of the
tional work. Fourth, state-analysis techniques, problem domain, such as symmetry, to reduce
implemented as a module of STAN that can be search. The competition version of STAN per-
exploited as a planner-independent system, formed only a preliminary symmetry analysis in
TIM, are used to acquire information about a which symmetric objects (those that are indis-
domain and problem encoding that is exploited tinguishable and, hence, do not form interest-
in instantiation and filtering of the plan graph. ingly different action instantiations) were iden-
The implementation of the plan graph in tified to reduce the number of action
STANis based on a careful reuse of much of the instantiations produced. Although STANwas able
central graph structure, to avoid repeatedly to detect certain forms of symmetry, the compe-
copying layer-independent information, to- tition version was not able to exploit it fully. A
gether with bit-level operations to support more advanced treatment has been developed
graph construction and careful filtering of the since the competition (Fox and Long 1999).
layer-dependent structures to reduce the retest- One of the most important features of STAN
ing carried out at subsequent layers. This that distinguishes it from other GRAPHPLAN-
implementation, the most recent version of based planners is its use of a highly efficient
which is described in full in Long and Fox implicit representation of the graph beyond
(1999), is efficient and relatively compact, the fix point. STAN avoids both construction
although the competition version of STAN(STAN and search of the plan graph beyond the fix
1.0) still allowed unnecessary wastage of space. point, where the graph is static. Instead, search
A similar approach, although introduced with is built on a collection of candidate goal sets
a slightly different purpose (to extend GRAPH- that are generated as failure sets at the fix point
PLAN to handle actions with duration), is dis- and that are pushed one layer forward to be
cussed in Smith and Weld (1999, 1998b). retried. This process in which failed goal sets
The plan graph is carefully analyzed during are promoted forward forms a kind of rolling
construction to produce several auxiliary rela- collection of goal sets at the fix point, which is
tionships between goals and between actions called a wave front (Long and Fox 1999). The
at each layer. In particular, STANidentifies order- efficiency gains this mechanism offers can be
ing relations between pairs of goals reflecting dramatic in certain problems and can also sig-
the order in which they must be satisfied so nificantly reduce the memory demands during
that both are true at a given level. Thus, a con- the process of constructing a solution.
siderable reduction in the search space is The exploitation of the results of state analy-
allowed by automatically selecting noops for ses of various kinds is an important feature of
goals that must be satisfied earlier than the cur- STAN. State analyses can be done in a prepro-
rent layer during search. Furthermore, certain cessing stage, using techniques that are planner
chains of ordered goals can prevent an entire independent, and the results fed into the plan-
goal set from being achieved at a given layer ning process and used to reduce, and even
without any search at all. eliminate, some of the more resource-intensive
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Articles
aspects of planning. Symmetry analysis, in Much work remains to be done in this area:
which symmetric objects and actions are iden- RIFOoffers IPPa huge benefit in many problems
tified to prune redundant search, is one such by filtering out many irrelevant objects,
form of state analysis. Another technique, cur- actions, and facts but at the price of possible
rently being integrated with STAN3, is the types incompleteness. As can be seen in Review of
and state-invariant inference analysis per- Results, all the planners were confounded
formed by the TIM module (Fox and Long when confronted with problem instances con-
1998). The competition version of STANwas not taining large numbers of ground-operator
fully integrated with TIM and therefore could instances. The ability to reduce these numbers
not make use of the inferred state invariants. It by intelligent filtering would appear to be a
could exploit the type structure inferred by TIM, critical element to successful planning.
but the competition domains had types sup- In contrast, some problems are hard not
plied, hence STAN did not have as large an because of the cost of construction of the graph
advantage over the other competitors as can be but because of the multiplicity of search paths
achieved with some domain encodings. More in the problem. This multiplicity is particularly
recently, TIM has been extended to allow the problematic in cases in which the problem
automatic identification of certain generic appears to be solvable long before it actually is
domain behaviors such as objects that traverse (the graph contains the nonpairwise, mutually
a map of locations and objects that can be car- exclusive goals long before the solution layer).
ried around such a network, together with the An example of such a problem is the complete-
objects responsible for carrying them. This graph traveling salesman problem (TSP) in
analysis can be exploited in a variety of ways, which the graph is completely connected so
but an initial use is in filtering useless action that the traveler is unconstrained in the order
instances from the initial action-instantiation of visits he makes. In this case, the problem is
phase common to GRAPHPLAN-based planners. that all the destinations could be visited within
Development of STAN During the develop- a single step, and any pair could be visited after
ment of the competition version of STAN,a pat- two steps. Thus, the problem appears solvable
tern was established of exploring the behavior after two steps but is not actually solvable until
of the planner on a family of problems to nsteps have passed, where nis the number of
understand what made them hard followed by sites to be visited. However, as n grows, the
constructing techniques to tackle the source of number of possible paths the traveler might
the difficulty in a domain-independent way. An have taken explodes exponentially, so that the
important lesson learned from this process, and search problem quickly becomes intractable.
from the competition itself, is that problems are STAN uses resource analysis to determine that
hard for a wide variety of reasons and that these only one destination can be visited at each
different sources of difficulty can lead to the step, so it does not search for a plan untilnlay-
development of techniques that are powerful in ers are constructed and can also ensure that
certain contexts but are simply useless over- every layer is used for a visit to a hitherto
head in others. Of particular interest were prob- unvisited site.
lems that appeared hard for STANyet were easy Unfortunately, there are other problems of
for other planners or are intuitively easy. similar character that are not yet adequately
One of the reasons problems can be hard, tackled by STAN. The gripper problem used in the
affecting GRAPHPLAN-style planners in particular, competition is an example: STANcorrectly deter-
is that domains can contain huge collections of mines that no more than two balls can be
instantiated actions that have no useful role in deposited at each time step. However, it does
the plan. Thus, you have both a large cost in not allow for the fact that the two balls must
the construction phase and, often, a large cost also be picked up and transported, requiring an
in the search phase when many branches must additional two steps (and a third to return to the
be explored. These branches often express the source for another load), so the resource analysis
same fundamental planning decisions but, does not help as much as one might hope.
because of the search in grounded actions, dif- GRAPHPLAN-style planners also suffer during
fer in details that are insignificant from the search from a problem of premature commit-
planning point of view. ment. This problem occurs because the use of
STAN attempts to deal with this problem in ground-action instances forces selection of
several ways: Type inference leads to a poten- objects to play particular roles in a plan often
tial reduction in the numbers of instantiated before constraints that would govern their
actions; the use of static conditions in instanti- choice become apparent. Constraint-solving
ation; and some preliminary work on filtering planners can benefit with these problems by
to remove some objects in some domains. making choices in the highly constrained parts
20 AI MAGAZINE
Articles
of the plan and propagating them into the less actions are significant. Differently declarative
constrained parts of the plan. Forward- and representations that are semantically equiva-
backward-chaining planners do not direct their lent can have distinct computational profiles.
planning strategies by exploiting the most The use of general reasoning algorithms offers
highly constrained parts of a plan structure, an important benefit because many researchers
which can lead to costly mistaken choices that in different areas of computer science devise
must be retracted. new algorithms and implementations for SAT
Some problems are hard because they have an testing each year and freely share ideas and
inherent combinatorial cost, and others are, in source code. SATis the general problem of deter-
principle, easy yet prove hard with current plan- mining whether there is a way to set a collec-
ning technology or at least with some current tion of identified variables to each be either
planning strategies. The gripper domain is a true or false so that a given logical expression
good example of the latter—a domain in which involving these variables is made true. As a
problems are trivial for human problem solvers, result of this shared work and the size of the
yet an optimal plan for this domain eluded all interested community, at any point in time,
the planners in the competition for instances the best general SATengines tend to be faster (in
larger than a dozen balls. More recent work on terms of raw inferences a second) than the best
STANhas explored the exploitation of symmetry specialized planning engines.
in problems such as the gripper that can reduce Interestingly, the GRAPHPLAN approach to
the difficulty dramatically (Fox and Long 1999). planning shares a number of features with the
Nevertheless, clearly much work remains to be SATPLAN strategy. Comparisons with SATPLAN
done in recognizing and exploiting features of show that neither algorithm is strictly superior.
problems that humans appear to identify with For example, SATPLAN is faster with a complex
ease. Furthermore, the representation of so- logistics domain; they are comparable on the
lutions to problems such as these remains an blocks world; and with several other domains,
issue: No human would represent the solution GRAPHPLANis faster.
to problems in the gripper domain as an explicit GRAPHPLAN bears an important similarity to
sequence of steps but would as a method for SATPLAN: Both systems work in two phases, first
generating these steps during execution (“Trans- creating a propositional structure (in GRAPHPLAN,
port the first two balls from room ato room b, a plan graph, in SATPLAN, a formula in conjunc-
then return and repeat until all balls are trans- tive normal form [CNF]) and, second, searching
ported.” The fact that the first two balls are not this structure. The propositional structure cor-
identified by name is an indication of the role of responds to a fixed plan length, and the search
symmetry for human problem solvers). reveals whether a plan of this length exists. Fur-
thermore, in Kautz and Selman (1996), it is
BLACKBOX shown that the plan graph has a direct transla-
It has often been observed that the classical AI tion to a CNF formula and that the form of the
planning problem (that is, planning with com- resulting formula is close to the original con-
plete and certain information) is a form of log- ventions for SATPLAN. It is hypothesized that the
ical deduction. Because early attempts to use differences in performance between the two
general theorem provers to solve planning systems can be explained by the fact that GRAPH-
problems proved impractical, research became PLAN uses a better algorithm for instantiating
focused on specialized planning algorithms. the propositional structure, and SATPLAN uses
However, the belief that planning required more powerful search algorithms.
such specialized reasoning algorithms was SATPLANfully instantiates a problem instance
challenged by the work of Kautz and Selman before passing it to a simplifier and a solver. By
(1996, 1992) on planning as propositional sat- contrast, GRAPHPLAN interleaves plan-graph
isfiability testing. SATPLANshowed that a general instantiation and simplification. Furthermore,
propositional theorem prover could be com- GRAPHPLAN uses a powerful planning-specific
petitive with some of the best specialized plan- simplification algorithm: the computation of
ning systems. The success of SATPLAN can be the mutual-exclusion relations between pairs
attributed to two factors: (1) the use of a logical of actions and facts.
representation that has good computational These observations have led to the creation
properties and (2) the use of powerful new gen- of a new system that combines the best features
eral reasoning algorithms such asWALKSAT(Sel- of GRAPHPLAN and SATPLAN. This system, called
man, Kautz, and Cohen 1994). Both the fact BLACKBOX, works in three phases. First, a plan-
that SATPLANuses propositional logic instead of ning problem (specified in a standard STRIPS
first-order logic and that we suggested the par- notation) is converted to a plan graph. Second,
ticular conventions for representing time and the plan graph is converted into a CNF formu-
SUMMER 2000 21
Articles
la. Third, the formula is solved by any of a vari- ing as well as a technique for reducing the size
ety of fast SATengines. of the CNF encodings by suppressing the gener-
The formula generated from the plan graph ation of clauses that are logically redundant.
can be considerably smaller than one generat- BLACKBOXwas designed to improve the plan-
ed by translating STRIPS operators to axioms in extraction phaseof GRAPHPLAN(that is, the search
the most direct way, as was done by the earlier within the plan graph for a solution). In the
MEDIC system of Ernst, Millstein, and Weld majority of the problems solved in the compe-
(1997). Furthermore, the mutual-exclusion tition, plan extraction was comparatively easy
relations computed in the plan graph can be once the plan graph was constructed. Systems
translated directly into negative binary clauses, that reduce the plan-graph structure and there-
which can make the formula easier to solve for by reduce the cost of constructing it enjoyed a
many kinds of SATengines. relative advantage over BLACKBOX in this con-
The competition version of BLACKBOXinclud- text. Problems that have a relatively much
ed the local-search SAT solver WALKSAT and the harder plan-extraction phase are included in
systematic SAT solver SATZ (Li and Anbulagan the BLACKBOX(1998) distribution.
1997) as well as the original GRAPHPLAN engine
(that searches the plan graph instead of the HSP: Heuristic Search Planner
CNF form). To have robust coverage over a vari- HSP is a planner based on the well-established
ety of domains, the system can use a schedule idea of heuristic search. Heuristic search algo-
of different solvers. For example, it can run rithms perform forward search from an initial
GRAPHPLAN for 30 seconds; then WALKSAT for 2 state to a goal state using a heuristic function
minutes; and, if still no solution is found, SATZ that provides an estimate of the distance to the
for 5 minutes. goal. The 8-puzzle is the standard example of
The BLACKBOX system introduces new SAT heuristic search and is treated in most AI text-
technology as well, namely, the use of random- books (Pearl 1983; Nilsson 1980). The main dif-
ized complete search methods. As shown in ference between the 8-puzzle and the approach
Gomes, Selman, and Kautz (1998), systematic to planning adopted in HSP is in the heuristic
solvers in combinatorial domains often exhibit function. Although in domain-specific tasks
a “heavy tail” behavior, whereby they get such as the 8-puzzle, the heuristic function is
“stuck” on particular instances. Adding a small given (for example, as the sum of the Manhat-
amount of randomization to the search heuris- tan distances), in domain-independent plan-
tic and rapidly restarting the algorithm after a ning, it has to be derived from the high-level
fixed number of backtracks can dramatically representation of the actions and goals.
decrease the average solution time, often from A common way to derive a heuristic function
hours to seconds. h(s) for a problemP is by relaxing Pinto a sim-
This randomization-restart technique was pler problem P’ whose optimal solution can be
applied to the version of SATZused by BLACKBOX. computed efficiently. Then, the optimal cost for
The variable-choice heuristic for SATZ chooses solving P’ can be used as a heuristic for solving
to split on a variable that maximizes a particu- P(Pearl 1983). For example, if Pis the 8-puzzle,
lar function of the number of unit propaga- P’can be obtained fromPby allowing the tiles
tions that would be performed if that variable to move into any neighboring position. The
were chosen (see Li and Anbulagan [1997] for optimal cost function of the relaxed problem is
details). The BLACKBOX version, SATZ-RAND, ran- precisely the Manhattan-distance heuristic.
domly selects among the set of variables whose In STRIPSplanning, the heuristic values for a
scores are within 40 percent of the best score. planning problem Pcan be obtained by consid-
The solver schedule used in the competition ering the relaxedplanning problem P’in which
was to run the GRAPHPLANengine for 2 seconds, all delete lists are ignored. In other words, P’is
then to convert the problem to CNF and run like Pexcept that delete lists are assumed emp-
SATZ-RAND for 10 restarts with a cutoff of 100 ty. As a result, actions can add new atoms but
backtracks. If one of the solvers showed that no not remove existing ones, and a sequence of
solution existed, the plan graph was extended actions solves P’when all goal atoms have been
by one layer and the schedule repeated. Note generated. As with all the other competition
that no one cutoff value is ideal for all planners, action schemas are first grounded in
domains. One way to address the problem is to an initial instantiation phase, so variables do
specify a sequence of increasing cutoff values not occur in actions.
in the solver schedule. It is not difficult to show that for any initial
The newest version of BLACKBOX includes an state s, the optimal cost h’(s) to reach a goal in
additional solver, RELSAT (Bayardo and Schrag P’ is a lower bound on the optimal cost h*(s) to
1997), based on dependency-directed backtrack- reach a goal in the original problem P. The
22 AI MAGAZINE