From: AAAI Technical Report FS-95-04. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved.
A Domain-Independent
Algorithmfor Multi-Plan Adaptation and Mergingin
Least-CommitmentPlanners
Anthony G. Francis, Jr. and Ashwin Ram*
College of Computing
Georgia Institute of Technology
Atlanta, Georgia 30332-0280
{centaur, ashwin} @cc.gatech.edu
http://www.cc.gatech.edu/ai/ai.html
Abstract
Solving problemsin manyreal-world domainsrequires
integratingknowledge
fromseveral past experiences.This
integration requires the dynamicretrieval of multiple
experiences
andthe extractionof their relevantsubparts.
Oursolution is the Multi-PlanAdaptor(MPA),a method
for merging
partial-orderplansin the contextof case-based
least-commitment
planning. MPA
providesthis ability by
extractingan intermediategoal statementfroma partial
plan, clipping a stored plan to the intermediategoal
statement,andthensplicing the clippinginto the original
partial plan. MPAis implemented in the NICOLE
multistrategyreasoningsystem,whereit is paired with
MOORE,
an asynchronous, resource-bounded memory
module.MooRE
initially retrieves its current"best guess"
but continuessearch, spontaneouslyreturning a better
retrievalas soonas it is found.
unless a case-based reasoningsystemhas the ability to
combineseveral past experiences, it will haveto resort
to expensive from-scratch reasoning in order to solve
the problem.
SomeCBRplanning systems combine multiple cases
during reasoning. However, they either gather all
partial plans at retrieval prior to adaptation (e.g.,
PRODIGY/ANALOGY,
Veloso 1994), or break plans
into snippets at storage time so they can be retrieved
individually (e.g., CEIJA, Redmond1990, 1992).
Neither of these approachesis entirely satisfactory, for
various reasons.
It is not entirely clear that all of the knowledge
needed
to solve a problemcan be assembledat the beginningof
problemsolving. For example,in the furniture example,
it is not entirely clear whetheror not the agent needsto
buy new sandpaper, and hence unclear whether the
agent should recall past experiences of buying
sandpaperat a hardwarestore. This uncertainty arises
out of several concems:the uncertainty of the world
state (how much sandpaper d~s the agent have?),
uncertainty in the effectiveness of agent actions (how
muchwoodwill a piece of sandpaper sand?) and the
potential of exogenousevents that can invalidate parts
of the plan (if a friend drops and scars a piece of the
furniture, ~11 the agent have enough sandpaper to
removethe scar, or will he need to buy more?). But it
can also arise out of the plan itself." until the agent has
decided on a design for the piece and how muchwood
vail be involved, it is unclear precisely howmuch
sandpaper is needed, and hence unclear whether or not
a plan should be retrieved. If someamountof sandpaper
is on hand, the goal of acquiring sandpaper maynot
evenarise until late in the planningprocess, whenit has
becomeclear that the amounton handis insufficient.
Precomputing case snippets also has drawbacks.
Whilethis allowsus to extract subparts of a case to meet
the needs of a component of a plan, these
subcomponentsneed to be computedat storage time.
Unfortunately, it is not clear that every useful
breakdownof a case can be computedin advance. For
example, in the foreign conference example, the two
past experiences mustbe closely interleaved to produce
a new plan. If the agent has not stored the passport
experience as a separate snippet, the agent maynot be
1. Introduction
Takingadvantageof past experiences is the foundation
of case-based reasoning. Whenconfronted with a
problem,a case-basedreasoner recalls a past experience
and adapts it to provide the solution to the newproblem.
Unfortunately, in manyreal-world domainswe cannot
count on a single past experienceto provide the outline
of a solution to our problems.For example:
¯ A graduatestudent askedto present his first paper
at an overseas conference must draw on separate
past experiencesin preparing talks for conferences
within his country and preparing his passport and
flight arrangementsfor vacations outside of his
country.
¯ A host planning his first large dinner party must
recall both the outline of a menuas served at
family gatherings and his separate experiences at
preparingindividual dishes for himself.
¯ Ahomehobbyistattemptinghis first large piece of
furniture must recall both past examplesof that
type of furniture to provide a design and
experiences with acquiring, assembling and
finishing individual components.
All of these problems have something in common:
every piece of the solution can be constructed entirely
out of the agent’s past experience (with suitable
adaptation), but no single past experience suffices to
solve the entire problem.For these types of problems,
* Thisresearch
wassupported
bytheUnited
StatesAirForce~oryGraduate
Fellowship
Progrmn,
bythe AirForceOffioeof ScientificResearch
under
Contraa
# F49620-94-1-0092,
andbytheGeorgia
Instituteof Technology.
19
able to extract that particular piece of a case if it is
retrieved-- if the agentwasable to retrieve it at all.
Whatis neededis a methodthat allows the mergingof
arbitrary numbers of plans at any point during the
adaptation process, and which allows the dynamic
extraction of relevant case subparts. Oursolution is the
Multi-Plan Adaptor (MPA), a novel method for
mergingpartial-order plans in the context of case-based
leastw.ommitmentplanning. The MPAalgorithm builds
on the Systematic Plan Adaptor (SPA; Hanks & Weld
1994), a case-based least-commitment planner that
annotates partially ordered plans with dependency
structures to allow later refitting and adaptation. SPA
shows significant improvements over generative
planning, but can only adapt one plan at a time and
hence for the types of problems described above must
resort to significant amountsof from-scratchplanning.
MPAovercomesthis limitation of SPAby extracting
an intermediate goal statement from a partial plan,
clipping a stored plan to the intermediate goal
statement, and then splicb~g the dipping into the
original partial plan. Depending
on the size of the plans
spliced and the retrieval algorithms used, MPAcan
producesignificant speedupsover SPA.
Becausethe cost of retrieval can potentially outweigh
the benefits of adaptation in an interleaved system,
developingheuristics for deciding whento retrieve is a
challenging problem. Our current implementation of
MPAin the multistrategy reasoning system NICOLE
USes
an asynchronous, resource-bounded memorymodule
called MOORE
that initially retrieves its current "best
guess" but continues to search, spontaneouslyreturning
a better retrieval as soonas it is found.
In this paper, we briefly review least-commitment
planning and howit can be used for adaptation. We
then present the MPAalgorithm, describe its
foundations in and extensions of the SPAalgorithm,
and then detail howMPAcan be used to address the
limitations of existing multi-plan systems. Wethen
discuss howMPA
can be integrated into various control
regimes, including systematic, pure case-based, and
interleaved regimes, and describe our implementationof
interleaved MPAin the NICOLE
system. Weconclude
the paper by reviewing other case-based planning work
and then outline our contributionsin the appendix.
elan
s~p I ~I Lr~ I ~ l
l~efir~rr~n~
4.Further
~
5.
R~ir~r~&n~
~
6.
Add
z~i~,~l ~1 u~°’V~l ~t-Xt" I o~a~ I "/~-~-.I
I ~,-.~’1", l-hrea~e ~ "~21-.3~.,-~L~’1 ~’cr,~51 ,t? q~ll
Figure 1. Ref’mementof Partial Plans
Least-commitment planners solve problems by
successive refinementof a partial plan derived fromthe
initial and goal conditions of the problem(Figure 1).
Plans are represented as sets of steps, causal links
between steps, variable bindings and ordering
constraints. Beginningwith a skeletal partial plan based
on the initial and goal conditionsof the problem,a leastcommitmentplanner attempts to refine the plan by
adding steps, links and constraints that eliminate open
conditionsor resolvethreats.
An open condition in a partially ordered plan occurs
whena plan step has a precondition that has no causal
link to an effect in a prior step in the plan that
establishes that condition. Open conditions can be
resolved by adding a new step that establishes the
desired effect and linking the preconditionto it, or by
linking the preconditiondirectly to an effect already in
the plan if oneexists.
A threat in a partially ordered plan occurs whenthe
condition established by the producingstep in a causal
link maybe clobbered by the effects of another step
before it is used by the consumingstep in the link.
Threats maybe resolved by adding ordering constraints
that movethe threatening step before or after the steps
in the causal link, or by addingbinding constrablts that
ensurethat the effects of the other step cannotunify with
the step of the causallink.
Givenan arbitrary sequenceof decisions to add steps
and bindings, there is no guaranteethat the partial plan
produced can be successfully refined into a correct
solution. An analytical failure occurs when an
incomplete partial plan cannot be further refined by
addingnewsteps, links or constraints.
SNLP(McAllester &Rosenblitt 1991) is a complete,
consistent and systematicpartial order planner that uses
a STRIPS-likenotation to represent steps in its partial
plans. Problemsolving in SNLPbegins with a list of
initial conditions and goal conditions, which SNIP
transformsinto a skeletal plan with a dummy
initial step
whosepostconditionsestablish the initial conditions and
a dummy
final step whosepreconditions matchthe goal
conditions. As outlined above, SNLPoperates by
repeated refinement in which open conditions are
resolvedand threats are eliminated.
2. Least Commitment Planning and
Systematic Plan Adaptation
2.1. Least Commitment Planning: SNLP
Least-commitmentplanning departs fi-om traditional
planning systems by delaying decisions about step
orderings and bindings as muchas possible to prevent
backtracking (Weld 1994). Dependingon the domain
and search strategy, least-commitment planning can
lead to substantial improvements
over traditional totally
ordered plans (Barret & Weld 1994; but for an
alternative view see Mintonet al 1994, Veloso&Blythe
1994, Veloso&Stone 1995).
2.2. Systematic Plan Adaptation: SPA
The Systematic Plan Adaptor algorithm (Hanks &Weld
1994) is an algorithm for case-based planning that
incorporates SNLPinto its adaptation mechanism.SPA
2O
I. Problem
Star, Front
2, Search CaseLibrary
4. AdJusttn]ttal ar~
final co,~dl~lOnS
I
,," ~ -.
--. l
2.3. Limits of SPA:AchievingSystematicity
and Completeness
3, Best
Matching Plan
One limitation of SPAis that it is a single-plan
adaptor; even if a new problem could be solved by
merging several plans, SPAmust choose only one and
adapt it to fit. This limitation arises fromSPA’sattempt
to maintain systematicity
and completeness. A
systematicplanner never repeats its workby considering
a partial plan more than once; a complete planner is
guaranteedto find a solutionif it exists.
SPA’sgenerative predecessor SNLPachieves both of
these properties through the clever design of its
refinement algorithm. WhenSNLPremoves a plan
fromthe search frontier, it selects a refinementto apply
and then replaces the plan with all possible
instantiations of the refinement. Since this process
consumes refinements and refinements are never
retracted, duplicate partial plans are never generated;
since all possible refinementsare generated, the planner
is guaranteedto not miss a solution.
In an adaptive planner like SPA, the picture is
complicated by the presence of retraction operators.
SPA ensures that the refinement and retraction
operators never undo each other’s work by marking
each plan in the frontier with a direction. SPAbegins
adaptation by placing the retrieved plan onto its search
frontier twice, markedonce for refinementand once for
retraction. The plan markedfor refinement is treated
precisely in the samewayas in SNLP:all of its possible
children are computedand placed on the frontier.
The copy of the plan markedfor retraction, however,
is treated differently. First, a refinementin the plan is
chosenand retracted. This retracted plan is placed on
the frontier and is markedfor further retraction. Then,
all of the alternative decisions that the planner might
have made in place of the retracted refinement are
generated, and these siblings are placed on the frontier
marked for refinement. This retraction-refinement
process achieves systematicity by ensuring that the only
decisions being retracted are ones that werepart of the
original partial plan in the first place; it achieves
completenessby ensuring that all of the alternative
decisions are considered.
Unfortunately,the desire to maintainthese properties
effectively bars SPAfrom incorporating additional
partial plans during problem solving. Because a plan
contains a set of refinements, SPAcannot simply
remove a plan from the frontier and splice a new
retrieved plan into it without losing its completeness
guarantee; nor can it leave both the original and adapted
plans on the frontier in an attempt to maintain
completenesswithout running the risk of re-generating
the adapted plan, hence violating systematicity. To
maintain both properties, all of the siblings of each
refinement spliced into the plan must also be addedto
the frontier -- a workablebut potentially costly solution.
5. Remove
sT.ep~
]inappropriate.
6. Search~1 the Spaceof Partial Plans
Figure 2. Fitting of Partial Plans
provides vast speedups over SNLP’sperformance by
retrieving single plans whichit fits and adapts, yet it
maintains SNLP’s properties
of soundness,
completeness,and systematicity.
SPAis basedon three key ideas: annotatepartial plans
with reasons for decisions, add a retraction mechanism
to removedecisions, and add a fitting mechanism
to fit
previous plans to current situations. Reasonstructures
take a middlegroundbetweena derivational trace of a
planner’s activity (e.g., Ihrig &Kambhampati
1994a,
Ram& Cox 1994, Veloso 1994) and an unannotated
plan. Like the partial-order plan representation itself,
which records necessary orderings and interactions
betweensteps without specifying a precise ordering,
reasons record the necessary dependencies between
refinements without specifying the precise ordering in
whichthe planner madethe choices.
Thereason structures are first used to fit a retrieved
plan to the newsituation (Figure 2). Theinitial and goal
conditions of a prior plan maynot match the current
situation, and it maycontain steps and links that are not
relevant to solving the new problem. To remedythis
situation, SPAadjusts the initial and final conditions of
the retrieved plan to match the current problem, and
then uses the reasonsto recursively eliminate steps that
attempt to resolve deleted goal conditions and links that
dependon deleted initial conditions.
Reasons are also used to select refinements for
retraction. Once a plan has been retrieved, it may
contain steps and constraints that would lead to
analytical failures in the current situation. Reasons
allow SPAto select past refinement decisions whichare
safe to retract (decisions uponwhichno other decisions
depend)and to eliminate them.
21
0. Search
in theSpace
of PartialPlates
Input:Apartial plan P, anda case library C.
Oulput: A newpartial plan P’.
&. Spl~:eRe[evan~
Steps
@----e
procedureMPA(P, Q:
1 P’ (-- Copy-Plan(P)
2. igs (-- GetlntermediateGoaJStatement(P3
3. p/an~ ReffieveB~tPl~m
(C, igs)
4. {dippin~mapping}
4- FitPlan(plan, igs)
5. for cgpin mapping
do
6. if Producer-Exists
(oc-gl-pair,P’)
7.
thenSplice-link(oc-gl-pair, P" dipping)
8.
else Splice-Step
(oc-g/-pair, P" dipping)
9. AddNewOpenCond-GoalPaJrs(mapping,
P’)
10.returnP’
Figure 4. Outline of The MPAAlgorithm
2. Extract
3, Search
Case
IntermediateGoal
L~rary
Statement
4. Best
5. Ad~Jsg
Matching conditions
and
Plan
remove
st et~a
of the plan that are not causally relevant to the
intermediate goal statement.
Intermediate goal statements are extracted by the
inverse of the representational trick with whichSNLP
constructs its initial skeletal plans. Recall that SNLP
builds the initial plan it considers by adding dummy
initial and final steps whosepost- and preconditions
matchthe initial and goal conditions of the problem.As
planning proceeds, open conditions in the goal
statement are resolved, but new open conditions are
posted as newsteps are added. These open conditions
themselvescan be extracted from the plan to form a new
goal statement. Similarly, the initial conditions of the
partial plan can be extracted and used as a newset of
initial conditions.1
Just like the original goal statement, the intermediate
goal statement can be used to retrieve and fit a partial
plan. However,the result of this process is not a
completefitted plan suitable for adaptation; it is a plan
clippingthat satisfies someor all of the openconditions
of the partial plan from which the intermediate goal
statement was derived.
Totake advantageof the plan clipping for adaptation,
it mustbe spliced into the original partial plan (Figure
3). Our splicing mechanismuses the intermediate goal
statement to produce a mapping I~ween the partial
plan and the plan clipping, pairing open conditions
fromthe partial plan with satisfied goal conditions from
the plan clipping. Theplan splicer uses this mappingto
performa guidedrefinementof the original partial plan,
selecting goal conditions from the clipping and using
the links and steps that satisfied themas templates to
instantiate similar steps and finks in the original plan.
Figure 3. Overviewof Multi-Plan Adaptation
3. Plan Merging
3.1. An Algorithm for Plan Merging: MPA
Because it adapts only one plan, SPAcan resort to
significant amounts of from-scratch planning even
when the knowledgeneeded to complete the plan is
present in the case library. To makethe most effective
use of the planner’s past experience,weneedthe ability
to recognize whena partial plan needs to be extended,
select plans to that address the deficiency, and then
extract and mergethe relevant parts of the retrieved
plan into the original plan.
The Multi-Plan Adaptor algorithm (MPA)resolves
this problem in SPAby allowing the retrieval and
merging of arbitrary numbersof cases at any point
during the adaptation process. MPA
further allows the
dynamicextraction of relevant parts of past cases. To
achieve this, the MPAalgorithm extends the SPA
frameworkin three crucial ways:
¯ extract intermediate goal statements from partial
plans
¯ use the fitting mechanismto clip plans for
merging
¯ build a plan splicer to mergetwoplans
Intermediate goal statements provide MPAwith the
ability to merge partial plans at any point of the
adaptation process and contributes to its ability to
dynamicallyextract the relevant subparts of retrieved
cases. MPA
translates the incompletestate of a partial
plan into a goal statement, allowing the systemto use
the sameretrieval mechanismsthat it used to retrieve
the initial plan. Oncea plan has been retrieved that
matchesthe intermediate goal statement, the relevant
subparts must be extracted. The plan fitting mechanism
performsthis extraction dynamically,removingportions
1 Unfortunately,since orderingconstraints andbindingconsn’aintsmay
be posted to the plan at any time, only lhe initial conditions can be
guaranteedto be valid conditions for the intermediate goal s~eme.nt.
Conditionsestablishedby other steps of the plan maybe clot~.xedby tile
addition of newsteps and neworderingconstraints. However,
it might be
possibleto developheuristics that select additionalinitial conditionsthat
are likely to hold, perhapsin conjunctionwith morecomplexretrieval,
titling andsplicing algorithms.In general, decidingwhichparts of a plan
can be exwactedto form a sensible and effective intemediate goal
statementis a ditfioalt andunsolvedproblerrh
22
As these steps are added, newmappingsare established
betweenopen conditions in the newsteps and satisfied
preconditions in the clipping and are addedto the queue
of mappingsthat the splicer is processing. Hence,the
plan splicer performsa backwardsbreadth-first search
throughthe causal structure of the plan clipping, using
links and steps in the clipping to guidethe instantiation
of links and steps in the original plan. Figure4 briefly
outlines the MPA
algorithm.
need to decide what experiences to combine and when
to combine them. Because the MPAalgorithm can
potentially be performed at any point during the
adaptation process -- using an initial skeletal plan
derived from the initial and goal statement, using a
fitted plan derived from retrieval, or using an adapted
plan after some arbitrary amount of retraction and
refinement- we have considerable flexibility
in
deciding what to retrieve, whento retrieve it and when
to mergeit.
Wehave considered three alternative control regimes,
each of which makes different commitments about
whento retrieve and whento adapt. Onone end of the
spectrum, Systematic MPApreserves SPA’s property of
systematicity by splicing all retrieved cases before
adaptation begins. On the other, Extreme MPAnever
performs(generative) adaptation and instead uses a set
of pivotal cases (Smyth &Kearle 1995) to guarantee
completeness.
Both Systematic and Extreme MPAmake extreme
commitments:either integrate all knowledgebefore
adaptation begins, or never adapt and rely solely on past
experience. An alternative approach is to allow plan
splicing at any point during adaptation. In the middle
stands Interactive MPA(MPA-I), a system that can
potentially attempt a retrieval at any time, either with
the initial skeletal plan or withpartial plans producedas
a result of adaptation.Sincethe results of splicing cause
large jumpsin the search space, the systemdeliberately
departs from the systematicity of SNLPand SPAin an
attempt to solve the problemwith less search.
However,allowing arbitrary plan retrieval and plan
splicing is not withoutcost. Performinga full search of
the system’s case library at every step of the problem
space could be computationallyprohibitive. Thecosts of
searching the case library at every step of the problem
space could outweigh the benefits of reduced search,
especially if the system enters a "slump" -- an
adaptation episode which begins and ends with the
application of relevant clippings, but which goes
through a series of intermediate plans for Maichthe
system cannot match any existing plans in its case
library. Clearly, it is worthwhileto retrieve and apply
clippings at the beginningand end of a slump,but a full
search of the case library at eachintermediatestep could
cost morethan the benefits that the initial and final
retrievals provide. This is the swamping
utility problem
-- the benefits of case retrieval can be outweighedby
the costs of that retrieval, leading to an overall
degradation in performanceas a result of case learning
(Francis & Ram1995).
Developing heuristics for deciding when and when
not to retrieve is a challenging openproblem.To solve
this problem, we have implemented a multistrategy
reasoning system called NICOLE
which pairs MPAwith
an asytu:hronous, resource-bounded memorymodule
called MooRE.In NICOLE,MPAand MOORE
share a
central blackboard. WhenMPA
requests a partial plan,
MOORE
returns its current best guess. However,the
retrieval request remains active, and as the MPA
adapts
3.2. The Efficiency of Plan Splicing
Both adapting a single partial plan and adapting merged
partial plans can produce significant benefits over
generative problem solving. The cost of generative
planning is exponential in the size of the final plan
produced,whereasfitting a plan is a linear operationin
the size of the plan. Hence, the potential exists for
substantial
improvement through retrieval
and
adaptationif an appropriate past plan exists, especially
for large plans. In certain domains, SPA has
demonstratedsignificant improvementsover generative
planning. However,if large gaps exist in the retrieved
partial plan, SPAmustresort to adaptation, which,like
generative problemsolving, has an exponential cost in
the numberof steps that needto be added.
Whilethis amountof adaptation maybe a significant
improvement over complete from-scratch problem
solving, the potential exists to reducethat evenfurther
by using MPAto clip and splice more partial plans.
Fitting a clipping and splicing a clipping are linear
operations in the size of the plan being spliced. Hence,
the potential exists for substantial improvement
through
plan merging if an appropriate past plan exists,
especially if the gaps in the existing plan are large. An
initial implementation of MPAfor a test domain
indicated significant speedups(beginning at 30%)over
SPAfor eventhe smallest examples(solution size of the
final plan = 5 steps).
However, both plan adaptation and plan merging
require the retrieval of a past plan, and that retrieval
cost mayoffset the benefits of adaptation or merging.
For SPA,retrieval costs are incurred once, before
adaptation begins, and hence it is simple to determine
whetherthe cost of retrieval will be offset by the benefits
of adaptation. For MPA,the picture is not so simple.
MPAallows plan merging at any point during
adaptation, and hence it is not clear from the MPA
algorithm itself whenretrieval will be performed,how
manyretrievals will be performed, and hence whether
those costs will be offset by the improvements in
problemsolving. In order to determine this, we must
embed MPAwithin a control regime that determines
whenand howoften retrieval will be performedbefore
we can precisely specify the benefits of multi-plan
adaptation.
4. Controlling Plan Splicing
Merelyhavingthe ability to splice plans together does
not allow us to take advantage of past experience. We
23
the plan the newpartial plans it constructs provide
additional cues for MOORE
to attempt further retrievals.
WhenMOORE
finds a new past case whose degree of
match exceeds a certain threshold, it signals MPA,
whichsplices it into the appropriatepartial plan.
5. Related Work
There are wide Ixxlies of work on both leastcommitmentplanning and case-based reasoning. The
mostrelevant exampleof that workto this research is of
course SPA, upon which MPAbuilds. Other similar
plan reuse systems include PRIAR(Kambhampati
Hendler 1992) an SPA-like system based on NONLIN,
and XII (Golden et al 1994), an SPA-like system that
plans with incomplete information. Hanks and Weld
(1995) discuss these and other plan reuse systems from
the perspective of the SPAframework.
MPA’splan splicing mechanism is in many ways
similar to DERSNLP
0brig & Kambhampati1994),
derivational analogy systembuilt on top of SNLPthat
uses eager replay to guide a partial order planner.
While DERSNLP’s
eager replay mechanismis in some
ways similar to a limiting case of Systematic MPAin
which a single plan is retrieved and spliced into a
skeletal plan derived froman initial problemstatement,
DERSNLP
goes beyond SPA’s reason mechanism and
includes a full derivational trace of problemsolving in
its cases. While DERSNLPand its extension
DERSNLP-EBL
focus on when it is profitable to
retrieve a partial plan, unlike MPA-I
they do not provide
the capability of interruptingadaptationas a result of an
asynchronousmemory
retrieval, nor do they provide the
ability to integratethe results of multipleplans.
Combiningmultiple plans in case-based reasoning is
not a new idea. The PRODIGY/ANALOGY
system
(Veloso 1994) can retrieve and mergethe results of
arbitrary numberof totally ordered plans during the
derivational analogy process. However, because
PRODIGY/ANALOGY
manipulates and stores totally
orderedplans, it runs into significant issues on deciding
howto interleave steps (Veloso 1994, p124-127),
issue MPAavoids because of its least-commitment
heritage. Furthermore, PRODIGY/ANAL(XkY
deliberately limits its capability to retrieve andcombinecases
onthe fly in an attemptto reduceretrieval costs.
TheJULIAsystem(I-Iinrichs 1992)also has the ability
to combinepieces of several past cases, but this is
largely a domain-dependentalgorithm for mergingdeclarative structures, rather than a domainindependent
planning system. The CELIAsystem (Redmond1990,
1992) stores cases as separate snippets, case
subcomponents
organized arounda single goal or set of
conjunctive goals. Snippets provide CELIAwith the
ability to retrieve andidentify relevantsubpartsof a past
case based on the system’s current goals. Note that
whilesnippetsare superficially similar to plan clippings,
plan clippings are constructed dynamically during
problemsolving, whereassnippets need to be computed
and stored in advance.
24
Clippingsare similar to macrooperators (Fikes et al.
1972) in that they use past experience to combine
several problemsolving steps into a single structure that
can be applied as a unit, allowing the system to make
large jumpsin the problemspace and avoid unnecessary
search. However,macrooperators differ from clippings
in two important ways. First, macro operators are
traditionally precomputedat storage time, whereas
clippings are computeddynamically;, second, macro
operators are fixed sequences of operators, whereas
clippings are partially orderedsets of operators that may
be resolvedin a widevariety of waysin the final plan.
Kambhampafi& Chen (1993) built and compared
several systemsthat retrieve partially orderedcase-like
"macro operators". They demonstrated that leastcommitmentplanners could take greater advantage of
past experiencethan totally-ordered planners becauseof
their ability to efficiently interleave newsteps into these
"maero-operators" during planning. While this work
focuses primarily on interleaving newsteps into single
past plans, the explanationsthe authors advancefor the
efficiency gains they detected could be extended to
suggest that least-commitment planners would be
superior to totally-ordered planners wheninterleaving
multiple plans. The completed MPA-Isystem should
provide us a testbed with which we can empirically
evaluatethis hypothesis.
6. Conclusion
Wehave presented the Multi-Plan Adaptor, an
algorithm that allows a case-based least-commitment
planner to take advantageof the benefits of several past
experiences. MPA
provides the ability to retrieve and
merge dynamically selected case components at any
point during the adaptation process by extracting an
intermediate goal statements from a partial plan, using
the intermediate goal statement to retrieve and clip a
past plan to the partial plan, and then splicing the
clippinginto the original partial plan.
Multi-planadaptation has the potential for substantial
speedupover single-plan adaptation, but in order for
those benefits to be realized MPAmust be embedded
within a control regime that decides whenthe system
attempts a retrieval, whenthe systemmerges, and when
the system resorts to adaptation. Wehave used the
NICOLE
multistrategy reasoning system to implementan
interactive algorithm called MPA-Iwhich allows the
retrieval of past cases at any point duringadaptation.
To cope with the potentially swamping cost of
retrieval at every adaptation step, MPA-Iis currently
paired with an asychronous, resource-bounded memory
modulecalled MOORE
that retrieves a "best guess" and
then continues to monitor the progress of adaptation,
returninga newor better retrieval as soonas it is found.
Appendix: Describing
the Contributions
A. Reasoning Framework:
1. Whatis the reasoningframework?
Thereasoningframework
is a case4xasedreasoningsy~emlayered on
top of a least-commitment
planner. This framework
can be embedded
in several control mgirms; an interleaved regime based on an
asynchronous mea~rymodule is impl~ted.
2. What benefits
can be gained that motivated using
adaptation ? reuse?
Adaptation/reuseof past problemsolving cases can eliminate vast
amountsof search and causesignificant speedupsin problemsolving.
3. What are ttre specific benefits and limitations of your
approach ?
Our approach can provide improvementover from-scratch problem
solvingandsingle-caseadaptation.Ho~vever,
it is cmrenflylimited to
mergingproblem-solving
casesor other caseswith a causal structure,
andlike all planningandlearningalgorithmsit is sensitiveto domain
characteristics.
4. What #wariants does it guarantee?
When
the domainaffords the use of past problemsolving experiences
and relevant experiencesare available, this nr,.th~ can reducethe
number
of stutes visited in the searchspace.
5. What are tire roles of adaptation, hwwledgeam1 reuse bt
your approach ?
A. Knowledge:
1. Whatdoes it encode?Plans
2. Howis it represented?Partial-order plans with a STRIPS-like
notation.
3. Howis it used? Toprovidethe framework
for newplans.
4. Howis it acquired?Throughgeneralive or case-basedproblem
solving.
B. Adaptation:
1. Whatis adapted?Plans (past problemsolving cases).
2. Whyis it adapted?Toavoidgenerativesearch.
3. What properties of the knowledge representation does
adaptation require or exploit? Plans must be annotated with
reasondata structures that allowretraction of decisions (for
adaptation)andplanfitting (for adaptationandnr.rging).
4. Howare the benefits measured?
In the numberof states in the
search spaceavoidedand/or problemssolving time.
5. Whatis gained?Past plansprovidean outline of a solutionto the
newproblem.
C. Reuse:
1. Whatis reused?Plans (past problem-solving
cases).
2. Whyis it reused? To guide the problem solver and avoid
generativesearch.
3. What properties does the reuse process place on the
adaptation process?Theadaptation process mustbe capable of
beingguidedby clippedpartial plans.
4. Howare tile benefits measured?
In the numlr.xof states in the
search spaceavoidedand/or problemssolvingtime.
5. Whatis gained?Pastplansprovidean outline of a solutionto the
newproblem.
Test cases x~re used to evaluate the algorithmsto verify that they
provided improven~.For these problems, ~ empirically tested
problemsolving methods(generative, tingle-plan, and mulli-plan)
against problem-solvingtime. This workis preliminary; a more
completeevaluationis in progress.
3. What comparisons were n~de with other methods ?
MPA
was tested against a generative planner (SNLP)and a casebased reasoner (SPA) and showedimpmvenxmts
over both on the
same
problems.
4. Howdoes the evaluation validate or illuminate your theory
of adaptation of knowledge for reuse?
Ourresearch providesan initial indication that muM-plan
adaptation
can be moreeffective thanplanningfromscratch.
5. What are the primary contributions of your research?
Ourresearch contributes an algorithmfor multi-plan adaptationfor
ease~ least-commitmentplanning and offers initial indications
that multi-planadap~onmaybe an efficient adaptationtechnique
References
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B. Task:
1. What is tire task? The doma&?
Thetask is problemsolving. The algorithmis domain-indepen~t.
2. Whatare tire inputs?
Problems
specifiedin termsof initial andfinal states.
3. Whatare the outputs?
Solutions to the problems in the form of partial-order plan
representations.
4. Whatare tire constraints on tire outputs?
A correct solution mustbe found ff one exists within the sy~rn’s
seareh-depth
limits.
5. Are there characteristics
of the domain that the method
requires, relies on, or exploits in some way?
Theme2hcxt
doesnot rely on anydomaincharacteristics.
C. Evaluation:
1. What hypotheses were explored?
For a certain class of domainsand problems,multi-plan adaptation
will be moreeffectiveat reducingsearchthansingle-planadaptation.
2. What type of evahtation?
25