From: AAAI Technical Report SS-92-01. Compilation copyright © 1992, AAAI (www.aaai.org). All rights reserved.
Completable Scheduling: An Integrated
Approach to Planning and Scheduling
MelindaT. Gervasioand GeraldF. DeJong
Beckman Institute
for Advanced Science and Technology
University of Illinois at Urbana-Champaign
405 N. Mathews Ave., Urbana, IL 61801
gervasio@cs.uiuc.edu
dejong@cs.uiuc.edu
Abstract
Theplannlng problem
has traditionallybeentreated separately
fromthe schedulingproblem.However,
as morerealistic domainsare tackled, it becomes
evidentthat the problem
of decidingonanordered
set of tasksto achievea set of goalscannot
be treated independently
of the problem
of actually allocating
resources
to the tasks. Doingso wouldresult in losingthe robustnessand flexibility neededto deal withimperfectlymodeled domains.Completable
schedulingis an approachwhich
integrates the twoproblemsby allowingan a priori planning
moduleto defer particularplanningdecisions, and consequentlythe associatedschedulingdecisions, until execution
time. This allows a completableschedulingsystemtomaximizeplan flexibility by allowingrantimeinformationto be
takeninto considerationwhenmakingplanningand scheduling decisions.Furthermore,
throughthe criterion of achievability placedon deferreddecisions,a completablescheduling
systemis able to retain muchof the goal--directednessand
guaranteesof achievement
affordedbya priori planning.The
eompletableschedulingapproachis further enhancedby the
use of contingentexplanation--based
learning, whichenables
a completableschedulingsystemto learn generalcompletable
plans fromexampleand improveits performancethroughexperience.Initial experimental
results showthat completable
schedulingoutperformsclassical schedulingas well as pure
reactive schedulingin a simpleschedulingdomain.
Introduction
Theplanning problemhas traditionally beentreated separately from the scheduling problem. Planning deals with the determinationof an ordered set of actions for achievinga set of
goals. In the context of scheduling domains,planning deals
with determiningan ordered set of tasks for a set of jobs. In
contrast, schedulingdeals with the actual assignmentof tasks
to machinesand is generally concernedmorewith finding the
best of several alternative task-machine assignments than
with finding aparticular task-machine assignment. As more
realistic scheduling domainshave been addressed, however,
it has becomeapparent that planning and scheduling cannot
be treated independently. The complexity of real-world domainsmakesperfect characterizations difficult to construct
and often unwieldy.To this end, researchers in both planning
and scheduling have investigated reactive approacheswhich
allow for decision-making during execution [Agre87, Firby87, Kaelbling88, Muscettola90, Ow88,Presser89].
However,the classical approachof first doingplanningand
then scheduling still remains a problem. Consider giving a
classical systemin a process planningdomainthe job of man-
117
ufacturing a particular part. Its planner mustdecide a priori
on an orderedset of actions or operations whichwill result in
the conversionof the raw material into the desired product.
Its scheduleris then given the responsibility of actually allocating resources and carrying out the operations on the machines. However,becausethe planner commitsthe system to
a particular set of operations, the scheduler maynot execute
the best plan. For example, the planner maynot be able to
guaranteethat the efficient newmilling machinewill be available and so choosethe older, slower one. However,during execution, the moreefficient machinemayturn out to be available, but the scheduler does not havethe option to alter the
plan. Furthermore, an over-constrained classical plan may
prevent quick fixes to unpredictable runtime situations, For
example,a chosendrill bit mayturn out to be unavailable,thus
rendering invalid those subsequentactions involving a correspondingly sized bolt and wrench. A simple fix wouldbe to
use a different drill bit, and switchto the appropriatelysized
bolt and wrench, but a scheduler with a completely--determinedplan does not have this capability.
A purely reactive approach,with no a priori planning, has
its ownproblems. Most manufacturing domains are fairly
well-behaved; there is muchinformation available a priori
and fairly accurate predictions can be madeabout the behavior of the world under particular circumstances. A purely
reactive approach which performs no projection cannot take
advantageof this informationto constrain its actions and prevent thrashing. Withthe planning problemand the scheduling
problem combined, the runtime decision-making problem
also becomesa larger and more complexone.
This research beganas an attempt to address the problems
with classical, a priori planningand purereactivity. In particular, completable planning was developed as an approach
which combinedthe goal--directedness and provably correct
plans of classical planningwith the flexibility and ability to
utilize runtime information afforded by reactive planning.
This enabled a completableplanner to moreefficiently deal
with the problemsarising from imperfect a priori information
whilestill retaining the benefits of planningbeforehandin relatively well-behaved environments. Morerecently, we have
been investigating scheduling, and we have found that many
of the techniquesoriginally developedas part of the completable approachto planningare also useful for solving someof
the problems which arise from scheduling in realistic domainswhere perfect a priori information about the environmentis unavailable. For example,in the scheduling scenario
above, a completablescheduling systemcould defer the deci-
sion
ofwhich
milling
machine
touseaswell
asthechoice
of
execution.In attachingtwopartsusinga bolt, all that a system
bit,
bolt,
andwrench
sizes.
During
execution,
itcanthen
use
mayknow
is that it will be givena bolt of somesize, butit may
additional
information
regarding
resource
availability
toadnot knowprecisely whatsize. However,
providedit has acdress
thedeferred
planning
decisions
andmake
theassociated cessto differentiy-sized
bits andwrenches,
it canplana driUscheduling
decisions
aswell.
ing operationfollowedby a boltingoperationwithoutspeciInthis
paper,
wepresent
anintegrated
approach
toplanning fying the precise bit and wrenchto use. Duringexecution,
andscheduling
called
completable
scheduling.
Wewill
first when
it is giventhe bolt, it canthendetermine
the appropriate
give
anoverview
ofthemain
ideas
behind
completable
plan- valuesfor bit size andwrenchsize. Completable
scheduling
ning,
andthen
discuss
theextension
toscheduling.
Wewill
allowsthe use of conjecturedvariablesto act as placeholders
thendiscuss
howcomplctable
schedules
arelearned
through for unspecifiedparametersettings providedachievability
anexplanation-based
learning
strategy
called
contingent proofscan be constructedfor their eventualinstantiation. By
EBL.
Finally,
wewill
briefly
discuss
theimplementation,
inallowingdeferred parametersettings, completableschedulcluding
some
preliminary
results
andongoing
experiments.ing enablesa systemto both plan aheadandyet remainflexible enoughto deal with someuncertainty.
Second,a schedulemaybe incompletedueto an undeterCOMPLETABLE
SCHEDULING
minablenumberof iterations. Animperfectworldmodelmay
includeincompletecharacterizationsof operationsandtheir
Overview of Completable Planning
effects. Consequently,
for an actionthat requiresrepetitionto
In completableplanning[Gervasio90a,Gervasio90b,Gervaachievesomegoal, the precise numberof iterations needed
sio91], a classical planneris augmented
with a reactivecommaynot be determinableprior to execution.For example,the
ponentwhichprovidesit withthe ability to defer planningdedepthto whicha millingoperationcuts througha part is decisions until executiontime. As an augmentedclassical
pendenton the face cutter used.Prior to execution,a system
planningapproach,completableplanningretains the advanmaynot knowwhichface cutter will be set up on the machine.
tages of classical planningwhilebuyinginto the advantages
However,
it knows
that regardlessof whiehface
cutter is used,
providedby reactivity. Fromclassical planning,completable
the desiredcut can be achievedby simplyrepeatingthe millplanningborrowsthe ability to constructprovably--correct
ing operationas manytimesas necessary.Bynot tying itself
plans for providinggoal--directedbehavior. Fromreactive
to a particularface cutter andconsequently
a particular numplanning,it borrows
planningflexibility andthe ability to utiber of iterations, duringexecutionthe systemcan chooseto
lize runtimeinformationin makingplanningdecisions. Comuse the currentset-up andsavethe cost of changingset-ups,
ptetableplanningachievesthe integrationthroughthe achievor it canelect to changeto a moreefficient set-up. Completability criterion, whichrequires everydeferred goal to be
able schedulingpermitsthe defermentof iteration decisions
provenachievable.Provingachievability requires proving
providedincrementalprogress whichconvergesto the goal
that there exists a plan whichwill achievethe goal. Ourrecan be proven.Through
this deferment,a completable
sy stem
searchhas shownthat provingthe existenceof a plandoesnot
can use imperfectoperationdescriptionsas well as makeoptinecessarilyentail determining
the planitself, andthe intuition
mizationsto a schedulebasedon runtimeinformation.
is that provingachievabilityrequires muchsimplerandmore
Third, a schedulemaybe incompletedueto an unidentifireadily available a priori knowledge
than full-blownplanable operationchoiceor task-machine
assignment.This case
ning. Acompletableplanneris thus able to construct proarises whenthere are multiple waysof achievingthe same
vably--correctplans in spite of incomplete
a priori informagoal fromdifferent states andthe systemlacks the necessary
tion, andin doingso providegoal-directednes
s to its reactive
a priori information
for identifyingwhichparticularstate will
component
whileallowingitself to defer decisionsandutilize
bereached.This case also arises whenthere
are multipleways
runtimeinformationin addressingdeferred goals.
of achievinga goal, withdifferentsituationsresultingin different preferencesamongthe various alternatives, andthe
Deferring Decisions
systemdoes notknow
aprioriwhichsituation will be reached.
Thedefermentof schedulingdecisionsis a powerfultool in
For example,in planningto shapean object, a systemmight
dealing with imperfecta priori information.Thecomplexity
use someor all of variouscutting operations,suchas milling,
of real-worlddomainsmakesit difficult to constructperfect
planing,sawing,or grinding.Whether
there are severalpossimodels.Evenwhenperfect modelsexist, their use often exble states requiringdifferent operationsormultipleapplicable
ceedsreasonablecomputational
bounds.Arealistic scheduloperationswith unknown
preferences,a systemcan use addiing systemis thus left to contendwith imperfectknowledge. tional runtimeinformationto makea more-informed
operaThereare four types of incompleteness
whichcan result from
tion choice. Completable
schedulingallowsa systemto defer
usingclassical planningtechniqueson imperfectinformation.
operationchoiceprovidedit canprovethat there exists a way
First, a schedulemaybe incomplete
dueto an unspecifiable
to reachthe next state regardless of whichof the possible
parameter
setting. Withthe lack of a fine-grainedandtractastates is reached.This defermentis useful for tworeasons.
ble worldmodel,a schedulingsystemmaynot be able to deFirst, it enablesa systemto use the samescheduleto achieve
termineprecise parametersettings a priori. For example,the
a goal fromanyof severaldifferent states. Second,it allows
parametersof an operationmaybe dependenton the propera systemto applypreferencesto a set of possibleoperations
ties of a particular object, whichmaynot be knownprior
to
using morecompleteand accurate runtimeinformation.
118
Fourth, a schedulemaybe incompletedue to an unorderable set of operations.Imperfecta priori information
mayresult in insufficientconstraintsfor completely
orderinga set of
operations.For example,in the constructionof twopans,the
only precedenceconstraints maybe betweenthe milling,
drilling, andtappingoperationsfor eachpanmi.e,the operations for the different panscan be orderedin any way.Dependingupona priori knownfactors such as the pans involvedandthe difficulty of changingset-ups as well as a
priori unknown
factors suchas the initial set-up andmachine
availability, particularorderingswill be moredesirablethan
others. Bydeferring the decision until all the factors are
known,a systemcan utilize runtimeinformationto makedecisions for moreoptimalorderings. Completable
scheduling
permitsthe defermentof orderingdecisionsprovidedthe different orderingsare all capableof achieving
the goal. In doing
so, a completable
plannercan utilize runtimeinformationin
makingmore-informedordering decisions for an unconstrainedset of actions.
Proving Achievability
Whileimperfecta priori information
is the primaryreasonfor
deferringdecisions,achievabilityis the primarycriterion for
deferment
in completable
scheduling.Byrequiringthat a deferred goal be provenachievable,completableschedulingenables the construction of incompleteyet provably-correct
plans. Previous workon achievability involved finding
proofsfor the existenceof plans to achievedeferredgoals.
Achievabllityproofs for deferred parametersettings and
numberof iterations are discussedin [Gervasio90a,Gcrvasio90b], andfor deferredoperatorchoicein [ Gervasi091
]. In
[Gervasio91],completableplanning wasalso extendedto
probabllisticdomains
by relaxingthe originalcriterion of absolute achievabilityto probableachicvabllity.
Scheduling
domainsgive rise to further newissues in achievability.In planning,the mainfocusis findinga plan,or sequenceof actions,whichachievesthe goalfroma giveninitial
state. In scheduling,the existenceof severalpossibleschedules is takenas a given, andthe focusis choosingonefrom
amongthemusing someset of preferencecriteria, maximizing particular performance
measures.Examplesof performmacegoals are meetingdeadlinesand minimizing
idle time.
Thus,simplydefininga goal to be achievableif there exists
a planfor it is insufficientfor scheduling.Achievability
must
also be relatedto the ideaof optimization
andrelative preferencesbetweenpossiblecoursesof action. For example,proving the achievabilityof the goalassociatedwithan unordered
set of actions is implicit in the constructionof a nonlinear
plan--i.e, actionsare left unordercd
if thereare noconstraints
requiring precedencerelations betweenthem.Thusthere exists a planfor achievingthe goal.However,
thereis the interesting issue of decidingona completeorderingduringexecution. This involvesseekingout additional informationfor
evaluatingthe differentoptionsas wellas carryingout the operations themselves.In tying the conceptof achievabilityto
optimization,wecanalso better investigatea primarymotivation for combining
classical andreactivetechniques:the ability to utilize mntime
informationin planning.Goal-directed,
119
robust behaviorin the face of uncertaintyis onereasonfor
augmenting
a classical plannerwith reactive abilities. However, anotherreasonto integratethe twoapproaches,
is to take
advantageof the wealthof informationwhichbecomesavailable at runtime.This additionalinformationfacilitates planning byhelpingto focusthe searchfor an appropriateaction.
LEARNING COMPLETABLE SCHEDULES
Explanation-basedlearning [DeJong86,Mitchell86] has
beendemonstrated
to be useful in improving
the performance
of various planningsystems[Bennett90,Chien89,Fikes72,
Hammond86,
Minton85],and in [Gervasio90a,Gervasio91]
wepresent an explanation-basedlearning strategy called
contingent EBLfor learning completableplans. Learning
completable
schedulesbasically involveslearningto distinguish betweena priori planning decisions and decisions
whichhaveto be madeor are better madeduringexecution.
Learningwhento defer decisionsinvolvesfirst identifying
the deferred decision, then constructingan achievability
prooffor the associateddeferredgoal. Thena completorfor
makingthe deferreddecisionduringexecutionmustbe incorporatedinto the learnedgeneralplan.
Identifying Deferred Decisions
Amaindifference betweenclassical plans andcompletable
plans is the existenceof deferred decisionsin completable
plans. In constructingan explanationfor howa giventraining
exampleachievesa target goal, an EBLsystemmustexplain
howeach action is chosenfor execution.In planning, this
usuallymeansverifyingthat previousactionsachievethe preconditionsnecessaryfor the executionof an action. However,
withthe additionof reactiveabilities andthe optionto utilize
runtimeinformation,a systemneedsto distinguish between
a priori satisfied preconditionsandruntime-verifiedpreconditions. Oursolutionis to allowthe systemto distinguishbetweena priori informationandruntime-gathered
information
andto prefera classicalproofof correctnessto an explanation
of achievability.Thus,in explaininghowan action is chosen
for execution,a systemfirst attemptsto explainits preconditions witha priori availableinformation.If this is unsuccessful, thenthe actionbeingexplainedis taggedas a potential
deferred decision, andthe systemattemptsto construct an
achievabilityexplanationfor the precondition.Onlyif it is
successfulis the learningprocessallowedto continue.Thefinal explanation
will thus containthe identifieddeferreddecisions as well as their supportingachievabilityexplanations.
Tyingthe conceptof achievabilityto optimization
addsfurther concerns.Anexplanationof executabilityis no longer
enough.Explanationsfor preferences mayalso need to be
constructed,andas with other deferreddecisions,the associated runtimeverified conditionsneedto be distinguished
froma priori satisfied conditions.Aswithproofsof correctnessandexplanations
of achievability,explanations
of preferences mayalso be constructedin standardEBLfashion.
Constructing Achievability Proofs
Toconstruct provably-correctplans, a completableplanner
mustconstructachievabilityproofsfor the deferredgoalsof
its incompleteplans. Whilethe mechanicsof constructing
proofsof correctnessvs. proofsof achievabilityare essentially the same--b(~huse standardEBLon a given domaintheory-there are somerequirementsneededfor a domaintheory
to be usedin provingachievability.
Therearefourtypesof deferreddecisionsandeachrequires
particular kindsof informationfor provingachievability.
First, deferred parametersettings mustbe represented,and
this is doneusingconjecturedvariables. Thesevariablesmay
onlybe introducedin the contextof the rules usedto construct
their corresponding
achievabilityexplanations,thus guaranteeing that everyconjecturedvariable in an explanationhas
a supponiugaehievability proof. Second,a systemmustbe
able to reasonaboutthe incrementalprogressachievedby a
repeatedaction. Thisrequiresactioncharacterizationsto inelude statementsregardingthe changesmadewith respect to
somemeasurablequantity. This can then be used to reason
about progress towardsthe goal. Third, the incompletely
known
situation requiringa deferredoperator choicemustbe
representedin sucha waythat the systemcan reasonaboutthe
spaceof possibilities. Achievabilitycan then be measured
in
termsof the eoverageprovided
bythe alternative actionsover
this space.Finally, provingachievabilitywithrespect to an
unordered
set of operationsis implicitin the absenceof precedenceconstraints betweenthe operations, whichmeansthat
anyof the possibletotal orderingswill achievethe goal.
Thesecondaspect of achievability, optimality, also imposescertain requirementson the domaintheoryusedto construct explanations.Theheuristics to be usedin making
dispatching or schedulingdecisions mustbe built in to the
domaintheory. Theseheuristics can then be used both for
constructinga priori explanationsandmakingruntimedecisions. In explainingparticular decisionsmadein a training
example,a systemcan then construct explanationsincorporating the heuristics and learn general completableplans
whichwill employ
the heuristics in future applications.
Incorporating Completors
Thefinal step in learning howto construct a completable
scheduleis to incorporatecompletionsteps into the learned
generalplan. Thereare four types of completorscorresponding to the fourdifferenttypesof deferreddecision.Thefirst,
a monitor,findsa valueto replacea conjectured
variable---i.e.
it’ determines
a specific parametersetting. Thesecond,a repeat loop,repeatedlyexecutesan actionuntil a particularexit
condition,the deferredgoal, is reached.Thethird, a conditional, evaluatesthe currentstate anddetermines
an appropriate actionbasedon whichconditionsare satisfied. Finally,the
fourth, a dispatcher, determinesa completeorderingfor an
unordered
set of operations,basedona givenset of heuristics.
Theachievabilityproofs constructedfor the deferred decisions addressedby these completors
are incorporatedinto the
explanationssupportingthe learnedplan. Thusthe achievability conditionsguaranteeingthe existenceof a completion
are also in the learnedplan. Provided
these conditions,along
with other preconditions,are satisfied in future instances,a
completion
is guaranteedto be foundfor the incompleteplan
yieldedby the learnedgeneralplan.
120
IMPLEMENTATION
A simpleschedulingdomaintheory has beenconstructedto
comparethe performanceofacompletableschedulingsystem
withthat of a purelyclassical scheduling
systemas well as a
purely reactive scheduling system. Thedomaininvolves a
single machine
whichcan be set up in variousways,eachsetup of whichis capableof performingsomeset of tasks. The
sametask maytake different processingtimes on different
set-ups. Furthermore,there is a set-up cost involvedin
changingset-ups. Ajob consists of apartially orderedset of
tasks, anda schedulingprobleminvolvesa set of independent
jobs. Initially, the onlyorderingcoustmints
between
tasks are
based on deadlines. However,additional precedenceconstraints maybe imposed
between
the tasksof a job if the a priori planningmodule
of the systemdeterminesthat onetask is
neededto establish the preconditionsfor anothertask. Uncertainty enters into the picture throughan unknown
initial state--i.e, the systemdoesnot knowa priori whichset-up will
be onthe machine
whenit starts executingits plan. Finally,
the goodnessof a scheduleis measured
by the length of time
takenby the systemto finish a set of jobs.
Preliminaryresults showthat a completable
system’sability to adapttovarying
initial states enablesit to constructmore
efficient plans/schedulesthan a classical scheduling,which
commits
itself to specific set-upsandcompletetask orderings
prior to execution. Furthermore,the completablesystem
needsless time both to learn a generalcompletable
schedule
as well as constructa specific completable
schedule,although
it doesincur the additionalcost of runtimeplancompletion.
Thecompletable
systemis also able to constructmoreefficient plans than a reactive systembecauseit is morefocused
in its searchfor an applicableaction, havingdeterminedas
manyprecedenceconstraints betweentasks as it can prior to
execution.Althoughboth use the sameheuristics for choosing between
multipleapplicableactions, the reactive system
has the additionalburdenof sorting out precedencerelations
betweentasks during execution. Furthermore,althoughthe
completable
systeminitially needsto constructa completable
schedule,the use of learninghelpsreducethe a priori planning
cost it incurs over the reactive scheduler.Weare currently
runningexperimentsto gather moredata aboutthe performanceof the three approaches
givendifferentdistributionsand
different machine/set-up/task-processing
profiles. Theresuits are expectedto helpidentifyparticulardomain
andproblemcharacteristics whichfavor the different approaches.
SUMMARY AND CONCLUSIONS
This workintegrates planning--thedeterminationof an orderedset of tasks--andscheduling--theassignmentof those
tasks toresource---throughcompletableplans.Becausecompletable plans are incomplete,additionalplanningis necessary duringexecution,whenschedulinghas begunto dispatch
the tasks. Thus,this workdiffers fromreactive approaches,
suchas those discussedin [Ow88,Prosser89,Smith90,Zweben90],whereplanningis separatedfromscheduling,andthe
mainapproachto uncertaintyin the environment
is to replan
whenthe constraintsof the original planare violated. While
replanningis a valuabletool whichanyreal systemwill even-
ceedings of The Eleventh International Joint Conferenceon Artificial Intelligence, Detroit, MI, August1989, pp. 590-595.
[DeJong86] G. E DeJoag andR. J. Moonoy,"Explanation-Based
Learning: An Alternative View," Machine Learning 1, 2 (April
1986), pp. 145-176. (Also appears as Technical Report UII.UENG-86-2208,AI Research Group, Coordinated Science Laboratory, University of Illinois at Urbana--Champaign.)
[Drvmmond90] M. Drummondand J. Bresina, "Anytime Synthetic Projection: MaximlzlngtheProbabilityofGoal Satisfaction,"
Proceedingsof the Eighth National Conferenceon Artificial Intelligence, Boston, MA,August 1990, pp. 138-144.
[Fikes72] R. E. Fikes, P. E. Hart and N. J. Nilsson,"learningand Executing Generalized Robot Plans," Artificial Intelligence 3, 4
(1972), pp. 251-288.
[Firby87] R. J. Firby, "An Investigation into Reactive Plnnningin
ComplexDomains,"Proceedings ofthc NationaI Conference onArtificiallntelligence, Seattle, WA,July 1987, pp. 202-206.
[Fox84] M. S. Fox and S. F. Smith, "ISIS--a knowledge-based
system for factory scheduling," Expert Systems 1, 1 (July 1984),.
[Gervasio90a] M. T. Gervasio, "Learning General Complotable
Reactive Plans," Proceedingsof the Eighth National Conferenceon
Artificiallntelligence,
Boston, MA,August 1990, pp. 1016-1021.
[Gervasio90b] M. T. Gervasio, "learning Completable Reactive
Plans Through Achievabillty
Proofs," Technical Report
UIUCDCS-R-90-1605,
Department of Computer Science, University of Illinois, Urbana,IL, May1990.
[Gervasio91] M.T. Gervasio and G. F. DeJong, "Learning Probably
Completable
Plans,"
Technical
Report
UIUCDCS--R-91-1686,
Department of Computer Science, University of Illinois, Urbana,IL, April 1991.
[Hammond86] K. H,rnmond, "CHEF: A Model of Case-Based
Planning," Proceedingsof the National Conferenceon Artificial Intelligence, Philadelphia, PA, August1986, pp. 267-271.
[Kaelbling88]L. P. Kaelbling, "Goals as Parallel ProgramSpecifications," Proceedingsof The SeventhNationaI Conferenceon Artificial Intelligence, Saint Paul, MN,August1988, pp. 60-65.
[Knobloek90]C. Knobloek,"learning Abstraction Hierarchies for
ProblemSolving,"Proceedings of the Eight National Conference on
Artificial Intelligence, Boston, MA,1990, pp. 923-928.
[Martin90] N.G. Martin and J. E Allen, "Combining Reactive
and Strategic Planning through DecompositionAbstraction," Proceedings of the Workshopon Innovative Approachesto Planning,
Scheduling and Control, San Diego, CA, November1990, pp.
137-143.
[Minton85] S. Minton, "Selectively Generalizing Plans for Problem-Solving," Proceedingsof the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, August1985, pp.
596-599.
[MitcheU86]T.M. Mitchell, R. Keller and S. Kedar--Caballi,"Explanation-Based Generalization: A Unifying View," Machine
Learning1, 1 (January 1986), pp. 47-80.
[Muscettola90]
N. Museettola and S. E Smith, "integrating
Planning and Scheduling To Solve Space Mission Scheduling Problems," Proceedings of the Workshopon Innovative Approachesto
Planning, Scheduling and Control, San Diego, CA, November
1990, pp. 220-230.
[Ow88]E S. Ow,S. Smith and A. Thiriez, "Reactive Plan Revision,"Proceedings of the Seventh National Conferenceon Artificial
Intelligence, St. Paul, MN,August1988, pp. 77-82.
[Presser89] P. Presser, "A Reactive Scheduling Agent," Proceedings of the Eleventh lnternationalJoint Conferenceon Artificial
Intelligence, Detroit, MI, August1989, pp. 1004-1009.
[Sacerdoti74] E. Sacerdoti, "Planning in a Hierarchy of Abstraction Spaces," Artificiallntelligence 5, (1974), pp. 115-135.
[Smith90] S. E Smith, P. S. Ow,N. Muscettola, J. Potvin and D.
C. Matthys, "OPIS: An Integrated Frameworkfor Generating and
Revising Factory Schedules," Proceedingsof the Workshopon lnnovativ e Approachesto Planning, Schedulingand Control, San Diego,
CA, November1990, pp. 497-507.
[Stefik81]
M. Stefik, "Planning and Metaplanning (MOLGEN:
Part 2),"ArtificiallnteUigence 16, 2 (1981), pp. 141-170.
[Zweben90] M. Zweben, M. Deal and R. Gargan, "Anytime Rescheduling," Proceedings of the Workshop on Innovative Approaches to Planning, Scheduling and Control, San Diego, CA,November 1990, pp. 251-259.
tnally need, our work first focuses on constructing plans
which are as flexible as possible to minimizethe need for failure recovery. In this sense, it is similar to ideas presented in
[Drummond90, Martin90]. Drummondand Bresina present
an algorithm for maximizingthe probability of goal satisfaction in the case of actions with different possible outcomes,
which is one of the problems the conditionals in completable
scheduling address. Martin and Allen also prove the achierability of goals deferred to the reactive planner,but they do so
using empirical methods, in contrast to the explanation-based
methods we use. Completable scheduling may also be viewed
as a shallow hierarchical planner, where runtime decisions are
at the lowest level. However,unlike other hierarchical planners and schedulers,
such as ABSTRIPS[Sacerdoti74],
MOLGEN
[Stefik81],
and ISIS [Fox84], a completable
scheduling system uses the achievability constraint to guarantee completability at lower levels. The ordered monotonic
hierarchies of ALPINE[Irmoblock90] are a similar idea. The
difference is that ALPINEperforms abstraction based on the
deletion of literals, while in proving achievability eompletable scheduling uses explicitly more general or abstract
knowledgeregarding the deferred goals and their properties.
The idea of deferred decisions is not a novel one---the least
commitmentprinciple is a basic foundation ofnonlinearplanning, for example. What completable scheduling does is extend the least commitmentprinciple to execution time and in
doing so, achieving a well-founded integration of planning
and scheduling. Unlike other reactive approaches, in which
all decisions are subject to deferment, in completable scheduling only achievable decisions may be deferred. This has
two main benefits. The first is that the cost of dynamicdecision-making is minimized, since only some goals must be
planned for and scheduled during execution. The second is
that the robustness and flexibility afforded by reactivity is
gained without losing the goal-directedness and guarantees
of success afforded by a prioriplanning. Additionally, the use
of contingent EBLenables a completable scheduling system
to improve its performance through experience. By learning
general completable schedules from example, the system can
amortize the cost of constructing a completable schedule over
the number of times the learned general schedule is applied
in future instances as well as reduce the planning cost incurred
by the system’s a priori planning module.
Acknowledgments. This research was supported by the Office of Naval Research under grants N-00014-86-K-0309
and N-00014-91-J-1563. We would also like tothank Scott
Bennett, Steve Chien, Jon Gratch, and Dan Oblingerfor many
interesting discussions, as well as Michael Shaw, for introducing us to the domain of process planning and scheduling.
References
[Agre87] P. Agre and D. Chapman,"Pengi: An Implementation of
a Theoryof Activity," Proceedingsof the National Conferenceon
Artificial Intelligence, Seattle, WA,July 1987, pp. 268-272.
[Bennett90] S. Bennett, "Reducing Real-world Failures of Approximate Explanation-based Rules," Proceedings of the Seventh
International Conferenceon MachineLearning, Austin, TX, 1990,
pp. 226--234.
[Chien89]
S.A. Chien, "Using and Refuting Simplifications:
Explanation-basedlearning of Plans in Intractable Domains,"Pro-
121