From: AAAI Technical Report SS-92-01. Compilation copyright © 1992, AAAI (www.aaai.org). All rights reserved.
JIGSAW:Preference-Directed,
Co-operative Scheduling
Theodore A. Linden
David Gaw
AdvancedDecision Systems,
a Division of Booz.Allen& Hamilton, Inc.
1500PlymouthSt.
MountainView, CA94043
linden@ads.corn
415-960-7562
Abstract*
Techniquesthat enable humansand machinesto cooperate in the solution of complex scheduling
problems have evolved out of work on the dally
allocation and scheduling of Tactical Air Force
resources. A generalized, formal modelof these
applied techniques is being developed.It is called
JIGSAW
by analogywith the multi-agent, constructive
process used whensolving jigsaw puzzles. JIGSAW
beginsfromthis analogyand extendsit by propagating
local preferencesinto globalstatistics that dynamically
influence the value and variable orderingdecisions.
The statistical projections also apply to abstract
resources and time periods--allowing moreopportunities to find a successful variable ordering by
reservingabstract resourcesanddeferringthe choiceof
a specific resourceor timepericxt
Keywords:Scheduling, constraint propagation,
statistical look-ahead,hierarchicalplanning,resource
abstractions,transformational
synthesis.
1. Introduction
For manyschedulingproblems,partial automation
is a realistic but difficult goal. Partial automation
meansthat human
schedulerscan participate in incremental schedulingdecisions. Algorithmsfrom operations research and mostheuristic search techniques
involve humansin the problemset up but not in the
generationof schedules. Thesealgorithmsworkwell
when the problem is modeled perfectly and is
* This workwaspartially supportedby the Defense
AdvancedResearch Projects Agency(DARPA)
under
contract DAAH01-90-0080
and partially supported by
IR&D
fundingfrcxn Advanced
De,ionSystems.
136
computationallytractable. Unfortunately,practical
schedulingproblemsoccur in very complexenvironments,it is usually impossibleto capture all of the
domaincomplexitiesin the formalmodel.In practice,
the results of fully automatedschedulingalgorithms
are used primarilyto debugthe problemset up. This
results in a verylarge debugging
loopthat is inefficient
and does not always converge to an acceptable
solution. Furthermore, details about myriads of
individualpreferencesare seldomhandledeffectively.
Whilea humanschedulermaynotice that an important
task in today’s scheduleis one on whichJohnJones
performedeffectively last week,it is impracticalto
expectthat the knowledge
acquisitiontask can capture
all thesesubtlepreferencesin advance.
A co-operative approachto schedule generation
exploits the strengths of both humansand automation,
but co-operationimplies that the schedulingsoftware
has to workwith an incompletemodelof the problem
domain. Humanscheduling decisions should be
viewed as dynamic extensions to that model.
Furthermore, many scheduling problems are
dominated by preferences rather than by hard
constraints, andthese preferencesneedto be exploited
in the samewaythat constraints are exploited in
constraint-directedscheduling.
2. Background and Overview
JIGSAWgeneralizes techniques originally
developed
to partially automatethe daily allocationand
scheduling of Tactical Air Force resources. The
complexity of the knowledge involved in this
schedulingproblemis such that, whendonemanually,
a team of 8-16 people worksover a period of 12 or
morehours. Aninteractive systemthat solves this
problemby allowing humansand the machineto make
incrementalschedulingdecisions wasdesignedthree
years ago, has undergone two years of user
evaluations, 1 and is now being hardened for
operational use. JIGSAW
is a generalization and
formalization of the automatedreasoningtechniques
originallydesignedfor this application.
JIGSAW
is an open collection of techniques that
allow humansto participate as schedules are constructed incrementally.JIGSAW
begins with a transformationalapproachmsimilar
to the transformations
commonly
used to compileprogramspecifications into
programsand to refine design specifications into
designs. Correctness-preserving transformations
encapsulate knowledgeabout incrementalallocation
andschedulingdecisions. Theyseparate the definition
of these decisionrules fromthe controldecisionsabout
whenthey should be invoked.
JIGSAW
extends this transformational approach
withstatistical look-ahead
techniques.Statistical lookaheaduses local constraintsandpreferencesto project
the expectedcontentionfor resourcesover time. These
statistical projectionsallowlocal schedulingdecisions
to be influencedby statistical knowledge
about the
global context. Statistical look-aheadenhancesboth
value and variable ordering techniques. Ourongoing
workextendsthesestatistical projectionsto deal with
abstract resourcegroupings.Partially determinedtime
intervals are also handledas abstract resources. An
assignmentof an abstract resourceto a task creates a
reservationfor an unspecifiedinstance of the ahsWact
resource. Thesereservations for abstract resources
enable incremental commitments
that provide more
opportunitiesto find variable orderingsthat avoidor
reducebacktracking.
The nameJIGSAW
is based on an analogy with
jigsaw puzzleswhere:
¯ ManyIndependent agentsmboth human and
automatedco-operateto construct a solution.
¯ The order in which scheduling decisions
are made is not predetermined by the
problem.
¯ Partial solutions can (usually) be evaluated
(pfobahly)extenstbleto an acceptablesolution.
JIGSAW
extends this analogy with a combination
of techniques for reasoning about preferences,
abstractionlevels, variableordering,anduncertainty.
Unlikejigsaw puzzles, JIGSAW
seeks a globally good
solutionby makinga series of local decisionsthat are
1Therealities of a largeimplementation
haveled to an
early focuson machineassistance for humandecisionmaking; implementation
of the automated
decision-wakiqg
techniquesonwhichJIGSAW
is basedis quite recent.
137
informedby statistical knowledge
abouthowthe local
decisionis likely to impactglobaloptimality.
Theoverall JIGSAW
approachinvolves associating
a transformation with each incremental, atomic
allocation and scheduling decision. The users can
commitsomeschedulingdecisions, and the automated
JIGSAW
techniques accept and work with partial
schedules developed by users. The users control
which transformations will be candidates for
execution. The control software invokes the
transformations that produce the most promising
extensionsof the currentpartial schedule.
3.
Exploiting Value and Variable
Ordering Opportunities
To fully exploit value and variable ordering
opportunities when constructing a schedule
incrementally,individual transformationsof partial
assignmentsshould be kept as atomic as possible.
Mostjob shopschedulingtechniquesexploit variable
ordering opportunities only at the level of complete
orders or resources;that is, they makeassignmentsto
all the tasks involvedin an order or they completely
schedule a single resource. Like Cortes [Fox &
Sycara 90, Sadeh 91], JIGSAW
enables separate
2decisions for each individual task or activity.
JIGSAW
allows a task to be assigned a resource or
scheduledinto a time period without simultaneously
committingto decisions about other tasks or times.
Furthermore, by introducing resource abstraction
hierarchies, JIGSAW
can reserve an abstract resource
for a task whiledeferringthe assignmentof a specific
resource or time interval. These assignments of
abstract resources allow more opportunities for
variableorderingheuristicsto be effective.
Whenallowing very small incremental transformationsthat maybe madein almostany order, one
has a problempreservingthe propertythat any partial
assignmentthat is generated can be extended to a
nearly optimalsolution. In particular, related tasks
mustall eventually receive consistent assignments,
tasks that are assigned an abstract resource must
eventuallyreceivespecific resources,tasks that receive
resources must eventually be scheduled, and tasks
assigned a flexible time period must eventually be
scheduled into a specific time interval. These
problemsare largely avoidedin earlier scheduling
systemswhereall of the decisionsassociatedwith an
order or resource are madesimultaneously;however,
2 JIGSAW’s
t~_~ksare equivalentto Cortes’activities.
Theterms"operation"and"variable"are also usedin the
literature withan equivalentmeaning.
this groupingof decisionslimits the opportunitiesto
fully exploit valueandvariableorderings.
JIGSAW
includes substantial bookkeepingfunctions andstatistics that summarize
the state of current
assignmentsandproject the probableeffects of future
assignments.Thisinformationis usedto inhibit transformations that are likely to interfere with the
completionof existing partial assignments.Projections about the expecteddemandon resources allow
the incrementaltransformationsto achievea balance
betweengreedy local optimization and altruistic
minimization
of resourceconflicts [Sycaraet al. 90].
The bookkeepingfunctions and statistics apply to
abstract as wellas specific resourcesandtimeperiods.
Reservationfor abstract resourcesare guaranteedin
that transformationsmakingassignmentsto other tasks
will preserveenoughinstancesof the abstract resource
to fulfill all prior reservations.Significantly,manyof
these samebookkeepingfunctions and statistics are
also useful to the humanexperts whoco-operatein the
problemsolving process.
basically a greedy algorithm augmentedwith plan
repair techniques.However,
the statistical look-ahead
techniques together with reservations for abstract
resourcesalso workin the context of backtrackingor
breadth-first search strategies. The choice of lhe
searchstrategy is controlledby the size of the problem
and the needto interact with human
schedulers,not by
the statistical look-ahead.Human
schedulersappearto
be mostcomfortablewith divide-and-conquer,greedy
algorithms,andplanrepair strategies---togetherwitha
very limited amount of breadth-first search and
backtracking.
Thecritical part of JIGSAW
is the inner loop where
statistics about expectedresource availability ate
projectedand a transformationthat doesnot needto be
deferred is found. This section summarizes
the steps
usedin the Tactical Air Forceschedulingproblemfrom
which JIGSAWevolved. A more formal, general
treatment can be found in [Linden 91], and we are
currently trying to formalizethese ideas moredirectly
in termsof Bayesiannetworksand decisontheory.
This description of the inner loop in JIGSAW
is a
Thebookkeepingfunctions and statistics are also
step toward generalizing the computations, not
used to dynamicallyselect the order in which the
transformationsare executed.Thegoal is to defer each
optimizing them. The Air Force application where
transformation until there is enoughinformation
these techniques were applied deals with file
optimizationissues; manyoptimizationsare available
available to predict that its decisionis a step toward
by reusing previouscomputations.
achievinga nearly optimalassignment.Notethat ff all
transformations meet this goal, then whenevera
Tte steps of the innerloopare:
specific task-resourceor task-time-periodpairing is
1. Local rating: Use constraints to identify the
required to achieve an optimal assignment, other
alternative resourcesand time periods that can be
Wansformations
will not use up the last instanceof the
assignedto each task, and use preferencesto order
resource
ortime
period
that
isneeded
bythis
task.
Of
or rate these possible values. This local rating is
course,
with
invocation
criteria
asstringent
asthis,
the
based on the easily-processed constraints and
problemis whethertherewillalwaysbe a
preferences directly associated with the task;
transformation
thatdoesnotneedtobedeferred.
An
initially, it doesnot deal with global issues like
experimentalhypothesisbeingevaluatedis: for many
resourceavailability.
large problems that are characterized by many
preferencesandthat canbe solvedadequatelyby teams
2. Globalstatistics: Translatethe local ratings for
of humanexperts, there will usually be some
eachalternative value assignmentinto a subjective
"obvious" transformation that does not need to be
probability that this assignmentwill be made,and
deferred. When
there is no such transformation,then
sumtheseprobabilitiesacrossall the tasks to project
either humanintervention or a branch and bound
globalstatistics aboutthe expecteddemand
for each
searchstrategycanbe usedeffectively.
resource. Comparisonof the expected demandfor
resources with the available resources identifies
In summary,the automated portion of JIGSAW
probablebottlenecks.
starts fromanyconsistentpartial assignment
(initially
from the empty assignment unless humanexperts
3. Tradeoff: Re-evaluate the alternative value
makesomeinitial decisions), finds a transformation
assignmentsin termsof whichchoiceis mostlikely
that is statistically the least in needof beingdeferred,
to be part of a globally optimalassignment.This
executes that transformation, and iterates. Humans
re-evaluation uses the statistics about resource
control the overall processandcaninterleavetheir own
contention and makesa trade off betweenlocal
decisionsbetweentransactioninvocations.
utility andglobalresourcecontention.
4. Statistical Projections
4. Commit:For one or more. tasks, "commit"to a
transformationthat is projected to lead towarda
In the TacticalAirForceapplication,
statistical lookgood complete assignment. Chooseto makethis
aheadwasused to give moresophisticationto whatis
138
commitmentfor tasks where the decision is
"obvious" and/or "influential":
a,
Obviousdecisions are those where one can
project a very high confidencelevel that a
decision made nowwill be "right." This
confidence
is evaluatedin termsof:
Strength of the local preference for the
proposedcommitment
relative to alternative
possible values. This maybe computedas
the delta betweenthe rating of the valueto
be committed
andthe rating of the next best
value.
The commitment’suse of low contention
resourcesbasedon the statistical projections
of the expecteddemandfor each resourceat
varioustimes.
- The quality of the current understanding
about howinteractions with other tasks
mightaffect this task.
b. Influential decisions are decisions which
clarify manyother decisions; for example,a
decision to commitbottleneck resources is
influential becauseit narrowsthe choicesthat
remainopenfor all others decisions.
5) Plan repair: Plan critics are available as a wayof
undoing a previous decisionmalong with the
decisionsthat directly dependon it. Plan critics
resolve conflicts that arise fromimperfectlookaheador fromchangingconditionsin the external
environment.
Plan critics havebeenincludedin the
design of JIGSAW
applications, but they havenot
yet beenaddedto the formal JIGSAW
model.
needto be involvedto helpevaluatethe feasibility and
effectivenessof the evolvingschedules.
6. References
[Fox &Sycara 90] MarkS. Foxand Katia P. Sycara,
"Overview of CORTES:A Constraint Based
Approachto Production Planning, Scheduling,
and Control," Proc. of the FourthInter. Conf.on
Expert Systems in Production and Operations
Management,May, 1990.
[Linden 91] Theodore A. Linden, "Preferencedirected, Co-operativeResourceAllocation and
Scheduling." Final Technical Report, DARPA
Order No. 6685, AdvancedDecision Systems
ReportTR-1270-3,Sept. 1991.
[Sadeh 91] NormanSadeh, "Look-aheadTechniques
for Micro-opportunistic Job ShopScheduling."
PhD Thesis, School of Computer Science,
CarnegieMellonUniversity, 1991.
[Sycaraet al. 90] Katia P. Sycara,S. Roth, N. Sadeh,
and M. Fox, "ManagingResourceAllocation in
Multi-Agent Time-constrained Domains."DARPA
Workshopon Innovative Approachesto Planning,
Scheduling, and Control., Morgan Kaufman
Publ., San Mateo,CA,Nov.1990, pp. 240-250.
5. Conclusions
JIGSAW
evolved from work on large scheduling
applicationsthat mustbe solvedco-operativelyand are
dominated by preferences rather than by hard
constraints. JIGSAW
exploits those preferences to
projectstatistical characteristicsof the globalsituation
whichare then usedto enhancelocal valueandvariable
ordering decisions. JIGSAW
extendsthese statistical
projections to abstract groupingsof resources and
allows partial schedulesto include reservations for
abstract resources. Thesereservations for abstract
resources open moreopportunities for value and
variableorderingtechniquesto be effective.
JIGSAWis proposed as one of a range of
scheduling techniques It is appropriate for large
resourceallocationandschedulingapplicationsthat are
currently solved by teams of humanexperts. It is
especially appropriate for problems where the
evaluationcriteria are complex,changing,andnot fully
formalized--problems for which humanschedulers
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