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Transcript of Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008 Constraint-Based Scheduling...
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Constraint-Based Scheduling
Adapted from slides by Stephen F. Smith
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Announcements
• 4/21 Lecture – Prof. Eric Nyberg of LTI will presenting on the Q&A technology in WATSON.
• Zico will be holding his normal office hours today from 3:00 – 4:00.
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Outline
• What is scheduling?
• Basic constraint-based scheduling models
• Managing schedule change
• Planning and Scheduling
• Coordinating Distributed Scheduling Agents
• Coordinators: A Distributed Scheduling Case Study
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
What is Scheduling?• Given problem constraints and objective criterion, figure out how to best execute
tasks with available resources over time
OP1,1 OP1,2 OP1,3
OP2,1 OP2,2
R1 R2rd1 dd1
dd2rd2
i j
st(i) + p(i) ≤ st(j), where p(i)is the processing time of op i
st(i) + p(i) ≤ st(j) V st(j) + p(j) ≤ st(i)
rd(j) ≤ st(i) for each op i of job j
i jR
Minimize ∑ |c(j) - dd(j)|
OP1,2OP2,1
OP1,3OP2,2OP1,1R2
R1
time
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
What is Planning and Scheduling?• Planning - Synthesis of
action sequences to achieve goals (what to do)
• Scheduling - Assignment of resources and times to actions to maximize performance (how and when)
OP1,1 OP1,2 OP1,3
OP2,1 OP2,2
R1 R2rd1 dd1
dd2rd2
st(i) + p(i) ≤ st(j), where p(i)is the processing time of op i
st(i) + p(i) ≤ st(j) ∨ st(j) + p(j) ≤ st(i)
rd(j) ≤ st(i) for each op i of job j
Minimize ∑ |c(j) - dd(j)|
i jR
i j
on(b,t)on(g,t)on(r,g)
on(b,r)on(g,r)
clear(b)clear(r)
stack(b,r)
stack(g,b)
putdown(r)
clear(g)
clear(x)clear(y)on(x,?)
preconds
¬on(x,?)on(x,y)clear(?)
postconds
stack(x,y)
clear(x)on(x,?)
preconds
¬on(x,?)on(x,t)
postconds
clear(?)
putdown(x)
Planning Scheduling
durative actions,temporal reasoning
maximizing # of goalsachieved, # of soft
constraints satisfied
resources
action selection from pre-computed resource& process alternatives
resource setup and state
constraints
In recent years, the distinction has started to blur:
OP1,1 OP2,2 OP1,
3
OP1,2
R2
R1 OP2,1
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Relationship to Planning• Fundamentally concerned with coordinating
multiple processes/agents– efficient use of shared resources
• Processes known in advance– action selection from pre-specified alternatives
• Restricted notion of state– availability, usage of shared resources
• Determination of when and how
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Classical Approaches from Operations Research
• Optimization– Determination of tractable problem classes– Mathematical programming models
• mixed-integer, non-linear optimization• decomposition, relaxation (bounding) techniques
– Criticism: idealized and otherwise restrictive problem formulations
• Priority dispatch rules– robust, practical decision-procedures but myopic
tendencies
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
AI Perspective
• Symbolic representations of time, resource capacity constraints
• Heuristic (tree) search formulation• Emphasis on broader picture
– ongoing continuous process versus static optimization task
– larger problem-solving context (integration with planning
– dynamic, uncertain environment
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Scheduling Research: The Last 15 Years
• Major advances in techniques for solving practical problems– Constraint solving frameworks– Incremental mathematical programming
models – Meta-heuristic search procedures
• Several significant success stories
• Commercial enterprises and tools
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Outline
• What is scheduling?• Basics of constraint-based scheduling
models• Managing schedule change• Planning and Scheduling• Coordinating Distributed Scheduling Agents• Coordinators: A Distributed Scheduling
Case Study
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Constraint-Based Search Models
Properties:– Modeling Generality/Expressiveness– Incrementality– Compositional
Current Solution
Constraint Propagation
CommitmentStrategies /Heuristics
ConflictHandling / Retraction Heuristics
Components:
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
What is a CSP?
• Given a triple {V,D,C}, where • V = set of decision variables• D = set of domains for variables in V• C = set of constraints on the values of
variables in V
• Find a consistent assignment of values to all variables in V
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
A Basic CSP Procedure1. [Filtering] - Propagate constraints to establish the current
set vd of feasible values for each unassigned variable d
2. If vd = Ø for any variable d , backtrack
3. If no unassigned variables or no consistent assignments for all variables, quit; Otherwise
4. [Variable Ordering] - Select an unassigned variable d to assign
5. [Value Ordering] - Select a value from vd to assign to d.
6. Go to step 1
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Formulating Scheduling Problems as CSPs
• “Fixed times” model – Find a consistent assignment of start times to activities– Variables are activity start times
• Disjunctive graph model– Post sufficient additional precedence constraints between pairs of activities to
eliminate resource contention– Variables are ordering decisions
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Fixed versus Flexible Times Scheduling
Some tradeoffs:– Flexibility of generated solutions– Convenience of search space
timeR1
OP2,1 OP1,2
OP2,1 OP1,2
time
OP1,2
OP2,1
R1
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Filtering (Propagation) Algorithms
• Role– Early pruning of the search space by eliminating
infeasible assignments– Detection of constraint conflicts
• Temporal Constraints– Simple Temporal Networks (Dechter 91)
• Resource Constraints– Dominance Conditions (Erschler 80), Edge Finding
(Nuijten 94, Balance Constraint (Laborie 01), ...
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Simple Temporal Networks• Edge-weighted graph of time points expressing constraints of the
form: atpjtpib
• The domain of each time point is a single interval (no disjunction)• Encodes broad range of constraints including
– Temporal relations:• finish-to-start <0, ∞> (precedence)• start-to-finish <t1,t2> (duration)• start-to-start <0,0> (same-start)• ...
– Metric bounds: offsets from time origin• Efficient computation of arc consistent solutions via all-pairs
shortest path algorithm
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
STN ExampleOP1,1 OP1,2 OP1,3
OP2,1 OP2,2
R1 R2rd1 dd1
dd2rd2
OP1,1
<d11,d11> <0,∞> <d12,d12>
<rd1,∞>
CZ(0,0)
<0,dd1>
<0,∞> <d13,d13>
OP1,2 OP1,3
OP2,1
<d21,d21> <0,∞> <d22,d22>
OP2,2
<rd2,∞> <0,dd2>
Schedule Op1,2 at time t1
<t1,t1>
Schedule Op2,1 before Op1,2
<0,∞>
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Pruning Ordering Alternatives• Let Opi and Opj be 2 unordered operations competing for R
• Then there are 4 possibilities (Erschler’s dominance conditions):
• LSTi < EFTj and LSTj ≥ EFTi -> Opi is before Opj
• LSTj < EFTi and LSTi ≥ EFTj -> Opj is before Opi
• LSTi < EFTj and LSTj < EFTi -> inconsistency
• LSTi ≥ EFTj and LSTj ≥ EFTi -> both options remain open
OPi
OPi
EarliestInterval
LatestInterval
ESTj LFTj
ESTi LFTi
Opi cannot precede OPj
R
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Edge Finding• S - a set of operations competing for resource R• O - an operation not in S also requiring R
10 20 30
OPi
OPj
OPk
EST(O) ≥ EST(S) + Dur(S)((LFT(S) - EST(S) < Dur(O) + Dur(S)) (LST(S) - EST(O) < Dur(O) + EST(O))
S = {OP ,OP }; O = OP Start Time OP ≥ 25kki j
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Scheduling An Activity (Fixed times schema)
Generate Possible Intervals
Generate Resources
IR1,1 IR1,2 IR2,1...
R1
AssignActivity:[Rtype1,Rtype2] [t1,t2]
R3 R4R2
...IR2,2 IR3,2... IR4,1 ...IR3,1
Acti ActkActjR2
Apply filtering techniques to start times, resource alternatives of unscheduled activities
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Configuring A Basic Scheduling Search Model
• Couple core search procedure with variable ordering heuristic and filtering algs. to produce greedy solution generator
• Embed in larger optimizing search by
IR1,1 IR1,2 IR2,1...
R1
AssignActivity:[Rtype1,Rtype2] [t1,t2]
R3 R4R2
...IR2,2 IR3,2... IR4,1 ...IR3,1
1. Backtracking over variable/value ordering choices
2. Dynamically changing the variable ordering and iteratively re-invoking the core procedure
3. using the solution generator to seed a local search
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Search Heuristics (Variable and Value Ordering)
• Resource Demand/Contention (Sadeh 91, Beck 97)– Identify bottleneck resource– Schedule (or sequence) those activities contributing most to demand
• Slack/Temporal Flexibility (Smith & Cheng 93)– Choose pair of activities with least sequencing flexibility– Post sequencing constraint that leaves the most slack
• Minimal critical sets (Laborie & Gallib 95)– Generalization to multi-capacity resources
• Resource Envelopes (Muscettola 04)
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Constraint-Posting Scheduling Models
– Conduct search in the space of ordering decisions• variables - Ordering(i,j,R) for operations i
and j contending for resource R
• values - i before j, j before i
– Constraint posting and propagation in the underlying temporal constraint network (time points and distances)
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Basic Constraint-Posting Cycle
Time feasible task network
Impose Capacity Constraint
Peak 1C
Peak 2
ResourceLeveling
Task 2
Task 1
Peak 1C
Peak2
Peak 2
ConstraintPropagation
C
Deadline 25
Task 2
Task 1 Time feasible task network
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Scheduling Search Procedures
• Constructive procedures– greedy, backtracking, LDS, ...
• Iterative repair and local search– “commit early and often” versus “least-
commitment” winnowing of solution set– emphasis on retraction heuristics as well
as constructive heuristics– well suited for incremental change
Will show example methods later in discussing oversubscribed problems
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Outline
• What is scheduling?• Basics of constraint-based scheduling
models• Managing schedule change• Planning and Scheduling• Coordinating Distributed Scheduling Agents• Coordinators: A Distributed Scheduling
Case Study
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Views on Scheduling under Uncertainty
• Design and use of scheduling policies
• Establish and maintain prescriptive schedules
Scheduler
Executor
Pro-active:Generate schedulesthat anticipateUncertainty
Reactive:Manage schedule in response to unexpected events
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Approaches to Managing Change
– Build schedules that retain flexibility
– Produce schedules that promote localized recovery (Supermodels - Ginsberg)
– Incremental re-scheduling techniques are a natural (e.g., that consider “continuity” as an objective criteria)
– Self-scheduling control systems
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Incremental Schedule Repair• Several competing approaches to maintaining continuity
in the schedules generated over time– Minimally disruptive schedule revision (temporal delay,
resource area)– Priority-based change – Regeneration with preference for same decisions– Extended local search
• Critical issue: how to trade solution stability concerns off against (re)optimization needs and computational cost
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Hedging Against Uncertainty• Temporal Networks with uncertainty [Vidal 96] - some
set of edges are contingent (e.g. uncertain duration)– strong controllability - analogous to conformant planning– dynamic controllability - solution can always be extracted as
uncertain arcs become known
• Contingent schedules– Disjunctive Temporal Networks [Moffit & Pollock 06]– Opportunity to make resource choices explicit; challenge is
managing combinatorics– Project likely failure points and generate explicit contingencies
[Drummond and Bresina 94, Hiatt et. al 09]
• Aversion dynamics [McKay 00]– adapt scheduling policy to minimize impact of unexpected
change
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Outline
• What is scheduling?• Basics of constraint-based scheduling
models• Managing schedule change• Planning and Scheduling• Coordinating Distributed Scheduling Agents• Coordinators: A Distributed Scheduling
Case Study
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Integrated Planning and Scheduling (as typically formulated)
G1G2
G3
Goals
A3 A2 A4
A5
A1R1
R2
R3
Schedule
Allocate resources (maybe) and Assign times
G1
Plan
A1 A2
A5A3
A4
G2
G3
Sequence goals and construct goal achieving action sequences
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Resource-Driven Problems
• Principal form of goal interaction is competition for resources
• Upfront planning process is separable and limited to achievement of individual goals
• At its core, these are essentially scheduling problems
• But allocation of resources introduces planning sub-problems
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Resource-Driven Problems
A3 A2 A4
A5
A1R1
R2
R3
Schedule
Allocate Resources and Assign times
G1G2
G3
Goals
G1
Plan
A1 A2
A5
A3
A4
G2
G3
Construct goal achieving action sequences
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Where’s the Planning in a Scheduling Problem?
• Managing shared resources– Resource support actions are needed to
“set up” resources for use
– These support actions depend on required usage states, which are determined by the scheduler’s sequencing decisions
IR1,1 IR1,2 IR2,1...
R1
AssignActivity:[Rtype1,Rtype2] [t1,t2]
R3 R4R2
...IR2,2 IR3,2 ... IR4,1 ...IR3,1
t1
Acti ActkR1
t2
IR1,1Setup S Setup IR1,2
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Scheduling the Hubble Space Telescope
• A complex single machine problem• Resource support actions
– Instrument reconfiguration– Pointing direction– Target lock
ObserveA Inst-1Target: X
ObserveB Inst-2Target: YSlewing(X,Y)
ChangeOver(Inst-1,Inst-2)
Setup Time IdleTime
TargetYVisibility ... ...visible not visible visible
Earliest Start Time
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
HSTS Solution
Detailed Schedule
OBS 1
OBS 2
WF state:
PC state:
WFPC state:
pointing state:
OBS 1OBS 2
OBS 3OBS 4
OBS 5
...
Proposals
OBS 1 OBS 2Telescope state
Abstract Schedule
Setup
Subgoaling temporalplanner
Single machine scheduler
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
What is missing?• Scheduling models gain their power by making restrictive
modeling assumptions– Resource “setup” as a sequence-dependent duration– Bounded dynamics of resource usage – Trades flexibility for scalability
• Explicit goal-directed reasoning can be used to overcome this limitation
– Extension to enable more idiosyncratic allocation options– Modular knowledge, performance requirements
• Challenge: How to effectively embed a planner within the scheduler search process?
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Solving Oversubscribed Problems
• Basic Setting: Resource constraints restrict the ability of some system of interest to perform tasks (achieve goals), and cumulative demand exceeds its capacity
• 2 sets of interacting decisions– Which subset of tasks to perform (goals to achieve)– How to allocate tasks to system resources over time
• Objective:– Maximize number of tasks performed, maximize resource
utilization, …
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Examples/Applications• Rover Task Planning [Smith 2004]• Telescope observation scheduling [Bresina et. al
96, Johnston and Miller 94, Muscettola and Smith 93, Giuliano et. al 08.
• Satellite observation scheduling [Barbulescu et.al 06, Frank et. al 02, Globus et. al 2003, Rabideau, Chein et. al]
• Military airlift allocation [Kramer and Smith 03]• Personal task management [Varakanthan and
Smith 08]
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Approaches to Oversubscribed Problems
• Planning Perspective– Emphasis on resource limitations other than time
(e.g., fuel)• Orienteering-type problems [D. Smith 04]
– General formulation as partial satisfaction planning• Specify preferences over goals and combine with other
preferences
• Scheduling Perspective– Selection and allocation of tasks to resources
under temporal constraints
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Oversubscribed Scheduling Research
• Has focused on problems where principal source of interaction between tasks (goals) is competition for resources over time
• Basic model:– Tasks (goals) have durations, resource requirements and feasible
time windows– Tasks may have priorities (indicating relative importance)– Resources may have reconfiguration (setup) constraints
• More complex settings: – High level tasks may decompose in HTN fashion into lower level
activity sequences or disjunctions (reflecting prior modeling of various process or resource choices)
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Representational Alternatives
• Permutation Space Search – Search in the space of task permutations– Permutation specifies a scheduling order– “Schedule builder” applied to construct schedule– Examples: Squeaky Wheel Opt., Genetic Algorithms
• Schedule Space Search – Search directly in the space of possible schedules. – Initial base solution is progressively revised and
improved over time.– Examples: Iterative Repair, Task Swap
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Basic Airlift Allocation Problem
AB
C
W1 W2
• Mission1:• pick up
cargo at A• deliver to B• then C.
Decisions:• Use resources
(e.g., aircraft) from wing W1 or W2?
• Start at what time?
• Mission2 …
• Mission-n
Requests:
Missions have priorities which must be strictly enforced
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Task Swapping[Kramer and Smith 2003,2004,2005]
Goal: Controlled schedule revision to accommodate additional tasks without relaxing constraints
Basic Approach– Temporarily relax priority constraint– Conduct repair-based search around the “footprint” of
an unassignable task t’s feasible execution window– If all tasks displaced to accommodate t cannot be
feasibly reinserted, Undo
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
An Example
Unassignable task, T1
T2
T5
T4
T6
T8T7
T9
T12
T10
T11
T15T13
CapR=7
T14
T3
R
T2Assigned task, T1
T5
T4
T6
T8T7
T9
T12
T10
T11
T15T13
CapR=7
T14
T3
R
Re-scheduled task T2
Un-scheduled task T2
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Retraction Heuristics
• Max-Flexibility = task-duration/feasible-window-size• Min-Conflicts = count intervals that are at-capacity which
conflict with a task’s feasible window.• Min-Contention = conflict-count * conflict duration
Unassignable task T6
C1 C2
T1
est st ft lft
T2
T3
T4
T5
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
General Task Swap Procedure
• Given an unassignable task t to insert into the schedule,
1. Identify where conflicts with that task exist.2. Retract 1 or more tasks in the conflicted areas to free
up capacity3. Schedule task t, and mark it as “seen.”4. Re-schedule the retracted tasks.5. If all retracted tasks cannot be re-scheduled, recurse
on them, most constrained first.6. If all tasks have been tested (seen) and some remain
unassignable, backtrack to original state.• Matched best performance on benchmark pickup-
and-delivery problems
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
An Experiment[Kramer, Barbulescu, Smith 07]
• Question: How does a schedule-based search procedure perform relative to a permutation-based search procedure in a given domain?
• Examine performance of two representative procedures on AFSCN and AMC domains – Schedule Space: Task Swap– Permutation Space: Squeaky Wheel Optimization
(SWO)
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
A Representative Permutation-Based Procedure: Squeaky
Wheel Optimization1. Generate a schedule with a schedule builder, based on a
task ordering (permutation).2. If all tasks are assigned, Return success, otherwise …3. If an iteration limit has been reached, re-apply the task
permutation resulting in the most assigned tasks, and stop, otherwise...
4. Analyze this schedule to identify unassigned tasks – the “squeaky wheels.”
5. Given some move operator, advance the squeaky wheel tasks a distance forward in the task ordering.
6. Repeat.
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
SWO: An Example(Iteration Limit = 10; Move Operator = Fixed distance, 2)
• Initial task ordering (permutation): (T7 T5 T1 T2 T4 T3 T6)
• Build schedule; T1, T4, T3 not assigned (Squeaky Wheels).
• New task permutation, after moving squeaky wheels forward 2:
(T1 T7 T4 T3 T5 T2 T6)
• Build schedule; T4, T5 not assigned.
• New task permutation, after moving squeaky wheels forward 2:
(T4 T1 T5 T7 T3 T2 T6)
• Build schedule; T1 not assigned.
• New task permutation, after moving squeaky wheels forward 2:
(T1 T4 T5 T7 T3 T2 T6)
• Build schedule; All tasks assigned successfully; END.
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Comparative Results
ICAPS 2009 Summer School
R1 58 45 49
R2 38 30 34
R3 27 18 20
R4 37 28 32
R5 19 13 15
Result: SWO outperforms TS.
Problem Initial Unassignables End SWO End TS
Ovals highlight statistically significant differences.
SWO vs. TS
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5
Problem Set
Un
assig
nab
le T
asks
SWO
TS
SWO vs. TS
100000
1000000
1E+07
1E+08
1E+09
1E+10
1E+11
1E+12
1E+13
1 2 3 4 5
Problem Set
Av
era
ge
Sc
ore
SWO
TS
Result: TS outperforms SWO
AFSCN Domain AMC Domain
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Domain Features
ICAPS 2009 Summer School
AFSCN AMCHard Priority Constraint? No Yes
Number of Tasks 419-483 983
Resource Capacity 1-3 4-37
Average Temporal Flexibility(task duration/window size)
(0.69968086 - 0.7595485)
0.49961752
• Most differences are a matter of degree, except for presence/absence of hard priority constraint
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Extended analysis• Generated a continuum of abstract domains ranging
from AFSCN to AMC– 1800 problems (grouped into 18 classes), varying size, slack,
capacity and priority
• Main conclusions:– SWO dominates in domains with no priority, regardless of other
factors– In presence of priority, both procedures perform comparably at
low levels of oversubscription, but at higher contention levels, TS dominates
– New hybrid technique demonstrated to produce new best solutions for a few of the AMC reference problems
ICAPS 2009 Summer School
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Outline
• What is scheduling?• Basics of constraint-based scheduling
models• Managing schedule change• Planning and Scheduling• Coordinating Distributed Scheduling Agents• Coordinators: A Distributed Scheduling
Case Study
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
57
What is Distributed Planning and Scheduling?
• A planning / scheduling process that involves more than one player (agent)– Coordinated goal achievement– Coordinated action selection– Coordinated task/resource allocation over time
• Why distribute the planning / scheduling process?– Many applications are inherently distributed– There can be performance advantages to distribution
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
58
Distributed Scheduling Problems
• Many scheduling applications are inherently distributed and mandate distributed solutions– Competing objectives (self-
interest)
– Control is already distributed
– Communication constraints and costs
– Computation constraints
– Dynamics
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Approaches to Distributed Scheduling
Self-schedulingsystems
Management of advance schedules
- Market mechanisms- DCOP- heuristic scheduling
• high dynamics• independent jobs/goals
• optimized team behavior• coordinated action
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Self-Scheduling SystemsMotivation: Problem too dynamic to consider use of
schedules
Basic Concept:• Distribute decision-making among individual
entities (machines, tools, parts, operators; manufacturers, suppliers)
• Specify local behaviors and protocols for interaction• Robust, emergent global behavior
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Self-Scheduling System Design
• Analogy to natural systems– [Parunak 97,98, Bonabeau et al 97,
Cicirello & Smith 02]
• “Engineered” self-interest (referred to generally as Mechanism Design)– [Dias, Stentz 03]
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
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Market Mechanisms
• Self-scheduling systems can be seen as a simple form of market– core contracting protocol for bidding on and awarding tasks
• In more stable task and resource allocation domains, construction of schedules can provide leverage– more informed, state-dependent bidding– management of shared dependencies
• Combinatorial auctions support simultaneous bidding for multiple tasks/resources– communication of constraints and preferences to a centralized
optimizer (the auctioneer)– tradeoff is the computational bottleneck introduced by
centralization
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Morley’s GM Paint Shop System
Dispatcher
PaintBooth
1
PaintBooth
2
Bid
Bid
Announcement(new truck)
Bid parameters:
- same color as last truck
- space in queue
- empty queue
“If bid for same color then award else if empty booth then award else if queue space then award”
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
TradeoffsAdvantages:
– Complexity reduction
– Simple, configurable software systems
– Robust to component failures
– More stable computational load
Problems:– No understanding of global optima (or how to achieve
global behavior that attends to specific performance goals)
– Prediction only at aggregate level (can become unstable)
Coordination Example
Assessment RegionAssessment Region
Receives job request
Receives job request
Generates BidGenerates BidGenerates BidGenerates Bid
Generates BidGenerates Bid
Generates BidGenerates Bid
Generates BidGenerates Bid
Generates BidGenerates Bid
Generates BidGenerates Bid
Bids are sent back to
Manager
Bids are sent back to
Manager
Bids are synthesized into
assignments
Bids are synthesized into
assignments
AnnouncementFrequency-Range: [F1 ..F2]Region: [(x1,y1)…(x4,y4)]Time-Window: [t1, t1’]Capability: RF-ReceiverExpiration: t2
AnnouncementFrequency-Range: [F1 ..F2]Region: [(x1,y1)…(x4,y4)]Time-Window: [t1, t1’]Capability: RF-ReceiverExpiration: t2
Assignments are sent back to
nodes
Assignments are sent back to
nodes
BidFrequency-Range: [Fi ..Fj]Region: [(xi,yi) (xj,yj)]Time-Window: [ti, tj]Location Dist: […]Availability Dist: […]
BidFrequency-Range: [Fi ..Fj]Region: [(xi,yi) (xj,yj)]Time-Window: [ti, tj]Location Dist: […]Availability Dist: […]
Manager sends announcement
to nodes
Manager sends announcement
to nodes
Coordination Example
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
FIRE Project: Multi-Rover Scenario[Simmons, et al. 2001-2004]
scientist
scientist
scientist
rover
rover
roverUI
UI
UI
• many scientists• many tasks/goals• relative priorities
• bandwidth• blackouts
• interface• broker• “OpTrader”
• heterogeneous• autonomous• limited resources
sim
ulat
or
... rover
......
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Scheduler-Driven Bidding Process
RoboTrader
Scheduler
Planning
Executive
RoboTrader
Scheduler
Planning
Executive
OpTrader
• Bid requests for new tasks initiated by OpTrader
– task(s) awarded to low cost bidder
• Agent Scheduler designed to minimize travel time
– Bid requests are evaluated by rescheduling to accommodate new task(s) and determining additional cost
– Prospective schedule retained in case of subsequent award
– Local cost synergistic with global cost
• RoboTraders also issue bid requests for undesirable tasks
– task(s) awarded to low cost bidder (unless cheaper to do task itself)
T1 T2 T3 T4 T5
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
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Continuous Trading• Traders are continuously auctioning and bidding for tasks
– Tasks that are up for bid cannot not be executed– A Trader can simultaneously be a bidder and auctioneer only if
the tasks it is bidding for are awarded before its own auction terminates
• Quiescence when no cost reducing trades can be foundBid Award
Bid AwardTrader A
Trader B
Carnegie Mellon SMU/SIM-TECH Workshop on Trends in P/S – Sept 11, 2008
Market-Based Scheduling
• Literature– Economics: Auction Theory– Network Flow Problems: Auction Algorithms [Bertekas
92]– Game Theory: [Wellman et al. 02] - Auction Protocols
for Decentralized Scheduling, ...– Computer Science: [Kurose & Simha 86] - Optimal
resource allocation in distributed computer systems, ...– Manufacturing: [Baker et al. 95], market-based
material flow