Scheduling: The State of the Art

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Scheduling The State of the Art
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Planning vs. Scheduling
A Continuum
Causal Reasoning
Resource Reasoning
--Research into planning and scheduling methods
has largely been de-coupled
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Why separate scheduling from planning?

• Clearly, Scheduling can be seen as a sub-problem
  of temporal planning (unlike scheduling, planning
  also contains action selection). So, why separate
  it?
• Reasons from automated planning point of view
• If multiple agents make their plans and execute
  them on central resources, separating resource
  scheduling from individual agent planning makes
  sense
• Even if a single agent is doing planning, it may
  be worth separating causal reasoning and resource
  reasoning
• Such de-coupling improves efficiency, but at
  the expense of global optimality guarantees
• Reasons from real world practice point of view
• Historically, in many domains, action selection
  and automated causal reasoning was out of
  question (either because it couldnt be modeled
  and solved or because the humans didnt want to
  delegate it to automated methods
• So, the only computer support for planning
  activity was given for resource scheduling
  (humans make plans, and schedulers do resource
  allocation)

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Simple job-shop Scheduling Brief Overview

• CSP Models
• Time point model
• Tasks as variables, Time points as values
• EST, LFT, Machine contention as constraints
• Inter-task precedences as variables (PCP model)

• Jobshop scheduling
• Set of jobs
• Each job consists of tasks in some (partial)
  order
• Temporal constraints on jobs
• Sequencing constraints
• Release times, deadlines, durations
• EST, LFT, Duration
• Contention/capacity constraints
• Each task can be done on a subset of machines

• CSP Techniques
• Customized consistency enforcement techniques
• ARC-B consistency
• Edge-finding
• Customized variable/value ordering heuristics
• Contention-based
• Slack-based
• MaxCSP BB searches

st1
LFT
P1,P2
T2
EST
st2
M
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Connections

• Scheduling seems to be bounded length planning
  where actions are already given to you!
• The CSP encoding for scheduling will be a special
  case of the CSP encoding for bounded length
  planning!
• The main difference is that in planning steps
  can correspond to one of many different actions,
  while in scheduling each step corresponds to a
  single action
• disjunctive scheduling allows disjunction of
  jobs
• Schedule optimality criteria are similar to
  temporal plan optimality criteria (makespan,
  tardiness, slack etc based)
• The action cost doesnt enter the picture since
  we dont have any action choice..
• Scheduling (at least in the unary capacity
  resource case) is equivalent to solving
  disjunctive temporal networks!

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11/3

• Scheduling continued
• Incompleteness and uncertainty (start)

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Minimizing Schedule Makespan

• Approach
• Establish lower and upper bounds on overall
  schedule end.
• Repeatedly apply PCP to find the best solution
  within these bounds.
• Details
• Generate schedule ignoring resource constraints
  to provide determine lower bound.
• Apply one or more dispatch scheduling procedures
  to provide upper bound.
• Apply PCP k times with common deadlines evenly
  distributed between these bounds.

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Job Shop Scheduling as a CSP
Disjunction typically comes through capacity
constraints
Start Point Representation
Variables Start time stil Domain
estil.lstil Precedence constraints
stil pil ? stjl Release
times/deadlines R ? sti1 sti1 pi1 ?
D Capacity Constraints stil pil ? stjl ?
stjl pjl ? stil
Capacity Constraints
Precedence Constraints
Making the problem harder --Multi-capacity
resources gtgt a machine that can
handle 4 jobs at a time --Disjunctive
activities gtgtschedule at least one of
the following tasks --Setup constraints
gtgtif you schedule task1, you need
to schedule 3 and 4
PCP Representation
Variables Ordering(i,j) for each task i and
j Domain i-before-j, j-before-I, means
dont care Dependent Var Sti Constraints Sequenc
ing constraints O(i,j)i-bef-j Capacity
constraints O(i,j)i-bef-j OR
O(I,j,R)j-bef-I
So, is not a
possibility Release times, deadlines R ? sti1
sti1 dui1 ? D Inter-variable constraints
O(i,j)i-bef-j gt sti pi lt stj
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The Choice Spectrum
planning
job-shop scheduling
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The Choice Spectrum
planning
job-shop scheduling
R3
R7
R1
Job1 task1 lt task2 lt task3 lt Job2 Job3
Ordering choices only
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The Choice Spectrum
cascading levels of choice







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The Choice Spectrum
resource choices (RCSP)
job-shop scheduling
planning
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11
umfagoggin clavitracle
fernambulator
8,17
Task4
Task7
Task2
Task5
Task1
Task8
Ordering choices Resource choices
Task3
Task6
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The Choice Spectrum
process8
Ordering choices Resource choices Process choices
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The Choice Spectrum
ambitious spacecraft
alternative processes
planning
job-shop scheduling
resource choices (RCSP)

• Observation choices
• Instrument choices
• Calibration target choices
• Ordering choices
• Communication choices
• Instrument status choices

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The Choice Spectrum
alternative processes
planning
job-shop scheduling
resource choices (RCSP)
Subset Selection ambitious spacecraft observation
scheduling process planning
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Start point vs. PCP(not all that unlike
State-space vs. PO)

• Solution to the Start point encoding is a single
  feasible schedule
• Handling of multi-capacity resources easy..

• Solution to the PCP encoding is a simple temporal
  network, all of whose dispatches are feasible
  schedules
• Sort of like PO planningwhich gives a PO plan,
  all of whose linearizations are valid plans
• Conventional wisdom is that PCP does not scale
  well to multi-capacity resource scenarios

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Contention-based Ordering Heuristics
Sadeh, 1991
demand
Individual Demand of O1 for Rj
demand
Aggregate Demand (of all O) for Rj
0
time
6
3
demand
Individual Demand of O2 for Rj
3
6
9
0
time
Most critical region
time
0
3
6
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Contention Aggregated curves found for each
resource Critical Region Where a resource is
contended the most Most Critical Unassigned
Operation Contributes the largest area in
critical region Variable Ordering
Heuristic Choose the most critical unassigned
operation
probability
Operation O1 Start Time Distribution
0
3
6
Start time
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Other Constraint Propagation Ideas
Arc-Bounds
Arc-bounds is related to 2-consistency While
edge-finding is related to k-consistency
Edge-Finding
Many other ideas --Energy-based propagation
--Time-table propagation etc. See
Laborie, AIJ 2002
Through Resource constraints
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Constraint Propagation
PCP SCHEDULING

• Pick ordering decision with the overall minimum
  slack
• minslack(u-gtv ) slack(v-gtu)
• Most constrained variable
• 2. Assign that ordering decision the value for
  which the slack
• is higher.
• Least constraining value
• ?B-slack slack/sqrt(S)
• S is the ratio of min and max slacks of a
  given ordering.
• to normalize for the variation 20 , 3
  vs. 4, 3

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Current State of Scheduling as CSP

• Constraint-based scheduling techniques are an
  integral part of the scheduling suites by ILOG/I2
  
• Optimization results comparable to best
  approximation algorithms currently known on
  standard benchmark problems.
• Best known solutions to more idiosyncratic,
  multi-product hoist scheduling application (PCB
  electroplating).
• Better in most large-scale problems than IP
  formulations

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Slides beyond thiswere not covered
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Need for Integration

• Most existing planners concentrate on action
  selection, ignoring resource allocation
• Plan-based interfaces
• Interactive decision support

• Most existing schedulers concentrate only on
  resource allocation, ignoring action selection
• E.g. HSTS operation scheduling

• Many real-world problems require both
  capabilities
• Supply Chain Management problems
• I2, ILOG, Manugistics
• Planning in domains with durative actions,
  continuous change
• NASA RAX experiment

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Why now?

• Significant scale-up in plan synthesis in last
  4-5 years
• 5/6 action plans in minutes to 100 action plans
  in minutes
• Breakthroughs in search space representation,
  heuristic and domain-specific
• Significant strides in our understanding of
  connections between planning and scheduling
• Rich connections between planning and CSP/SAT/ILP
• Vanishing separation between planning techniques
  and scheduling techniques

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Approaches for Integration

• Extend schedulers to handle action and resource
  choices

• Extend planners to deal with resources, durative
  actions and continuous quantities

• Coupled Architectures
• De-coupled
• Loosely Coupled (RealPlan System)

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Approaches

• Decoupled
• Existing approaches
• Monolithic
• Extend Planners to handle time and resources
• Extend Schedulers to handle choice
• Loosely Coupled
• Making planners and schedulers interact

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Decoupled approaches(which is how Project Mgmt
Done now)
Management

Technology Development
MS Project
Mid-lower manager
(scheduling)
(task planning)
Implementers
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Extending Planners

• ZENO Penberthy Weld, IxTET Ghallab
  Laborie, HSTS/RAX Muscettola extend a
  conjunctive plan-space planner with temporal and
  numeric constraint reasoners
• LPSAT Wolfman Weld integrates a disjunctive
  state-space planner with an LP solver to support
  numeric quantities
• IPPlan Kautz Walser 99 constructs ILP
  encodings with numeric constraints
• TGP Smith Weld 99 supports actions with
  durations in Graphplan

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Actions with Resources and Duration
Load(Ppackage, Rrocket, Llocation)
Resources ?h robot hand Preconditions
Position(?h,L) ?s, ?e
Free(?h) ?s
Charge(?h) gt 5
?s Effects holding(?h, P)
?s, ?t1
depositing(?h,P,R) ?t2, ?e
Busy(?h)
?s, ?e Free(?h)
?e
Charge - .03(?e - ?s) ?e Constraints
?t1 lt ?t2 ?e -
?s in 1.0, 2.0
?s
?e
1,2
Pos(?h,L)
Hold(?h,P)
dep(?h,P)
Free(?h)
Free(?h)
Busy(?h)
Capacity(robot) 3
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What planners are good for handling resources and
time?

• State-space approaches have an edge in terms of
  ease of monitoring resource usage
• Time-point based representations are known to be
  better for multi-capacity resource constraints in
  scheduling
• Plan-space approaches have an edge in terms of
  durative actions and continuous change
• Notion of state not well defined in such cases
  (Too many states)
• PCP representations are known to be better for
  scheduling with single-capacity resources

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Extending Scheduling
process8
Ordering choices Resource choices Process choices
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Monolithic Architectures Scale Poorly

• Extended planning systems are hard to control
• RAX uses a very error-prone hand-coded search
  control strategy
• Extended scheduling systems tend to lose
  effectiveness due to increased disjunction
• Monolithic systems can sometimes show
  counter-intuitive behavior (by multiplying search
  failures)

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Loosely Coupled Architectures
Causal Plan
PLANNER
SCHEDULER
Schdule

• Schedulers already routinely handle resources
  and metric/temporal constraints.
• Let the plannerconcentrate on causal reasoning
• Let the scheduler concentrate on resource
  allocation, sequencing and numeric constraints
  for the generated causal plan

Need better coupling to avoid inter-module
thrashing.
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Making Loose Coupling Work

• How can the Planner keep track of consistency?
• Low level constraint propagation
• Loose path consistency on TCSPs
• Bounds on resource consumption,
• LP relaxations of metric constraints
• Pre-emptive conflict resolution
• The more aggressive you do this, the less need
  for a scheduler..
• How do the modules interact?
• Failure explanations Partial results

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RealPlan--Master/Slave
Srivastava Kambhampati ECP,99 AAAI, 2000
Planner does causal reasoning. Scheduler
attempts resource allocation If scheduler
fails, planner has to restart
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Performance of Master-Slave Coupling
When scheduler fails, no specific guidance is
given to the planner
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RealPlan Peer-to-Peer
Explanation-directed backtracking between
Planner and Scheduler
Set of actions that
cannot be scheduled
Planners CSP
Schedulers CSP
Variables goals
Variables Actions
Values actions
Values Resources
Resource constraints
actons
activated by the
selected
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Inter-module Dependency Directed Backtracking
Set of actions that
cannot be scheduled
Planners CSP
Schedulers CSP
Variables goals
Variables Actions
Values actions
Values Resources
Resource constraints
actons
activated by the
selected
Generate compact explanation of the Schedulers
failure in allocating resources
Schedulers Task
Explanation Generation
Explanation Translation
Interfaces Task
Translate the explanation into the form that make
sense to the planner.
Use the translated explanation to generate plan
that avoid this failure.
Generation of Alternative Plan
Planners Task
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Subset of variables that can not be assigned
values (reason of failure)
Resource Domains A1, A2 , A3 R1 , R2 A4, A5
S1 , S2 , S3 Resource Constraints A1 ? A2
A2 ? A3 A1 ? A3 A4 ? A5
A1 R1
(A1 , A2 , A3)
N1 A1 R1
A2 R2
N1 A1 R1, A2 R2
A4 S1
N1 A1 R1, A2 R2 , A4 S1
A3 R1
A3 R2
N1 A1 R1, A2 R2 , A4 S1 , A3 R1
N1 A1 R1, A2 R2 , A4 S1 , A3 R2
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Executor
Next-Generation Realplan
Mission Profile
Execution status Replanning requests
Plans with annotated waypoints
Evolving specs
CSP-based Finite capacity resource scheduler
A temporal planner supporting causal plan
synthesis
Mission modifications Plan criticism
Mixed Integer/Linear programming module for
metric constraints
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Summary Conclusion

• Motivated the need for integrating Planning and
  Scheduling
• Discussed the state of the art in Planning and
  Scheduling
• Discussed approaches for Integrating them
• Loosely coupled architectures are a promising
  approach