Refinement Planning: Status and Prospectus

1
Happy Spring Break!
2
Scheduling The State of the Art
3
Planning vs. Scheduling
A Continuum
Causal Reasoning
Resource Reasoning
Important ACTION prec/Effect models not needed
--Research into planning and scheduling methods
has largely been de-coupled
4
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
• Certain resource constraints may not be available
  at planning time and so the planner has to
  postpone them to a separate scheduling phase
• 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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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
5
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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Scheduling vs. HTN Planning

• You can think of each job as an HTN non-primitive
  task, and the specific taks for doing that job as
  it reduction
• Simple scheduling assumes that
• Unique Reduction Each non-primitive task has a
  single reduction schema
• One-level Reduction Each reduction schema
  contains only primitive tasks
• Disjunctive scheduling relaxes Unique
  reductiona task may have multiple reductions
  (all of which still leading directly to primitive
  tasks)

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Scheduling vs. Bounded Length Planning

• The way planning graphs are converted into CSP
  encodings have

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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
Solution of PCP scheduling is an STP
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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
9
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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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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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