Planning and Scheduling

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Planning and Scheduling
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Some background

• Many planning problems have a time-dependent
  component
• actions happen over time intervals,
• goals have time windows when they should be
  achieved
• Need to synchronize with other agents
• Normal Situation calculus, STRIPS, etc. dont
  support this very well
• Planners choose actions to achieve goals. Picking
  a time line is typically seen as scheduling

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Handling time in planners

• How should we model temporal problems
• Do we need new planning algorithms or will
  modifications on others be enough?
• Can we plan first, then schedule? Should the two
  be merged?

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Different time-related issues in planning

• If actions take different time intervals,
  partial-order planners must account for this
• Actions with continuous effects e.g. drive
  truck from LA to San Francisco
• Concurrent/simultaneous actions may have
  different effects or preconditions

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Actions with continuous effects

• Drive from LA to SF takes 5 hours. Location
  changes continuously
• If the action gets interrupted e.g. need to
  recall the truck 1 hour later. Where is it?
• Some approaches situation calculus with
  differential equations for the state, event
  calculus.

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Concurrent actions

• Synergy to open the door, hold handle down and
  pull simultaneously neither action achieves
  anything alone
• Interference if two actions require the same
  resource (e.g. a spanner), cannot both take place
  simultaneously

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Generalizing STRIPS

• STRIPS action if preconds hold in current
  situation, can apply action now, and effects
  hold in next situation.
• If action takes place over an interval should
  preconds hold just when the action starts?
  Throughout the interval? When do the effects take
  place?

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Temporal Graph Plan

• Consider the question can we use Graphplan ideas
  for temporal planning?
• What are the problems, if actions have different
  durations?

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TGP action model

• STRIPS actions, plus start time, end time,
  duration
• All preconds must hold at the start
• Preconds not affected by the action must hold
  throughout execution
• Effects are undefined during execution and only
  hold at the final time point

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Temporal planning graph

• Propositions and actions monotonically increasing
• Mutexes monotonically decreasing
• Nogoods are monotonically decreasing
• So..

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Cyclic planning graph
Earliest start time
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Distinguishing mutex conditions

• Some mutexes are always true eternal
• Some can become false conditional
• Action/Proposition mutex

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Propagating mutexes

• Can maintain which are conditional or eternal
  mutexes

• Note these are temporal conditions, essentially
  on when instances of A and P can coexist

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Solution extraction
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Dealing with uncountable choices..

• The algorithm makes every action take place as
  late as possible by using persistence ONLY when
  nothing else would work.

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Approximating mutex conditions

• Checking disjunctions can be expensive, so try to
  maintain a form like

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Conclusions

• Can extend mutex reasoning to temporal case
• But its not easy!

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ASPEN

• Combine planning and scheduling steps as
  alternative conflict repair operations
• Activities have start time, end time, duration
• Maintain most-commitment approach easier to
  reason about temporal dependencies with full
  information
• C.f. TLPlan

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Temporal constraints
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Activity decompositions
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Conflict types
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Contributors for a non-depletable resource
violation
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Contributors for a depletable resource violation
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Domain-independent heuristics

• Prefer to solve conflicts that require new
  activities, then timeline conflicts
• To repair a conflict, prefer moving activities,
  then adding a new activity
• Try to solve conflicts while introducing as few
  others as possible

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Conclusions

• Successfully integrates planning and scheduling
• Does it do so in the most profitable way?
• What can we say about guarantees for the
  algorithm?