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. don’t 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 it’s 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?