planning and scheduling. 2 usc information sciences institute some background many planning problems...
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Planning and Scheduling
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2USC INFORMATION SCIENCES INSTITUTE
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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3USC INFORMATION SCIENCES INSTITUTE
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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4USC INFORMATION SCIENCES INSTITUTE
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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5USC INFORMATION SCIENCES INSTITUTE
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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6USC INFORMATION SCIENCES INSTITUTE
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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7USC INFORMATION SCIENCES INSTITUTE
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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8USC INFORMATION SCIENCES INSTITUTE
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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9USC INFORMATION SCIENCES INSTITUTE
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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10USC INFORMATION SCIENCES INSTITUTE
Temporal planning graph
Propositions and actions monotonically increasing
Mutexes monotonically decreasing
Nogoods are monotonically decreasing
So..
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11USC INFORMATION SCIENCES INSTITUTE
Cyclic planning graph
Earliest start time
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12USC INFORMATION SCIENCES INSTITUTE
Distinguishing mutex conditions
Some mutexes are always true – eternal
Some can become false – conditional
Action/Proposition mutex
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13USC INFORMATION SCIENCES INSTITUTE
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14USC INFORMATION SCIENCES INSTITUTE
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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15USC INFORMATION SCIENCES INSTITUTE
Solution extraction
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16USC INFORMATION SCIENCES INSTITUTE
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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17USC INFORMATION SCIENCES INSTITUTE
Approximating mutex conditions
Checking disjunctions can be expensive, so try to maintain a form like
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18USC INFORMATION SCIENCES INSTITUTE
Conclusions
Can extend mutex reasoning to temporal case
But it’s not easy!
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19USC INFORMATION SCIENCES INSTITUTE
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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20USC INFORMATION SCIENCES INSTITUTE
Temporal constraints
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21USC INFORMATION SCIENCES INSTITUTE
Activity decompositions
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22USC INFORMATION SCIENCES INSTITUTE
Conflict types
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23USC INFORMATION SCIENCES INSTITUTE
Contributors for a non-depletable resource violation
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24USC INFORMATION SCIENCES INSTITUTE
Contributors for a depletable resource violation
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25USC INFORMATION SCIENCES INSTITUTE
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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26USC INFORMATION SCIENCES INSTITUTE
Conclusions
Successfully integrates planning and scheduling
Does it do so in the most profitable way?
What can we say about guarantees for the algorithm?