Planning and Scheduling. 2 USC INFORMATION SCIENCES INSTITUTE Some background Many planning problems...

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?