heuristic planning with time and resources

Heuristic Planning with Time and Resources

--Sapa, TP4, and others

Quiz1: Expressiveness of Temporal Action

• ZENO

• TGP

• TP4

• Sapa

ts te

ts te

ts te

effectprecondition

Sapa and TP4Sapa TP4

Search Direction

Search Space

Branching Rule

Extension

Concurrency

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Sapa and TP4Sapa TP4

Search Direction

Search Space

Branching Rule

Extension

Concurrency

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Sapa: search space

S = ( P, M, II, Q, t)

P: set of predicates that are true

M: set of functions representing metric-resources

II: set of persistent conditions that need to be protected for a while

Q: queue containing scheduled future events

t: time stamp

P= {(pi, ti)|ti<t}: set of predicates that are true at t and achieved at ti

Sapa: Search Space

The initial state S0=(P,M,II,Q,t)P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources

II: persistent conditions

Q: scheduled future events

t: time stamp

--P= (pi, to), piIp

--M given resource constraints--Q empty, II empty

Sapa: Search Space

The state S=(P,M,II,Q,t)entails the goal G if

P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources

II: persistent conditions

Q: scheduled future events

t: time stamp

--(pi, ti)G, (pi, tj)P, tj<=ti, no event in deletes pi

-- eQ adds pi at tj, tj<=ti

Sapa: Action Application

Giving S=(P,M,II,Q,t), an action A is applicable in S if:

P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources

II: persistent conditions

Q: scheduled future events

t: time stamp

-- All instant-pre(A) |= P,M

-- eff(A) not interfere with

II and Q

-- no eQ interferes with

persistent-pre(A)

Sapa: branching rule

Choose an action A applicable in S,if A != no-op

S’ = ApplyInstantaneousUpdates ( S, A )Q’ = AddDelayedEvents ( Q, S, A)

Else S’ = SS’.t = eventTime( Front(Q) )While eventTime(Front(Q)) == S’.t

e = Dequeue(Q);S’ = ApplyEffect(S’, e );

TP4: search space

S = ( E, F, t)

E: set of predicates that are required to be true

t: time stamp

F= {(ai, i)}: action ai is planned to start at t- i

TP4: Search Space

The initial state S0=?• E={pi}: pi is required to be true at t

• F= {(ai, i)}: action ai is planned to start at t- i

• t: time stamp

S0= (G, NULL)

The final state S ?

{S= (E, NULL)|EIp}

TP4: Action Application

S=(E,{(aj,j)},t)

A set of actions SE is applicable in S if

• E={pi}: pi is required to be true at t

• F= {(ai, i)}: action ai is planned to start at t- i

• t: time stamp -- every action is compatible with each other;

--pE, aSE, padd(a), a is compatible with bF

TP4: branching rule

Choose a set of actions SE applicable in S,

define: Fnew = { (a, dur(a)| aSE }

adv = min{, a!=no-op}

then’ = {pre(a) | (a,)FFnew}

F’ = { (a, adv)| (a,)FFnew, adv}

S’ = (E’, F’)

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Extension

Concurrency

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Quiz 2: Concurrency

qpre(a)

!qdelayed-effect(b)

Quiz 2: Concurrency

qpre(a)

!qdelayed-effect(b)

Quiz 2: Concurrency

qinstant-effect(a)

!qdelayed-effect(b)

Quiz 2: Concurrency

qinstant-effect(a)

!qdelayed-effect(b)

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Extension Easy? Limited?

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Extension

Heuristic

Path Cost

Integrating resource

Forward chaining Backward chaining

Sapa: Extension?

P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources

II: persistent conditions

Q: scheduled future events

t: time stamp

an action A is applicable in S=(P,M,II,Q,t) if:

-- All instant-pre(A) |= P,M

-- eff(A) not interfere with II and Q

-- no eQ interferes with persistent-pre(A)

II = { (prea, t2 ) }

All (pre(a), -t1) |= P, M

TP4: Extension?

A set of actions SE is applicable in S=(E, F, t) if:

-- every action is compatible with each other;

--pE, aSE, padd(a), a is compatible with bF

E={ p| p is true during [t1, t2] }

• E={pi}: pi is required to be true at t

• F= {(ai, i)}: action ai is planned to start at t- i

• t: time stamp

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Extension Easy? Limited?

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Extension Easy? Limited?Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Heuristic

Path Cost

Integrating resource

Forward chaining Backward chaining

Sapa: Heuristic Function

Relaxed temporal planning graph(RTPG)

-- no delete list

-- no resource consumption

Max-span?

Min-slack?

Max-slack?

Sum-slack?

Sum-action?

Sum-duration?

Sapa: Heuristic Function

Max-span? Min-slack? Max-slack? Sum-slack?

Sum-action? Sum-duration?

TP4: Heuristic Functions

kFa

iFa

kiiikk

apreHFEH

,)(max),(,),(

*

),(

*

,)(),(),(

** Fa

i

ii

apreEHFEH

,max),( *

||,

* EHEHmEEE

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Extension Easy? Limited?Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Heuristic RTGP DP

Path Cost depends c(S, S’)=adv

Integrating resource

Forward chaining Backward chaining

TP4: Incremental Branching

• Estimating the cost of Partial States– Estimate lower bounds on p

• Ordering predicates in a state-- decreasing order of “difficulty”

• Right-shift equivalence-- if an action was applicable but was not used, then it

won’t be used

Sapa and TP4Sapa TP4

Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Extension Easy? Limited?Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Heuristic RTGP DP

Path Cost depends c(S, S’)=adv

Integrating resource

Forward chaining Backward chaining

Resource Management

• Producible

• Consumable

• Reusable

• Shareable

• Non-shareable

• Limited-capacity

Sapa: resource management

• Producable, consumable, non-shareable

Sum-duration

Sum-action

• Shareable ?

TP4: resource management

• Reusable & Non-shareable?

• Reusable & Limited-capacity?

• Consumable & non-producible?

Sapa and TP4Sapa TP4

Search Direction Forward chaining Backward chaining

Search Space S=(P,M,II,Q,t) S=(E,{(aj,j)},t)

Branching Rule Sound complete Sound, incomplete

Extension Easy? Limited?

ConcurrencyProposition lock

Non-shareable resourcesProposition lock (“holding”)

Path Cost depends c(S, S’)=adv

Heuristic RTGP DP

Integrating resource

Easy if inadmissible hard

Quiz3: Continuous Change

• ZENO?

• Sapa?

• TGP & TP4?

Experiments

TGP

ZENO

TP4 Sapa

expressiveness

perf

orm

ance

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