Heuristic Planning with Time and Resources
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Transcript of Heuristic Planning with Time and Resources
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Heuristic Planning with Time and Resources
--Sapa, TP4, and others
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Quiz1: Expressiveness of Temporal Action
• ZENO
• TGP
• TP4
• Sapa
ts te
ts te
ts te
effectprecondition
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Sapa and TP4Sapa TP4
Search Direction
Search Space
Branching Rule
Extension
Concurrency
Path Cost
Heuristic
Integrating resource
Forward chaining Backward chaining
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Sapa and TP4Sapa TP4
Search Direction
Search Space
Branching Rule
Extension
Concurrency
Path Cost
Heuristic
Integrating resource
Forward chaining Backward chaining
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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
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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
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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
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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)
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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 );
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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
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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}
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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
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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’)
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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
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Quiz 2: Concurrency
qpre(a)
!qdelayed-effect(b)
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Quiz 2: Concurrency
qpre(a)
!qdelayed-effect(b)
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Quiz 2: Concurrency
qinstant-effect(a)
!qdelayed-effect(b)
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Quiz 2: Concurrency
qinstant-effect(a)
!qdelayed-effect(b)
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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
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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
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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
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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
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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
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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
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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?
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Sapa: Heuristic Function
Max-span? Min-slack? Max-slack? Sum-slack?
Sum-action? Sum-duration?
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TP4: Heuristic Functions
kFa
iFa
kiiikk
apreHFEH
,)(max),(,),(
*
),(
*
,)(),(),(
** Fa
i
ii
apreEHFEH
,max),( *
||,
* EHEHmEEE
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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
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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
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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
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Resource Management
• Producible
• Consumable
• Reusable
• Shareable
• Non-shareable
• Limited-capacity
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Sapa: resource management
• Producable, consumable, non-shareable
Sum-duration
Sum-action
• Shareable ?
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TP4: resource management
• Reusable & Non-shareable?
• Reusable & Limited-capacity?
• Consumable & non-producible?
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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
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Quiz3: Continuous Change
• ZENO?
• Sapa?
• TGP & TP4?
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Experiments
TGP
ZENO
TP4 Sapa
expressiveness
perf
orm
ance
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