SAPA: A Domainindependent Heuristic Temporal Planner

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(No Transcript)
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Buenos dias, amigos. Obviamente este es al
articulo de Binh Minh. De todas maneras, yo lo
convenci de que seria mejor para el usar su
tiempo en trabajar en otro articulo proximo mas
que en visitar Toledo, un pueblo del oeste medio
en Ohio. Yo entiendo que esta es basicamente la
estrategia que Malik uso para presentar tambien
el articulo de Romain.
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Talk Outline

• Temporal Planning and SAPA
• Action representation and search algorithm
• Objective functions and heuristics
• Admissible/Inadmissible
• Resource adjustment
• Empirical results
• Related future work

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Planning

• Most academic research has been done in the
  context of classical planning
• Already P-SPACE complete
• Useful techniques are likely to be applicable in
  more expressive planning problems

• Real world application normally has more complex
  requirements
• Non-instantaneous actions
• Temporal constraints on goals
• Resource consumption

Classical planning has been able to scale up to
big problems recently
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Related Work

• Planners that can handle similar types of
  temporal and resource constraints TLPlan, HSTS,
  IxTexT, Zeno
• Cannot scale up without domain knowledge
• Planners that can handle a subset of constraints
• Only temporal TGP
• Only resources LPSAT, GRT-R
• Subset of temporal and resource constraints TP4,
  Resource-IPP

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SAPA

• Forward state space planner
• Based on BachusAdy.
• Make resource reasoning easier
• Handles temporal constraints
• Actions with static and dynamic durations
• Temporal goals with deadlines
• Continuous resource consumption and production
• Heuristic functions to support a variety of
  objective functions

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Action Representation

• Durative with EA SA DA
• Instantaneous effects e at time
• te SA d, 0 ? d ? DA
• Preconditions need to be true at the starting
  point, and protected during a period of time d, 0
  ? d ? DA
• Action can consume or produce continuous amount
  of some resource

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Searching time-stamped states
Search through the space of time-stamped states
S(P,M,?,Q,t)
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Search Algorithm (cont.)

• Goal Satisfaction
• S(P,M,?,Q,t) ? G if ?ltpi,tigt? G either
• ? ltpi,tjgt ? P, tj lt ti and no event in Q deletes
  pi.
• ? e ? Q that adds pi at time te lt ti.
• Action Application
• Action A is applicable in S if
• All instantaneous preconditions of A are
  satisfied by P and M.
• As effects do not interfere with ? and Q.
• No event in Q interferes with persistent
  preconditions of A.
• When A is applied to S
• S is updated according to As instantaneous
  effects.
• Persistent preconditions of A are put in ?
• Delayed effects of A are put in Q.

S(P,M,?,Q,t)
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Heuristic Control
Temporal planners have to deal with more
branching possibilities ? More critical to have
good heuristic guidance
Design of heuristics depends on the objective
function
? In temporal Planning heuristics focus on richer
obj. functions that guide both planning and
scheduling
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Objectives in Temporal Planning

• Number of actions Total number of actions in the
  plan.
• Makespan The shortest duration in which we can
  possibly execute all actions in the solution.
• Resource Consumption Total amount of resource
  consumed by actions in the solution.
• Slack The duration between the time a goal is
  achieved and its deadline.
• Optimize max, min or average slack values

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Deriving heuristics for SAPA
We use phased relaxation approach to derive
different heuristics
Relax the negative logical and resource
effects to build the Relaxed Temporal Planning
Graph
AltAlt,AIJ2001
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Relaxed Temporal Planning Graph
Heuristics in Sapa are derived from the
Graphplan-style bi-level relaxed temporal
planning graph (RTPG)

• Relaxed Action
• No delete effects
• No resource consumption

while(true) forall A?advance-time
applicable in S S Apply(A,S)
if S?G then Terminatesolution S
Apply(advance-time,S) if ?(pi,ti) ?G such
that ti lt Time(S) and pi?S then
Terminatenon-solution
else S S end while
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Heuristics directly from RTPG
A D M I S S I B L E

• For Makespan Distance from a state S to the
  goals is equal to the duration between time(S)
  and the time the last goal appears in the RTPG.
• For Min/Max/Sum Slack Distance from a state to
  the goals is equal to the minimum, maximum, or
  summation of slack estimates for all individual
  goals using the RTPG.

Proof All goals appear in the RTPG at times
smaller or equal to their achievable times.
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Heuristics from Solution Extracted from RTPG
RTPG can be used to find a relaxed solution which
is then used to estimate distance from a given
state to the goals
Sum actions Distance from a state S to the goals
equals the number of actions in the relaxed plan.
Sum durations Distance from a state S to the
goals equals the summation of action durations in
the relaxed plan.
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Heuristics from Solution Extracted from RTPG
RTPG can be used to find a relaxed solution which
is then used to estimate distance from a given
state to the goals
Sum actions Distance from a state S to the goals
equals the number of actions in the relaxed plan.
Motivation Planning progresses by adding
actions to achieve goals. Thus, choose state
closer to the goals in terms of total number of
actions.
Sum durations Distance from a state S to the
goals equals the summation of action durations in
the relaxed plan.
Motivation Choose state closer to the goals in
terms of total action durations instead of number
of actions. Thus, favor actions with shorter
durations.
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Resource-based Adjustments to Heuristics
Resource related information, ignored originally,
can be used to improve the heuristic values
Adjusted Sum-Action h h ?R ?
(Con(R) (Init(R)Pro(R)))/?R?
Adjusted Sum-Duration h h ?R
(Con(R) (Init(R)Pro(R)))/?R.Dur(AR)
? Will not preserve admissibility
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Aims of Empirical Study

• Evaluate the effectiveness of the different
  heuristics.
• Ablation studies
• Test if the resource adjustment technique helps
  different heuristics.
• Compare with other temporal planning systems.

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Empirical Results

• Sum-action finds solutions faster than sum-dur
• Admissible heuristics do not scale up to bigger
  problems
• Sum-dur finds shorter duration solutions in most
  of the cases
• Resource-based adjustment helps sum-action, but
  not sum-dur
• Very few irrelevant actions. Better quality than
  TemporalTLPlan.
• So, (transitively) better than LPSAT

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Comparison to other planners

• Planners with similar capabilities
• IxTet, Zeno
• Poor scaleup
• HSTS, TLPLAN
• Domain dependent search control
• Planners with limited capabilities
• TGP and TGP
• Compared on a set of random temporal logistics
  problem
• Domain specification and problems are defined by
  TP4s creator (P_at_trik Haslum)
• No resource requirements
• No deadline constraints or actions with dynamic
  duration

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Empirical Results (cont.)
Logistics domain with driving restricted to
intra-city (traditional logistics domain)
Sapa is the only planner that can solve all 80
problems
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Empirical Results (cont.)
Logistics domain with inter-city driving actions
The sum-action heuristic used as the default
in Sapa can be mislead by the long duration
actions...
?
Future work on fixed point time/level propagation
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Conclusion

• Presented SAPA, a domain-independent forward
  temporal planner that can handle
• Durative actions
• Deadline goals
• Continuous resources
• Developed different heuristic functions based on
  the relaxed temporal planning graph to address
  both satisficing and optimizing search
• Method to improve heuristic values by resource
  reasoning
• Promising initial empirical results

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Related Work

• Planners can handle similar types of temporal and
  resource constraints TLPlan, HSTS, IxTexT, Zeno
• Cannot scale up without domain knowledge
• Planners that can handle a subset of constraints
• Only temporal TGP
• Only resources LPSAT, GRT-R
• Subset of temporal and resource constraints TP4,
  Resource-IPP

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Future Work

• Exploit mutex information in
• Building the temporal planning graph
• Adjusting the heuristic values in the relaxed
  solution
• Relevance analysis
• Improving solution quality
• Relaxing constraints and integrating with
  full-scale scheduler

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