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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Filtering, Decomposition and Search Space Reduction for Optimal Sequential Planning (FDP System) St ephane

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

Filtering, Decomposition and Search Space Reduction for Optimal Sequential Planning

(FDP System) St´ ephane Grandcolas Cyril Pain-Barre

InCA Team Laboratoire des Sciences de l’Information et des Syst` emes (LSIS) UMR CNRS 6168 Marseille, France

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 1/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

Plan of the Talk

1

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 2/36

SLIDE 3

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Framework Quick Presentation

1

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 3/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Framework Quick Presentation

A Hybrid Planner

FDP (Filtering and Decomposition for Planning)

ptimal sequential planner

classical planning assumptions several techniques:

from planning :

consistency rules goal reachability estimation (future) heuristic search

from the CSP field :

filtering decomposition no-good recording

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 4/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Framework Quick Presentation

FDP in a Nutshell

planning-structure kind of planning graph incrementally extended with a given maximal size (no termination criterion on unsolvable problems) filtering of inconsistent actions and literals search for a solution in a planning-structure currently, a kind of depth-first search (complete procedure) several decomposition strategies reduction of the search space :

no-good recording goal-reachability estimation pruning of some redundant action sequences

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 5/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Framework Quick Presentation

FDP in a Nutshell

planning-structure kind of planning graph incrementally extended with a given maximal size (no termination criterion on unsolvable problems) filtering of inconsistent actions and literals search for a solution in a planning-structure currently, a kind of depth-first search (complete procedure) several decomposition strategies reduction of the search space :

no-good recording goal-reachability estimation pruning of some redundant action sequences

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 5/36

SLIDE 7

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

1

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 6/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Planning-Structure : Definition

Given the problem P = (A, I, G, L),

k, Va, Vl, d

is a planning-structure for P where: k : size of the planning-structure, Va = {y0, . . . , yk−1} : action variables, Vl = {xi,l}0≤i≤k,l∈L : literal variables, d : domain function

∀yi ∈ Va − → domain d(yi) ⊆ A, denoted Ai, ∀xi,l ∈ Vl − → domain d(xi,l) ⊆ {⊤, ⊥}, denoted Di,l.

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 7/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Planning-Structure : Graphical Representation

planning-structure of size k

. . . A1 Ak−1 A

k−1

L

k

L

1

L L

2

L

action steps literal steps

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 8/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Planning-Structure : Detailed Representation

Step i of the planning-structure

domain { } the literal the literal domain { , } variable xi,p has variable has action variable has domain { , } y i q r p s a 2

i

L

p r s q

L i+1 Ai

x i,s a 1 a 3 a 1 a 3

Initially, all the variables are undefined literal variables have {⊤, ⊥} as domain action variables have A as domain

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 9/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Valid Plan in a Planning-Structure

goals q r p s t p r q s t a 2 a 2 a 2 a 1 a 1 a 3 a 1 a 3 a 3

A valid plan is an assignment of the variables of Vl ∪ Va that : respects the domains valids the initial state literals (closed-world assumption) valids the goals in the last state respects the preconditions and effects of the chosen actions respects the persistence of the literals not affected by actions

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 10/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Preliminary Removals in the Structure

Before searching, some values for literals are removed:

q r p s p r q s a 2 a 2 a 2 a 1 a 1 a 1 a 3 a 3 a 3

in L0 according to I ∀l ∈ I, ⊥ is removed from D0,l ∀p (proposition) ∈ I, ⊤ is removed from D0,p in Lk according to G ∀l ∈ G, ⊥ is removed from Dk,l Consequences some actions and some literals become then inconsistent

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 11/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Inconsistent Values for Literal and Action Variables

5 possibilities for a literal value to become inconsistent logical consistency forward persistence backward persistence all actions delete

pposite always required

3 possibilities for an action value to become inconsistent falsified precondition falsified effect effect required

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 12/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Planning-Structure Solution Consistency and Filtering

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 14/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Search Method Summary

combination of several techniques depth-first search (complete) decomposition strategies consistency maintenance (after removals) pruning properties

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 15/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Decomposition Strategies

basic decompositions actions at a given step possible values of a literal at a given step action set splitting at a given step more sophisticated any combination is also possible

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 16/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Decomposition Strategy: Action Sets Splitting

splitting of a action sets at a given step choice of a step i (such that card(Ai) > 1) choice of a splitting of the action set Ai (currently always in 2 sets) illustration

S1 S2 S where

i

A = E F U

where

i

where

i

A = F A = E

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 17/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Decomposition Strategy: Action Sets Splitting

splitting of Ai choice of a literal l, and 2 action sets E and F such that : E = {a ∈ Ai | l ∈ eff (a)} F = {a ∈ Ai | l ∈ eff (a)}

bjectives

to minimize |card(E) − card(F)| balancing as much as possible generated sub-problems hardness causes immediate removals

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 18/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Current Search Strategy

forward-chaining (choice of the closest step to initial state)

A0 A1 Ai−1 Ai Ai+1 Ak−1 . . . . . .

undefined steps defined steps

decomposition by splitting if card(Ai) > 3, actions enumeration otherwise

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 19/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Search Space Reduction

Currently 4 techniques nogood states recording estimation of the goals reachability removing of irrelevant actions pruning of some redundant action sequences

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 20/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Nogood States Recording

. . . L

completely defined state

. . .

d : distance to the goal state

Nogood L, d (after a search failure) failure each time we encounter again L at a distance d′ where d′ ≤ d

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 21/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Unreachable Goals

Early detection of missing goals unreachability Li : a completely defined state at step i M : missing goals in Li

. . . L . . .

M = {l ∈ G | l is not true in Li} Maximal number of satisfied goals in subsequent steps b =

k−1

maxa∈Aqcard(eff (a) ∩ M) Unreachability criterion if b < card(M) the missing goals can’t be satisfied

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 22/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Relevant Actions and Literals

immediate criterion goals are relevant actions of Ak−1 that add goals are relevant relevance criterion propagation by regression to the actions that add relevant literals to the preconditions of the relevant actions to the literals that are relevant at the next step property actions that are irrelevant can be safely removed without loss of completeness/optimality new consistency rule irrelevant actions are removed at anytime during the search

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 23/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Redundant Action Sequences

Independent actions a and a′ are independent if neither deletes a precondition or effect

f the other, and neither adds a precondition of the other :

∀l ∈ eff (a), ¬l ∈ pre(a′) ∪ eff (a′) and l ∈ pre(a′) ∀l ∈ eff (a′), ¬l ∈ pre(a) ∪ eff (a) and l ∈ pre(a) property independent actions can be executed in any order, even in parallel (commutativity in [Haslum & Geffner, 2000]) pruning objective in sequential planning if the sequence (a, a′) is considered then (a′, a) should not

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 24/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering

admissible 2-sequence the sequence (a, a′) is admissible if : a′ deletes a precondition of a

r a′ deletes an effect of a
r a adds a precondition of a′

2-sequence ordering constraint (a, a′) is an ordered 2-sequence if : a and a′ are not the opposite one of the other and

either (a, a′) is admissible

r (a, a′) and (a′, a) are not admissible, and a ≺ a′

(where ≺ is an arbitrary total order over the action set)

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 25/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering : Example

let a1 ≺ a2 ≺ a3 ≺ a4 be the order dependence network

adds a precondition removes a precondition

a 3 a 1 a 4 a 2

possible action sequences a3 a2 a1 a4 a3 a2 a4 a1 a3 a4 a2 a1 a2 a3 a1 a4 a2 a3 a4 a1

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 26/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering : Example

let a1 ≺ a2 ≺ a3 ≺ a4 be the order dependence network

adds a precondition removes a precondition

a 3 a 1 a 4 a 2

possible action sequences a3 a2 a1 a4 a3 a2 a4 a1 a3 a4 a2 a1 a2 a3 a1 a4 a2 a3 a4 a1 red sequences are not generated

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 26/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering : Limitations

let a1 ≺ a2 ≺ a3 be the order dependence network

1 a

3 a

2 a

adds a precondition (p)

assumption p is false possible action sequences a2 a3 a1 a3 a1 a2 a3 a2 a1

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 27/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering : Limitations

let a1 ≺ a2 ≺ a3 be the order dependence network

1 a

3 a

2 a

adds a precondition (p)

assumption p is false possible action sequences a2 a3 a1 a3 a1 a2 a3 a2 a1 red sequence is not generated

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 27/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

2-sequence Ordering : Limitations

let a1 ≺ a2 ≺ a3 be the order dependence network

1 a

3 a

2 a

adds a precondition (p)

assumption p is false possible action sequences a2 a3 a1 a3 a1 a2 a3 a2 a1 red sequence is not generated problem it remains two ordered sequences that are equivalent

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 27/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Level Ordering

method action steps are organized in levels each level contains an ordered sequence of independent actions

rdered sequence of independent actions

2 level 1 level 3 level i level

a0 a1 a2 a3 a4 a5 a6

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 28/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Level Ordering : Predecessor Constraint

Predecessor of an action a is a predecessor of a′ if : either (a, a′) is admissible

r a and a′ have some contradictory precondition

Predecessor constraint each action in a level > 1 must have a predecessor in the previous level

2 level 1 level i level

a a’ predecessor

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 29/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work Search and Problem Decomposition Search Space Reduction

Level Ordering : Construction

2 level 3 level j level 1 level

a’ a

Ai Ai−1

addAction(a′, level1, . . . , levelj)

1

if levelj contains the opposite action of a′ then

2

return UNORDERED (failure)

3

if levelj contains a predecessor for a′ then

4

return NEW LEVEL

5

if j > 1 and levelj−1 contains the opposite action of a′ then

6

return UNORDERED (failure)

7

if j > 1 and a′ ≺ a then return UNORDERED (failure)

8

return SAME LEVEL

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 30/36

SLIDE 44

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

1

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 31/36

SLIDE 45

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

Efficiency of Ordering Constraints

series problem nops nlit len mksp no ordering 2-sequences ordering level ordering calls time (s) calls time (s) calls time (s) diverse hanoi7 238 94 127 127 572128 22.22 243271 17.24 243095 17.54 mprime-16 7374 402 6 5 52332 3.67 7883 11.36 27008 28.3 mystery-19 6521 562 6 6 3622 2.2 939 9.77 1086 24.13 mystery-30 4085 412 9 6 288276 32.27 56728 12.27 71656 19.95 xy-world-f10 200 40 10 1 2668 0.04 194314 1.6 429714 3.89 IPC3 driverlog-7 252 93 13 6 1327338 23.46 458658 15.55 382669 15.93 FreeCell4-4 1616 183 18 7 2937247 606.43 2015834 526.92 1757852 480.53 satellite3 188 66 11 265571 1.33 93153 0.76 81652 1.0 zeno-2-5 392 58 11 5 1589396 27.48 474647 11.33 431475 13.25 zeno-2-6 408 64 15 6 1663353 28.48 718539 18.67 587418 19.89 IPC4 airport-8 295 443 62 26 1018914 197.88 280170 47.12 294058 52.32 airport-14 347 493 60 26 938428 213.51 261852 50.11 276649 57.52 PSR-22 112 56 33 25 4863697 58.41 2782675 40.02 3445088 58.71 PSR-25 9400 58 9 9 4366 12.3 1063 21.6 988 52.45 PSR-31 661 63 19 16 357316 22.75 123109 12.01 133223 14.8 PSR-46 98 60 34 29 2051278 27.02 1355273 19.62 1594195 27.45 IPC5

penstacks-8

115 37 23 148639 2.22 148645 2.24 148619 2.25 pathways-04 153 120 17 8 1682561 6.42 207644 2.25 464218 3.98 pipesworld-4 656 154 11 6 389901 34.54 203215 24.64 218230 30.49 pipesworld-8 2672 204 11 7 5111567 962.65 3333348 874.66 3278904 1270.67 pipesworld-21 3272 376 14 14 1464159 612.53 412206 228.15 480551 293.18 storage-11 460 146 17 11 1036518 41.78 340937 21.32 302371 19.75 storage-12 690 164 16 9 5148404 260.14 1890755 144.24 1665728 139.23 storage-13 282 181 18 18 865743 30.56 453124 21.3 493605 21.6 storage-14 564 203 19 11 8466543 373.42 6976067 427.76 6166156 391.88 TRUCK-3 789 191 20 16 1276518 29.39 686433 23.61 852849 25.96 TRUCK-4 936 226 23 18 56439409 1147.61 34699517 961.3 39998454 1104.57 TRUCK-7 1104 275 23 18 18345815 514.95 10756026 447.73 11676481 430.37 St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 32/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

FDP versus some sequential planners

series problem nops nlit len mksp 2-seq. ord. level ord. BFHSP back BFHSP forw time sec. time sec. time sec. time sec. diverse hanoi7 238 94 127 127 17.24 17.54 – – mprime-16 7374 402 6 5 11.36 28.3 474.77 – mystery-19 6521 562 6 6 9.77 24.13 736.41 99.73 mystery-30 4085 412 9 6 12.27 19.95 257.26 2363.65 xy-world-f10 200 40 10 1 1.6 3.89 63.7 249.92 IPC3 driverlog-7 252 93 13 6 15.55 15.93 1.61 664.3 FreeCell4-4 1616 183 18 7 526.92 480.53 71.26 1918.86 satellite3 188 66 11 0.76 1 0.16 130.51 zeno-2-5 392 58 11 5 11.33 13.25 1.54 298.21 zeno-2-6 408 64 15 6 18.67 19.89 10.85 773.24 IPC4 airport-8 295 443 62 26 47.12 52.32 82.58 30.64 airport-14 347 493 60 26 50.11 57.52 125.62 33.7 PSR-22 112 56 33 25 40.02 58.71 94.62 113.13 PSR-25 9400 58 9 9 21.6 52.45 17.02 63.82 PSR-31 661 63 19 16 12.01 14.8 3.59 256.44 PSR-46 98 60 34 29 19.62 27.45 918.62 66.61 IPC5

penstacks-8

115 37 23 2.24 2.25 0.33 0.56 pathways-04 153 120 17 8 2.25 3.98 0.69 131.89 pipesworld-4 656 154 11 6 24.64 30.49 – 631.79 pipesworld-8 2672 204 11 7 874.66 1270.67 – – pipesworld-21 3272 376 14 14 228.15 293.18 – – storage-11 460 146 17 11 21.32 19.75 359.17 85.33 storage-12 690 164 16 9 144.24 139.23 3833.09 1479.21 storage-13 282 181 18 18 21.3 21.6 47.44 141.34 storage-14 564 203 19 11 427.76 391.88 4592.37 5076.33 TRUCK-3 789 191 20 16 23.61 25.96 21.53 406.52 TRUCK-4 936 226 23 18 961.3 1104.57 89.98 – TRUCK-7 1104 275 23 18 447.73 430.37 154.69 5837.18 St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 33/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

FDP versus Satplan

series problem nops nlit len mksp 2-seq. ord. level ord. Satplan Satplan 2006 time sec. time sec. time sec. time sec. diverse hanoi7 238 94 127 127 17.24 17.54 – – mprime-16 7374 402 6 5 11.36 28.3 2.6 9.09 mystery-19 6521 562 6 6 9.77 24.13 12.04 2.2 mystery-30 4085 412 9 6 12.27 19.95 9.31 1.64 xy-world-f10 200 40 10 1 1.6 3.89 0.03 0.01 IPC3 driverlog-7 252 93 13 6 15.55 15.93 0.07 0.07 FreeCell4-4 1616 183 18 7 526.92 480.53 399.96 1.46 satellite3 188 66 11 0.76 1.0 – – zeno-2-5 392 58 11 5 11.33 13.25 2.41 0.19 zeno-2-6 408 64 15 6 18.67 19.89 0.87 0.12 IPC4 airport-8 295 443 62 26 47.12 52.32 1.42 2.56 airport-14 347 493 60 26 50.11 57.52 1.94 3.03 PSR-22 112 56 33 25 40.02 58.71 98.73 17.46 PSR-25 9400 58 9 9 21.6 52.45 129.25 87.33 PSR-31 661 63 19 16 12.01 14.8 9.37 3.45 PSR-46 98 60 34 29 19.62 27.45 – 166.48 IPC5

penstacks-8

115 37 23 2.24 2.25 – – pathways-04 153 120 17 8 2.25 3.98 0.11 0.12 pipesworld-4 656 154 11 6 24.64 30.49 384.79 0.71 pipesworld-8 2672 204 11 7 874.66 1270.67 273.29 14.93 pipesworld-21 3272 376 14 14 228.15 293.18 – 91.4 storage-11 460 146 17 11 21.32 19.75 332.05 95.24 storage-12 690 164 16 9 144.24 139.23 53.06 37.39 storage-13 282 181 18 18 21.3 21.6 – 201.8 storage-14 564 203 19 11 427.76 391.88 294.33 35.0 TRUCK-3 789 191 20 16 23.61 25.96 191.29 70.95 TRUCK-4 936 226 23 18 961.3 1104.57 – 568.48 TRUCK-7 1104 275 23 18 447.73 430.37 – 718.7 St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 34/36

SLIDE 48

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

1

Overview Framework Quick Presentation

2

Structure, Solutions and Filtering Planning-Structure Solution Consistency and Filtering

3

Search and Search Space Reduction Search and Problem Decomposition Search Space Reduction

4

Experimental Results

5

Conclusion and Future Work

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 35/36

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Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

Conclusion & Future Work

Conclusion FDP is an optimal sequential planner quite performant consistency rules adapted to any kind of decomposition (forward, backward, bidirectional, undirected) unlike other CSP approaches, the search control is total Future work termination criterion better action sets splitting heuristics (hm family or Pattern Databases) valued actions planning with resources

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 36/36

SLIDE 50

Overview Structure, Solutions and Filtering Search and Search Space Reduction Experimental Results Conclusion and Future Work

Conclusion & Future Work

Conclusion FDP is an optimal sequential planner quite performant consistency rules adapted to any kind of decomposition (forward, backward, bidirectional, undirected) unlike other CSP approaches, the search control is total Future work termination criterion better action sets splitting heuristics (hm family or Pattern Databases) valued actions planning with resources

St´ ephane Grandcolas, Cyril Pain-Barre FDP System. AAAI’07, 24 July 2007, Vancouver 36/36