ai – week 18 + 19 ai planning – plan generation algorithms: graphplan lee mccluskey, room 2/09...

AI – Week 18 + 19AI Planning – Plan Generation Algorithms: GraphPlan

Lee McCluskey, room 2/09Email [email protected]

http://scom.hud.ac.uk/scomtlm/cha2555/

This lecture I have broken the habit of a lifetime and inserted some slides from someone else!! They are from Dana S. Nau’s collection from his and Ghallab and Traverso’s book on AI Planning (see ‘resources’ in the website to find them)

mailto:[email protected]

http://scom.hud.ac.uk/scomtlm/cha2555/

Artform Research Group

Relaxing …..

One way to reduce branching factor in a problem is by relaxing!! :

First create a relaxed problem -- remove some restrictions of the original problem

The solutions to the relaxed problem will include all solutions to the original problem

Then do a modified version of the original search. Restrict its search space to include only those actions that occur in solutions to the relaxed problem


The Graphplan algorithm

1. Designed in the mid-1990’s

2. Generally faster than any other known algorithm at that time

3. Produces optimal (parallel) plans

4. Introduced the MOST INFLUENTIAL TECHNIQUE IN PLANNING –

The Planning Graph


Parallel Operators

Two operators can be applied „in parallel“ if their outcome does not depend on the order of execution

Drive T1 A B, Drive T2 C D Operators a and a' interfere if:

del(a) ^ (add(a') U pre(a')) is not empty, or del(a') ^ (add(a) U pre(a)) is not empty

Allowing sets of non-interfering operators at each step in the plan can make plans shorter => potentially fewer search iterations


The Graphplan algorithm : Outline

1. Incrementally construct a planning graphAssume all applicable ground operators are applied in

parallel to the initial state predicates; Produce new state and repeat.Stop when goal predicates are all present in state.2. Construct mutual exclusion constraintsConstrain ground operators that cannot be executed

together3. Do solution extractionSearch backwards considering only actions in the planning

graph


state-level i

effectsMaintenance actions: propagate literals to the next level. These represent what happens if no action in the final plan affects the literal.

state-level i-1

state-level 0 (the literals true in s0)

The Planning GraphAlternating layers of ground literals and actions

All actions that might possibly occur at each time step

All of the literals asserted by those actions

action-level i

preconditions


Example

due to Dan Weld (University of Washington) Suppose you want to prepare dinner as a surprise for your sweetheart

(who is asleep)

Initial State s0 = {garbage, cleanHands, quiet}

Goal g = {dinner, present, garbage}

Action Preconditions Effects

cook() cleanHands dinner

wrap() quiet present

carry() none garbage, cleanHands

dolly() none garbage, quiet

Also have the maintenance actions: one for each literal


Example (continued)state-level 0:

{all atoms in s0} U {negations of all atoms not in s0}

action-level 1:{all actions whose prconditions are satisfied in s0}

state-level 1:{all effects of all of the actions in action-level 1}

Action Preconditions Effects

cook() cleanHands dinner

wrap() quiet present

carry() none garbage, cleanHands

dolly() none garbage, quiet

Also have the maintenance actionsdinner

present

dinner

present

state-level 0 state-level 1action-level 1


Mutual Exclusion

Two actions at the same action-level are mutex if Inconsistent effects: an effect of one negates an effect of the other Interference: one deletes a precondition of the other Competing needs: they have mutually exclusive preconditions

Otherwise they don’t interfere with each other Both may appear in a solution plan

Two literals at the same state-level are mutex if Inconsistent support: one is the negation of the other, or all ways of achieving

them are pairwise mutex


Example (continued) Augment the graph to indicate mutexes carry is mutex with the maintenance

action for garbage (inconsistent effects) dolly is mutex with wrap

interference ~quiet is mutex with present

inconsistent support each of cook and wrap is mutex with

a maintenance operation

Action Preconditions Effectscook() cleanHands dinnerwrap() quiet presentcarry() none garbage, cleanHandsdolly() none garbage, quiet

Also have the maintenance actions dinner

present

dinner

present



dinner

present

dinner

present

Example (continued)

Check to see whether there’s a possible plan

Recall that the goal is{garbage, dinner, present}

Note that

All are prossible in s1

None are mutex with each otherThus, there’s a chance that a plan existsTry to find it

Solution extraction



Solution Extraction

procedure Solution-extraction(g,j)

if j=0 then return the solution

for each literal l in g

nondeterministically choose an actionto use in state s j–1 to achieve l

if any pair of chosen actions are mutex

then backtrack

g’ := {the preconditions of the chosen actions}

Solution-extraction(g’, j–1)

end Solution-extraction

The level of the state sj

The set of goals we are trying to achieve

state-leveli-1

action-level

i

state-level

i

A real action or a maintenance action


Example (continued)

Two sets of actions for the goals at state-level 1

Neither works: both sets contain actions that are mutex

dinner

present

dinner

present



Example (continued)

dinner

present

dinner

present

dinner

present

state-level 0 state-level 1action-level 1 state-level 2action-level 2


Example (continued)

Solutionextraction

Twelve combinationsat level 4 Three ways to

achieve garb Two ways to

achieve dinner Two ways to

achieve present

dinner

present

dinner

present

dinner

present



Example (continued)

Several of the combinations look OK at level 2

Here’s one of them

dinner

present

dinner

present

dinner

present



Example (continued)

Call Solution-Extraction recursively at level 2

It succeeds Solution

whose parallel length is 2

dinner

present

dinner

present

dinner

present



RECAP: The Graphplan algorithm

1. Incrementally construct a planning graphAssume all applicable ground operators are applied in

parallel to the initial state predicates; Produce new state and repeat.Stop when goal predicates are all present in state.2. Construct mutual exclusion constraintsConstrain ground operators that cannot be executed

together3. Do solution extractionSearch backwards considering only actions in the planning

graph


Graphplan’s limiting assumptions / drawbacks:

Need to create ground instances of everything – all actions and all literals - many of the groundings may be irrelevant. The groundings may lead to an enormous/infinite database!

the goal is a set of literals If the goal literals are found in the graph very

early on, then solution extraction at each subsequent level may be very inefficient..


Conclusions Before Graphplan came out, most planning

researchers were working on plan or state space planners

Graphplan caused a sensation because it was so much faster

Many subsequent planning systems have used ideas from it IPP, STAN, GraphHTN, Blackbox, TGP, LPG

Several of them are much faster than the original Graphplan

(see PLANET website for how to download them)


Rocket Exercise: First Layer..

at-rocket(London)

at(c1,London)

at(c2,London)

¬at-rocket(Paris),

¬at(c1,Paris)

¬at(c2,Paris)

¬in-rocket(c1)

¬in-rocket(c2)

¬ at-rocket(London),

at-rocket(Paris)

¬ at(c1,London),

in-rocket(c1)

¬ at(c1,London),

in-rocket(c2)

at-rocket(London)

at(c1,London)

at(c2,London)

¬at-rocket(Paris),

¬at(c1,Paris)

¬at(c2,Paris)

¬in-rocket(c1)

¬in-rocket(c2)

move(London,Paris)

load(c1,London)

load(c2,London)



at-rocket(Paris)

¬ at(c1,London),

in-rocket(c1)

¬ at(c1,London),

in-rocket(c2)

at-rocket(London)

at(c1,London)

at(c2,London)

¬at-rocket(Paris),

¬at(c1,Paris)

¬at(c2,Paris)

¬in-rocket(c1)

¬in-rocket(c2)

Unload(c1,Paris)

Unload(c2,Paris)

move(London,Paris)

load(c1,London)

load(c2,London)

at(c1,Paris)

at(c2,Paris)


at-rocket(Paris)

¬ at(c1,London),

in-rocket(c1)

¬ at(c1,London),

in-rocket(c1)

at-rocket(London)

at(c1,London)

at(c2,London)

¬at-rocket(Paris),

¬at(c1,Paris)

¬at(c2,Paris)

¬in-rocket(c1)

¬in-rocket(c2)

Second Layer… GoalsPresent –But no consistentAction sequence

Need a Third Layer…

ai – week 18 + 19 ai planning – plan generation algorithms: graphplan lee mccluskey, room 2/09...

Documents

actions actionlevel

original problem n

relaxed problem slide

planning graph

new state

literal slide

effects maintenance

asleep initial state