A HİERARCHİCAL GOAL-BASED FORMALİSM AND ALGORİTHM FOR SİNGLE-AGENT PLANNİNGAAMAS ‘12

Utku Şirin

1560838

OUTLİNE

Planning and Domain Models Hierarchical Goal Network (HGN) Planner

formalism and proof of its capabilities An algorithm for HGN planning, Goal

Decomposition Planner (GDP) Experimental Results Comments and Conclusions

AUTOMATED PLANNİNG

What is automated planning? There is goal and current situation, aim is to

achieve the goal by executing possible actions Current situation is defined by states Repeatedly;

execute an executable action, apply the changes to the state and check whether the goal is satisfied

How to do these automatically, fast, and in less number of steps?

Important ability for computurized agents Robotic Agents Game-Playing Agents Web-service Agents etc...

DOMAİN MODELS Planner should have a domain model defining the states, actions

and the relation between the actions and states How to build domain models?

Hand-crafted planner module Huge development effort !

Domain-configurable planner Utilization of a domain-model file Most of the uses are Hierarchical Task Network (HTN) Planning

There are methods dividing tasks into subtasks (will be analyzed deeper) Does not focus on goals, but tasks Just apply the tasks until there is no remaining tasks

Easier with respect to hand-crafted planning module Problem of lacking of task and goal correspondence makes it hard to translate

classical planning domains into HTN domains, hence to prove soundness Can we do better ?

Hierarchical Goal Network (HGN) Planner Similar to HTN formalism, but easier to develop domain models More flexible Integrates domain-independent heuristics Decomposes goals rather than tasks Provably HGN has same expressivity power as HTN, is sound and complete

FORMALİSM Classical Planning

Domain D is a finite-state transition system S is a set of states, each state is a finite set of ground atoms

Ex: onTable(block1), on(block2,block1) G is the specification of the goal state comprised of a set of

ground atoms O is a set of operators which is a triple

(head(o), pre(o), eff(o)) Each action is a ground instance of an operator An action a is executable in a state s if s╞ pre(a) (s entails pre(a))

Meaning that s satisfies the preconditions of action a After execution an action a, the new state s’ is

s’ = (s - eff-(a)) ∪ eff+(a) A plan = <a1, …, an> is executable in s if each action ai is

executable in the state produced by ai-1. A solution to a classical planning problem P = (D, s0, g) is , if δ(s0, )

╞ g, where D is the domain, s0 is the initial state and g is a goal definition

HİERARCHİCAL GOAL NETWORK (HGN) PLANNİNG Similar to classical planning but have methods

additionally A HGN method m is a quadruple (head(m), pre(m),

sub(m), post(m)) head(m) and pre(m) same as the ones in operators for

classical planning sub(m) list of goals <g1, …, gk> where each gi is a goal

formula post(m) = gk ; if sub(m) is non-empty

post(m) = pre(m) ; otherwise Relevance: An action a or a method m is relevant for a

goal formula g if eff(a) or post(m) entails at least one literal in g. Provides smaller search space than a classical planner

A HGN domain is D’ = (D,M) where D is a classical planning domain and M is the set of methods

PROOFS HGN planning is sound and complete. These are

proved by mapping HGN planning problem to classical planning problem Soundness:

HGN planning domain is D = (D’,M), where D’ is a classical planning domain

Every action executable in D is also executable in D’ Hence, every solution to problem P = (D, s0, g) is also a solution to

P = (D’, s0, g) Hence, HGN planning is sound.

Completeness For a path x in classical domain D, there can be constructed a

method m that specifies each state in x as a sub-goal in its sub(m). Then a single action will achieve each subgoal completing the path Hence for each classical planning problem P = (D, s0, g), there is a

HGN planning problem P’ = ((D, M), s0, g) where P and P’ have same set of solution

PROOFS HGN formalism expressivity power is equal to

HTN formalism From HGN formalism construct HTN formalism

Map subgoals to subtasks with same preconditions <g1, … , gk> mapped directly to <tg1, … , tgk> In HTN, however, it is needed to define primitive tasks

as well. So, define a new primitive task for each tgi having same precondition as gi and no subtasks (that’s why it is primitive, indeed).

From HTN formalism construct HGN formalism Map subtasks to subgoals with same preconditions <t1, … , tk> mapped directly to <fint1, … , fintk>

A LİTTLE BİT HTN

Associate methods with networks

Critics for different types of network

ALGORİTHM, GOAL DECOMPOSİTİON PLANNİNG (GDP)

GDP İS SOUND AND COMPLETE

Soundness, if GDP returns a plan, it is a solution indeed. Induction on length of the solution n

For n = 0, it means s0╞ g If is a solution of length k < n returned by GDP Then ’ of length k+1 returned by GDP is also a solution

as line 11 appends a relevant action/method u to the plan

Completeness, if there is a solution, then GDP will return it Induction on length of the solution n

For n = 0, GDP will return it as s0╞ g Assume there is a solution of length k and GDP returns it Then GDP returns solutions of length k+1 as at line 11

GDP appends relevant action/method

DOMAİN-İNDEPENDENT HEURİSTİCS

One of the most important contribution of HGN planning formalism

Line 9-13 was choosing action/methods nondeterministically, however, it can be chosen based on a heruistic value

So, line 9-13 will be replaced as below:

DOMAİN-İNDEPENDENT HEURİSTİCS

How to calculate heruistic value for each action/method:

First propositional

level in which p

appears in Plannig Graph

States-Levels

Action-Levels

PLANNING GRAPH

EXPERİMENTS An HTN planner SHOP2, a classical planner FF and the HGN planner GDP are compared in five

different domains DOMAINs:

Logistics Transportation Domain: There several cities. At each city there are several post-offices Aim is to move specified number of packages to different cities Intracity transportation is done via trucks Intercity transportation is done via airplanes Trucks and airplanes are unlimited

Blocks-World: There are n-many blocks in a specified configuration Convert the initial configuration to goal configuration by obeying the following rules:

Move one block at a time A block may be put on another block or table

Depots: Combination of Logistics and Blocks-World domain Trucks have hoist just like the arms of robots in Blocks-World domain Stacking the crates becomes Blocks-World domain

Towers of Hanoi: There are three sticks in which several disks are places on it Disks are put in such a way that each disk is smaller than the disk that it is put on it Move disks from one stick to other by obeying the following rules

Move one disk at a time No disk may be put onto a smaller disk

3-City Routing The only newly written domain, hence it is a weak domain model There are 3 cities Each city has several locations and locations are connected with roads arbitrarily in the cities There is one random road connected city1 to city3 and one random road connected city2 to city3 Aim is to go from city1 or city3 to city2

RESULTS

Logistics Domain Results For n = 15, 20, …, 60 packages

GDP-h does not bring much overhead for heuristic function calculation

FF has strong heuristics

RESULTS

Blocks-World Domain Results For n = 10, 20, …, 100 blocks

FF has known problems with Blocks-World GDP-h has heuristic value calcuation time

overhead GDP-h results in a bit smaller plans

RESULTS

The Depots Domain Results For n = 10, 20, …, 80 crates

FF cannot solve more than 24 crates GDP-h heuristic overhead is significant, also

have almost same plans with the other planners

RESULTS Towers of Hanoi Domain Results For n = 3, …, 14 rings

SHOP2 could not solve problems for n > 12 and GDP and GDP-h cound not solve problems for n > 14

Both is due to stack overflow, hence thought as implementation issue, FF did not use a stack

FF has very bad planning results while the others have almost optimal path results

RESULTS 3-City Routing Domain Results

All previous domains are strong and very well defined domains

This one is constructed as a weak domain model having only one method for HGN and three corresponding methods for HTN

For n = 10, 20, …, 100 cities

GDP and SHOP2 could not solve except for n = 10

FF may solve the problems up to n = 60, after that point it even could not parse the problem file

GDP-h solved all problems quickly and nearly optimal

The reason for the success of the GDP-h is the guided search thanks to the heuristics

As the model is weak, the other planners do not have enough information to constraint the search space and do a lot of backtrackings, however, GDP-h uses heuristic to be able to guide its search and narrow its search space

As a conclusion, we can say that if there is a strong domain model, heuristic calculation most probably will result in a overhead and give not significantly better result; however, if the model is weak than contribution of heuristic function is crucial

RESULTS Domain Authoring

Subjective to developers Measures as number of lisp symbols and compared for GDP and SHOP2

planners GDP almost always have less number of symbols HTN specifies more than one task to achieve a goal formula. It defines a

decomposition task, several primitive tasks and deletion-check conditions, while, GDP only needs to speficify those as goals and let the planner choose the appropriate action to do with

respect to the goal. There is a need for different base cases for each method in HTN, however, GDP does not need such bases cases as the semantic of a goal provides to do nothing if a goal is true.

COMMENTS AND CONCLUSİONS No cross-domain explanations for the experiments. For

example, why FF is unsuccessfull is not answered. Just the results are shown and it is said that GDP is capable enough the others, even produces better results for weak domain models.

Almost everything is compared with HTN but HTN is not explained, at least in principle. Moreover, main difference is not shown algorithmically. What was doing HTN and now what is the thing that HGN is not doing, thereby resulting better. For example, can we use heuristics in SHOP2 planner. I guess we can, and if we can, it may also produce similar results.

HGN is more intutive when comparing both, hence, seems good contribution to the literature (since 1974). However, HTN is being used many many years, hence more comprehensive comparison is expected

So the only contribution of HGN is the easy development domain models, which is even a subjective criteria.

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ANY COMMENTS OR QUESTİONS ?