Satisfaction And Its Application To Ai Planning

Dynamic Flexible Constraint Satisfaction and Its Application to AI Planning Ian Miguel AI Group Department of Computer Science University of York

Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Constraints ,[object Object],[object Object],[object Object],[object Object],[object Object]

The Constraint Satisfaction Problem (CSP) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Specify allowed combinations of assignments of values to variables.

Applications ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example CSP – Course Scheduling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],These unary constraints determine the domains in this simple example.

Solving CSPs ,[object Object],[object Object],[object Object],[object Object],Root 1 st variable 2 nd variable

Course Scheduling: A Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Problem Changes… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Weakness 1: Static Formulation ,[object Object],[object Object],[object Object],[object Object],[object Object]

Dynamic CSP ,[object Object],[object Object],[object Object],[object Object]

Solving Dynamic CSPs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Course Scheduling ,[object Object],[object Object],Problem 1 Problem 2 Solution: Lectures = 4 Exercise = 3 Training = 1 Solution: Lectures = 3 Exercise = 4 Training = 1 ,[object Object],[object Object],[object Object],Incompatible with solution to problem 1

The Problem Changes Again… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Weakness 2: Hard Constraints ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Flexible CSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solving Flexible CSPs ,[object Object],[object Object],[object Object],[object Object],[object Object],New bound E.g. 3 violated constraints. Equals bound: 3 violated already. Prune.

Course Scheduling ,[object Object],[object Object],Problem 2 Problem 3 Solution: Lectures = 3 Exercise = 4 Training = 1 ,[object Object],[object Object],Incompatible with solution to problem 2

The Gap in the Market ,[object Object],[object Object],[object Object]

Dynamic Flexible CSP ,[object Object],Flexible CSP Techniques Dynamic CSP Techniques DFCSP Instance Restriction Relaxation Recurrent Activity … Max Weighted Max Weighted Preference Fuzzy … Solution methods

Fuzzy rr DFCSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two Algorithms ,[object Object],[object Object],[object Object],[object Object],[object Object]

Flexible Local Changes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Flexible Local Changes: Operation ,[object Object],[object Object],[object Object],[object Object],1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 … Sub-sub problem solved. Sub-problem solved.

Experiments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Experiments: Measurements ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Results: Search Effort ,[object Object],[object Object],[object Object]

Search Effort: Trends ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Search Effort: Trends ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Results: Stability ,[object Object],[object Object]

Stability: Trends ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Utility of Dynamic Information ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Part II Application to AI Planning

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],AI Planning c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1

Characteristics of AI Planning ,[object Object],[object Object],[object Object],[object Object],[object Object]

Flexible Planning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Can relax, with associated damage to resultant plan Imperative Preference

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l  , l 1 , l 2 , l T }

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l  , l 1 , l 2 , l T }

Graphplan ,[object Object],[object Object],[object Object],[object Object],[object Object],Initial Conditions Actions 1 Propositions 1 . . . . . . . . . ,[object Object],[object Object],[object Object]

The Flexible Planning Graph ,[object Object],Actions 1 Propositions 1 . . . . . . . . . l 2 l 3 l 1

The CSP Viewpoint ,[object Object],[object Object],[object Object],Actions 1 Propositions 1 . . . . . . . . . l 2 l 3 l 1

Plan Synthesis via Fuzzy rr DFCSP ,[object Object],[object Object],Goal Sub-problem ,[object Object],[object Object],[object Object]

Guiding Overall Search ,[object Object],[object Object],[object Object],Goal Sub-problem

4-step Solution ,[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l  , l 1 , l 2 , l T } Satisfaction: l 1

6-step Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l  , l 1 , l 2 , l T } Satisfaction: l 2

Compromise-free Solution ,[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l  , l 1 , l 2 , l T }

Flexible Graphplan: Observations ,[object Object],[object Object],[object Object],[object Object]

Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Future Work ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Acknowledgements ,[object Object],[object Object]

Satisfaction And Its Application To Ai Planning

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Satisfaction And Its Application To Ai Planning