At the Intersection of Planning and Constraint Programming

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Slides of the Invited Talk at the CAEPIA Workshop
on Planning, Scheduling and Temporal
Reasoning(Held on November 11, 2003 by Alexander
Nareyek)
Note that because the slides do not contain the
verbal components of the talk, it might be hard
or even misleading to study the document if you
did not attend the talk. The demos are also not
included. Most of them are part of the
DragonBreath Engine, which can be downloaded
at http//www.ai-center.com/projects/dragonbreath
/
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Title At the Intersection of Planning and
Constraint Programming Abstract General
frameworks for formulating and solving search
problems, like constraint programming, integer
linear programming or propositional
satisfiability, provide useful means to tackle
planning problems. While usually not as efficient
as specialized search techniques, general
frameworks support a modular and flexible
modeling, and readily available solvers already
draw on a huge pool of research on search. This
talk will give an overview of related planning
approaches, placing special emphasis on
constraint programming. Bio Alexander Nareyek
received his diploma and Ph.D. from the TU
Berlin. Since 2002, he is on an Emmy Noether
fellowship of the German Research Foundation
(DFG), and is guest researcher at Carnegie Mellon
University. His main research interests include
the generation and execution of behavior plans
for goal-driven intelligent agents. He is also
active in the application area of computer games
and serves as chairperson of the IGDA's
Artificial Intelligence Interface Standards
Committee (AIISC).
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At the Intersection ofPlanning and Constraint
Programming

• Alexander Nareyek
• Carnegie Mellon University

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Action Planning

• Preconditions
• State changes
• (Operations)

Action Types
own.location Bridge
own.location River
jump()
Goals

• Satisfaction
• Optimization

own.location Sauna
Maximize number of jump() until 6pm
Extensions

• Numerical values Resources

• Real-time computation

• Open world

• Highly complex goals

• Social interaction

• Incomplete knowledge

• External events

• Dynamics

• Temporal planning

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Efficiency Trade-Offs
Flexibility Expressiveness
Efficiency
Application-specific solutions
Very general and modular solutions
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Propositional Satisfiability (SAT)

• Specifying a problem by a conjunctive normal form
  (a conjunction of disjunctions)
• Example
• (A or B or C) and (A or D)
• Many ways to represent a planning problem
• Example
• At for every action A at time t
• Ft for every fluent F at time t

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Propositional Satisfiability (SAT)
Disadvantages

• Bad scaling behavior
• Very hard to express numerical relations
• Domain-specific knowledge is compiled away

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Integer Linear Programming (ILP)

• Specifying a problem by linear inequalities and a
  linear combination to be minimized or maximized
  additional integer constraints
• Example
• 4x 3y 15 int(x) int(y) max(8x 2y)
• Many ways to represent a planning problem
• Example
• At for every action A at time t
• Ft for every fluent F at time t

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Integer Linear Programming (ILP)
Disadvantages

• Bad scaling behavior
• Better for problems with limited discreteness
• Domain-specific knowledge is compiled away

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Constraint Programming (CP)
Lets get hands-on
DragonBreath Engine Demo
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Constraint Programming (CP)
Solution concepts

• Local search
• Refinement search

A,B,C ? 1,100 A lt BA B C
Propagation
Commitment
A ? 1,100 B ? 2,100 C ? 3,100
C 10
A ? 1,8 B ? 2,9 C 10
A 1
A 1 B 9 C 10
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Constraint Programming (CP)

• Modeling/solving full planning by constraint
  programming
• Using CP technology for subproblems within
  conventional planning

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Constraint Programming (CP)
CP Technology for Subproblems
Constraint posting during a regular planning
process
Resource Energy, Energy ? 0,20
Action MoveToDoor Energy - 2 Action Recharge
Energy 20
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Constraint Programming (CP)
CP Technology for Subproblems
Constraint posting during a regular planning
process
Simple temporal problems (STPs)
B
A
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Constraint Programming (CP)
CP Technology for Subproblems
Constraint posting during a regular planning
process

• Passive test on satisfaction
• Limited interaction between CSP solving
• and the actual planning process

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Constraint Programming (CP)
Handling Planning by CP

• Planning with maximal graphs
• Completely capturing planning within constraint
  programming

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Constraint Programming (CP)
Handling Planning by CP

• Planning with maximal graphs
• All possible plans are included in the CSP (like
  SAT and ILP approaches)
• Many ways to represent a planning problem
• Example
• Dot the action performed at time t
• Addholding_B, 3 ?
• Do3 in ADDholding_B
• Do3 not in PREholding_B

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Constraint Programming (CP)
Handling Planning by CP
Completely capturing planning within CP

• Extension of the basic CP paradigm necessary
• Search for constraint graph as part of the
• search process
• Structural Constraint Satisfaction

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Constraint Programming (CP)
Structural Constraints
Non-Overlap
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Constraint Programming (CP)
Structural Constraints
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Constraint Programming (CP)
Structural Constraints
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The EXCALIBUR Agents Planning System
The Planning Model
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The EXCALIBUR Agents Planning System
The CP Model
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Constraint Programming (CP)
The CP Model
Lets get hands-on
The EXCALIBUR Agents Planning System
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Conclusions

• We need efficient AND flexible technology
  Constraint programming is great for this!
• For pure efficiency gain goals, study the
  technologies used in constraint programming!

For literature references Constraints and AI
Planning by Alexander Nareyek, Robert Fourer,
Eugene C. Freuder, Enrico Giunchiglia, Robert P.
Goldman, Henry Kautz, Jussi Rintanen and Austin
Tate