1. 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/

2. 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).

3. At the Intersection of Planning and Constraint Programming Alexander Nareyek Carnegie Mellon University 5 0 1

4. Action Planning Action Types: Preconditions State changes (Operations) Goals: Satisfaction Optimization own.location == Bridge own.location = River jump() own.location == Sauna Maximize number of jump() until 6pm Extensions: Temporal planning Numerical values & Resources… Real-time computation Open world Highly complex goals Social interaction Incomplete knowledge External events Dynamics

5. Efficiency Trade-Offs Flexibility Expressiveness Efficiency Application-specific solutions Very general and modular solutions Conventional PlanningModal Logics

6. 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: A t for every action A at time t F t for every fluent F at time t …

7. Propositional Satisfiability (SAT) Bad scaling behavior Very hard to express numerical relations Domain-specific knowledge is compiled away Disadvantages:

8. 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: A t for every action A at time t F t for every fluent F at time t …

9. Integer Linear Programming (ILP) Bad scaling behavior Better for problems with limited discreteness Domain-specific knowledge is compiled away Disadvantages:

10. Constraint Programming (CP) Lets get hands-on: DragonBreath Engine Demo

11. Constraint Programming (CP) Local search Refinement search Solution concepts: A,B,C [1,100] A < B A + B = C Propagation:Commitment: A [1,100] B [2,100] C [3,100] C = 10 A [1,8] B [2,9] C = 10 A = 1A = 1 B = 9 C = 10

12. Constraint Programming (CP) Modeling/solving full planning by constraint programming Using CP technology for subproblems within conventional planning

13. Constraint Programming (CP) Constraint posting during a regular planning process CP Technology for Subproblems Resource Energy, Energy [0,20] Action MoveToDoor : Energy 2 Action Recharge : Energy 20

14. Constraint Programming (CP) Constraint posting during a regular planning process CP Technology for Subproblems Simple temporal problems (STPs) A B [2,5] C [3,7] [2,3] D [1,4]

15. Constraint Programming (CP) Constraint posting during a regular planning process CP Technology for Subproblems Passive test on satisfaction Limited interaction between CSP solving and the actual planning process

16. Constraint Programming (CP) Handling Planning by CP Planning with maximal graphs Completely capturing planning within constraint programming

17. 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: Do[t] the action performed at time t Add[holding_B, 3] Do[3] in ADD[holding_B] && Do[3] not in PRE[holding_B]

18. 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

19. Constraint Programming (CP) Structural Constraints Non-Overlap Sum ActionTask DurationStart ActionTask DurationStart Less Nonextensible Conventional Constraint Extensible Conventional Constraint Variable Extensible Conventional Constraint Extensible Object Constraint Extensible Object Constraint

20. Constraint Programming (CP) Structural Constraints

21. Constraint Programming (CP) Structural Constraints

22. The E XCALIBUR Agents Planning System The Planning Model

23. The E XCALIBUR Agents Planning System The CP Model Action Resource Constraint Resource Type State Resource Constraint Resource Type moveAB Action Type Action Task Constraint Begin EndOperation Action Task Feet moveAB3545 Resource Type Location Temporal Reference State Precondition Task 35@A Resource Type State Task Temporal Reference Contribution 45 arrive@B Resource Type

24. Constraint Programming (CP) The CP Model Lets get hands-on: The E XCALIBUR Agents Planning System

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