1. Debugging Constraint Models with Metamodels and Metaknowledge
Eugene C. Freuder1
Richard J. Wallace1
Tomas E. Nordlander2
1Cork Constraint Computation Centre
University College Cork
2SINTEF

2. Outline Model Debugging Ananke 1.0 Future Work Example Related work
Interface
Meta Knowledge
Metrics
Preliminary Results
Future Work

3. Model Debugging Given: a CSP model that is incorrect in some respects
Not yet complete
World has changed
(World needs to be changed)
Given: a Knowledgeable User, who knows that a given assignment should be possible
Goal: to adjust model to accommodate the new information

4. Model Debugging - Small Example
A meeting scheduling problem
3 meetings – A, B, C ( Variables )
Each meeting can be held at 11 AM or 1 PM ( Domain values )
Meeting A must be held before meeting B ( Constraint )
Meeting B must be held at the same time as C ( Constraint ) A B C
< =

5. Model Debugging - Small Example
Modeller A B C
< =
1 PM  DA
User

6. Model Debugging - Small Example
Modeller
{solutions} =∅
???
User

7. Model Debugging - Small Example
Modeller
{solutions} =∅
1 PM  DA !
User

8. Small Example 1 PM  DA ! What if we allow A to occur after B?
Modeller
What if we allow A
to occur after B?
1 PM  DA !
User

9. Model Debugging - Small Example
Modeller
Okay A B C
<> = ?
User

10. Related Work Partial CSP Interactive constraint solving
(usually) different metric
Interactive constraint solving
Here, adjusting our model, not telling user that a given assignment is infeasible
Constraint-based matchmaking
There, system suggested solutions, user indicated additional constraints
Here, user indicates solutions, system adjusts constraints

11. Outline Model Debugging Ananke 1.0 Future Work Example Related work
Interface
Meta Knowledge
Metrics
Preliminary Results
Future Work

12. Ananke 1.0
Present system goes under the name, “Ananke”, a Greek goddess who was the “personification of destiny, necessity and fate”, i.e. the Goddess of Constraints
In its full manifestation, Ananke is intended serve as a general environment for acquiring and modifying constraint models
An inspiration for this work is Teiresias, an early system that used meta-knowledge to improve incomplete or incorrect rule bases

13. Ananke 1.0 Interface

14. Model & User Suggestion

15. Maximal Match

16. Suggestions

17. Ananke Debugging Overview
Partial
Complete
Range
No solution
Expected solution MK
ES found
CSP
Search
User
Suggested changes
Debug
Previous Users
Any
=<
=>
<
> ∅ =
<>
CSP MK
CSP loaded
Expected solution inserted
Meta Knowledge added
Constraints
Search heuristic
Complete Search Start
If solution found, user informed. And can then check other expected solutions.
If solution NOT found, closeness appear along with the DEBUG option
DEBUG
Meta Constraints are added
A branch and bound algorithm with a cost function that aim to find the minimum change on constraint to include the solution.
Cost function is decided by the user
RESULT: a set of constraint changes
Meta Knowledge
Model

18. Metaknowledge To guide the Search Heuristic
Missing solution(s) are represented by a “missing solution constraint” (ms-constraint) over a subset of the problem variables
e.g. A = 1 PM
To guide the Search Heuristic

19. Metrics
Basic metric: number of solutions added by the changes in constraints - Since this is often too hard to compute, we would like to use some surrogate metric
Step measure according to possible relaxations among the values of the meta-variable A B C
< =
Any
=<
=>
<
> ∅ =
<>
1 step

20. Metrics Tuple measure = number of extra tuples allowed by a relaxation
Example of tuple metric
For |d| = 5
Any
=<
=>
<
> ∅ =
<> 10 10 5
{1,2,3,4,5}
{1,2,3,4,5} A B C
< = 10 10 5 10 10 5 5 10 10

21. Heuristics
Order changes in a constraint according to cost function involved
Restrict search to meta-variables for “link constraints” – i.e. constraints adjacent to unmatched variables in partial solution

22. Outline Model Maintenance Ananke Future Work Example Related work
Interface
Meta Knowledge
Metrics
Preliminary Results
Future Work

23. Algorithm Simple branch and bound – based on chosen metric
Looks for all minimal relaxations that give a CSP with desired solution(s)
When new best-cost CSP found, calls CSP solver to check feasibility
ECAI 2008 Workshop on Modeling and Solving Problems with Constraints
21 July 2008

24. Preliminary Results

25. Outline Model Debugging Ananke 1.0 Future Work Example Related work
Interface
Meta Knowledge
Metrics
Preliminary Results
Future Work

26. Future Work Improve algorithms Enlarge scope of meta-CSPs
Take advantage of CSP and MAX-CSP methods
Expand on heuristics (e.g. vary focus)
Enlarge scope of meta-CSPs
Greater number of constraint types
E.g. Allen’s Algebra
Make interface more flexible
User should be able to indicate that solutions should be present that have a certain property (not just A = 1 PM)

27. THE END