1. CSC5240 Combinatorial Search and Optimization with Constraints
Tutorial Notes 7

2. CSC5240 Tutorial 7 Global Constraints in ILOG Paper Presentation
Project Proposal

3. Global Constraints
Often-seen sub-problems (complex constraints) in modeling with specific AC-revise() procedure
ILOG provides a number of global constraints :
IloAllDiff
IloDistribute
IloSequence
IloAllMinDistance
IloPartition
IloAllNullIntersect
IloEqUnion …

4. IloAllDiff
Restrict each value to appear at most once among the variables. 1 2 3

5. IloAllDiff
Restrict each value to appear at most once among the variables. 3 2 3

6. IloDistribute
Often called “cardinality constraints” or “global cardinality constraints” (gcc)
Used to restrict the number of occurrences of each value among the variables.
Special Case: AllDiff constraint
The number of occurrences of each value is 1

7. IloDistribute
How about restricting each value to appear within a range of number of times?
E.g. Given variables x, y, z D(x) = D(y) = D(z) = {1,2,3} Among x, y, z, we want to have - value 1 to appear [1,2] times - value 2 to appear [0,1] times - value 3 to appear [0,3] times
Is the following assignment correct? 1 1 2

8. IloDistribute
E.g. Given variables x, y, z D(x) = D(y) = D(z) = {1,2,3} Among x, y, z, we want to have - value 1 to appear [1,2] times - value 2 to appear [0,1] times - value 3 to appear [0,3] times
Is the following assignment correct? 3 3 3

9. IloDistribute
IloDistribute is used to count the number of variables that takes a given value in an array.
cards – An array storing the occurrence range for each value [1..2], [3..4], [0..5]
values – an array of values
vars – an array storing the variables
IloDistribute(IloEnv env, IloIntVarArray cards, IloNumArray values, IloNumVarArray vars); 1 2 3

10. IloDistribute The arrays cards and values must be of the same length.
For each i, cards[i] is equal to the number of occurrences of values[i] in the array vars.
IloDistribute(IloEnv env, IloIntVarArray cards, IloNumArray values, IloNumVarArray vars);

11. IloDistribute
e.g. the value stored in values[2] should occur in the array vars 3 to 5 times. cards[2] = IloIntVar(env, 3, 5);
e.g. the value stored in values[3] should occur in the array vars at most twice. cards[3] = IloIntVar(env, 0, 2);
IloDistribute(IloEnv env, IloIntVarArray cards, IloNumArray values, IloNumVarArray vars);

12. Example: BIBD Recall the BIBD problem in Tutorial 1, Assignment 1/2.
Incidence matrix:
A v by b binary matrix
Exactly r ones per row
Exactly k ones per column
A scalar product of lambda between any pair of distinct rows

13. Model
Use IloDistribute !

14. Using global constraints
However, if you just post those global constraints, ILOG may not call their specific AC-revise() methods
E.g. ILOG will use a set of disequalities to replace IloAllDiff()
If you really have to enforce hyper-arc consistency on those global constraints, set the filter level to the extended level
...
model.add(IloAllDiff(env, x));
solver.setDefaultFilterLevel(IloAllDiffCt, IloExtendedLevel);

15. Demonstration
Click here to open the code!

16. Presentation Communicate key ideas Don’t get bogged down in details
Use a top-down approach
Introduction
Body
Technicalities
Conclusion

17. Top-down Approach Introduction Body Motivate the audience
Define the problem
Discuss earlier work
Emphasize the contributions
Body
Delineate major results
Explain the significance of the results

18. Top-down Approach Technicalities Conclusion
Present the key theorem / result / overview of the implementation
Show and explain the experimental results, if any
Try to be as succinct and clear as possible
Conclusion
Weave earlier statements into a coherent synopsis
State open problems
Indicate that your talk is over

19. Some Guidelines Remind, don’t assume Don’t over-run
Maintain eye contact, control your voice and motion
Don’t overload a single slide with too much information
Use colours and fonts effectively
Use pictures, tables, and examples
Prefer words over symbols, and pictures over words

20. Questions and Answers
Prepare additional slides to anticipate questions on confusing technicalities
Some questions are intended to see how you react to criticism under pressure
Be prepared, be polite, avoid getting involved in a lengthy exchange
Don’t confuse “I don’t know” with “it is not known”

21. Several deadlines Assignment 2 deadline: 10 Nov., 2009
Paper presentation:
19 Nov., 2009 (Lecture time)
21 Nov., 2009 (Saturday morning)
You have to your project proposal with pages to Jimmy on or before 20 Nov. (Friday)
Project Presentation:
18 Dec., 2009

22. END