CONSTRAINT PROGRAMMING

1. CONSTRAINT PROGRAMMING Computer Science Seminar April 9th, 2004 Kerem Kacel

2. OUTLINE • Introduction • History • The Method • Constraint Logic Programming • Applications • Pros/Cons • Discussion

3. What is Constraint Programming? • Software technology • Describe and solve large, combinatorial problems • 2 steps • State the constraints of the problem • Find a solution satisfying all of the constraints

4. What is a Constraint? • Defined on a set of variables • A relation on their domains • e.g. “The circle is inside the square” • Does NOT necessarily specify values • Does restrict values

5. Properties of Constraints • Express partial information • X > 0 • Heterogeneous • Y = ABS(X) • Non-directional • X = Y+1 also means Y = X-1

6. Properties of Constraints (2) • Additive • X<4, X>1 also means X>1, X<4 • Declarative • “The pen is on the table” • Usually dependent • X + Y = 5, X * Y = 6

7. OUTLINE • Introduction • History • The Method • Constraint Logic Programming • Applications • Pros/Cons • Discussion

8. Some History • Constraint Satisfaction Problems (CSPs) were formalized in early 70s • Constraint Logic Programming (CLP) emerged in early 80s, named by IBM • Prolog II was the first • Later • CHIP (Constraints Handling in Prolog) • Prolog III

9. Some History • Cosytec • Founder of “Global Constraints” • Helped solve a large class of problems • Planning, scheduling, sequencing • ILOG SOLVER • Constraint programming classes for C++, Java

10. OUTLINE • Introduction • History • The Method • Constraint Logic Programming • Applications • Pros/Cons • Discussion

11. METHOD • Define the problem as a CSP (Constraint Satisfaction Problem) • Solve the CSP

12. What is a CSP? • Constraint Satisfaction Problem • Set of variables X = {x1,…,xn} • Domains Di for each variable • Set of constraints • An example CSP • A::{1,2}, B::{1,2}, C::{1,2} • A = B, A ≠ C, B > C

13. Solving a CSP • Example CSP • A::{1,2}, B::{1,2}, C::{1,2} • A = B, A ≠ C, B > C • Generate & Test • For every value assignment in the domains, check if constraint is met • e.g. A = 2, B = 2, C = 1

14. Solving a CSP • Example CSP • A::{1,2}, B::{1,2}, C::{1,2} • A = B, A ≠ C, B > C • Back-Tracking • Start with a specific assignment • Change values one by one until a solution is reached

15. Solving a CSP • Problem: These methods are inefficient • Other methods are being researched to optimize

16. OUTLINE • Introduction • History • The Method • Constraint Logic Programming • Applications • Pros/Cons • Discussion

17. Constraint Logic Programming • Constraints + LP = CLP • Platforms: • CHIP • ECLiPSe

18. OUTLINE • Introduction • History • The Method • Constraint Logic Programming • Applications • Pros/Cons • Discussion

19. APPLICATIONS • Assignment problems • Personnel assignment • Scheduling problems • Class schedules in schools • Production planning • Database Systems • Ensure consistency of data

20. APPLICATIONS • Natural Language Processing • Construction of efficient parsers • Electrical Engineering • Locating faults in circuits • Molecular Biology • DNA sequences

21. PROS/CONS • + Declarative • Describe the problem, not solution • + Semantics • Clean, elegant languages • - Unpredictable • We don’t know how efficient

22. DISCUSSION • “Were you to ask me which programming paradigm is likely to gain most in commercial significance over the next 5 years I’d have to pick Constraint Logic Programming, even though it’s perhaps currently one of the least known and understood.” Dick Pountain, BYTE, February 1995