CONSTRAINT PROGRAMMING

Computer Science Seminar

April 9th, 2004

Kerem Kacel

OUTLINE

Introduction History The Method Constraint Logic Programming Applications Pros/Cons Discussion

What is Constraint Programming?

Software technologyDescribe and solve large,

combinatorial problems 2 steps

State the constraints of the problemFind a solution satisfying all of the

constraints

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 valuesDoes restrict values

Properties of Constraints

Express partial informationX > 0

HeterogeneousY = ABS(X)

Non-directionalX = Y+1 also means Y = X-1

Properties of Constraints (2)

AdditiveX<4, X>1 also means X>1, X<4

Declarative“The pen is on the table”

Usually dependentX + Y = 5, X * Y = 6

OUTLINE

Introduction History The Method Constraint Logic Programming Applications Pros/Cons Discussion

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

Some History

CosytecFounder of “Global Constraints”

• Helped solve a large class of problems• Planning, scheduling, sequencing

ILOG SOLVERConstraint programming classes for

C++, Java

OUTLINE

Introduction History The Method Constraint Logic Programming Applications Pros/Cons Discussion

METHOD

Define the problem as a CSP (Constraint Satisfaction Problem)

Solve the CSP

What is a CSP?

Constraint Satisfaction ProblemSet of variables X = {x1,…,xn}

Domains Di for each variableSet of constraints

An example CSPA::{1,2}, B::{1,2}, C::{1,2}A = B, A ≠ C, B > C

Solving a CSP

Example CSPA::{1,2}, B::{1,2}, C::{1,2}A = B, A ≠ C, B > C

Generate & TestFor every value assignment in the

domains, check if constraint is mete.g. A = 2, B = 2, C = 1

Solving a CSP

Example CSPA::{1,2}, B::{1,2}, C::{1,2}A = B, A ≠ C, B > C

Back-TrackingStart with a specific assignmentChange values one by one until a

solution is reached

Solving a CSP

Problem: These methods are inefficient

Other methods are being researched to optimize

OUTLINE

Introduction History The Method Constraint Logic Programming Applications Pros/Cons Discussion

Constraint Logic Programming

Constraints + LP = CLP

Platforms:CHIPECLiPSe

OUTLINE

Introduction History The Method Constraint Logic Programming Applications Pros/Cons Discussion

APPLICATIONS

Assignment problemsPersonnel assignment

Scheduling problemsClass schedules in schoolsProduction planning

Database SystemsEnsure consistency of data

APPLICATIONS

Natural Language ProcessingConstruction of efficient parsers

Electrical EngineeringLocating faults in circuits

Molecular BiologyDNA sequences

PROS/CONS

+ DeclarativeDescribe the problem, not solution

+ SemanticsClean, elegant languages

- UnpredictableWe don’t know how efficient

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