ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Constraint Satisfaction Problems in Python

Michael Sioutis

Department of Informatics and TelecommunicationsNational and Kapodistrian University of Athens

July 14, 2011

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Table of Contents

1 Introduction

2 Constraints in Python

3 Examples

4 Questions

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Definition

A Constraint Satisfaction Problem consists of:

A Finite set of variables: V1,V2, ...,Vn.

A Nonempty domain of possible values for each variable:DV1 ,DV2 , ...,DVn .

A Finite set of constraints: C1,C2, ...,Cn.

Each constraint Ci limits the values that variables can take(e.g., V1 6= V2).

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Definition

A state is defined as an assignment of values to some orall variables.

A consistent assignment is an assignment that does notviolate the constraints.

A complete assignment is an assignment that includes allvariables.

A problem solution is a complete and consistentassignment.

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Benefits

Standard representation pattern.

Generic goal and successor functions.

Generic heuristics (no domain specific expertise).

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Applications

Scheduling the time of observations on the Hubble SpaceTelescope

Airline schedules

Cryptography

Computer vision → image interpretationScheduling your MS or PhD thesis exam ,

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Constraint Programming In Python Possible?

Constraint satisfaction problems are mathematicalproblems defined as a set of objects whose state mustsatisfy a number of constraints or limitations.We only need to specify the problem, even better if wecould do it in Python...

We can!

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Python Constraint Library

Python module python-constraint1 offers solvers forConstraint Satisfaction Problems over finite domains insimple and pure Python.

Download and install python-constraint from here:http://labix.org/download/python-constraint/

python-constraint-1.1.tar.bz2

After you setup, you should be able to run the followingcommand on a python shell:

from constraint import *

1http://labix.org/python-constraint

Michael Sioutis Constraint Satisfaction Problems in Python

http://labix.org/download/python-constraint/python-constraint-1.1.tar.bz2http://labix.org/download/python-constraint/python-constraint-1.1.tar.bz2http://labix.org/python-constraint

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Features Of Python-Constraint

Solvers

Backtracking solverRecursive backtracking solverMinimum conflicts solver

Predefined constraint types

FunctionConstraintAllDifferentConstraintAllEqualConstraintExactSumConstraintMaxSumConstraintMinSumConstraintInSetConstraintNotInSetConstraintSomeInSetConstraintSomeNotInSetConstraint

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Basic Example

Solve the a + b = 5, a ∗ b = 6 algebra relation.from constraint import *

problem = Problem()

problem.addVariable(’a’, range(5))

problem.addVariable(’b’, range(5))

problem.addConstraint(lambda a, b: a + b == 5)

problem.addConstraint(lambda a, b: a * b == 6)

solutions = problem.getSolutions()

print solutions

[{’a’: 3, ’b’: 2}, {’a’: 2, ’b’: 3}]

Michael Sioutis Constraint Satisfaction Problems in Python

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

Advanced Example

Solve the 3× 3 Magic Squares2 problem.from constraint import *

problem = Problem()

problem.addVariables(range(0, 9), range(1, 9+1))

problem.addConstraint(AllDifferentConstraint(), range(0, 9))

problem.addConstraint(ExactSumConstraint(15), [0,4,8])

problem.addConstraint(ExactSumConstraint(15), [2,4,6])

for row in range(3):

problem.addConstraint(ExactSumConstraint(15),

[row*3+i for i in range(3)])

for col in range(3):

problem.addConstraint(ExactSumConstraint(15),

[col+3*i for i in range(3)])

solution = problem.getSolution()

print solution

{0: 6, 1: 7, 2: 2, 3: 1, 4: 5, 5: 9, 6: 8, 7: 3, 8: 4}

2http://en.wikipedia.org/wiki/Magic_square

Michael Sioutis Constraint Satisfaction Problems in Python

http://en.wikipedia.org/wiki/Magic_square

ConstraintSatisfactionProblems in

Python

MichaelSioutis

Outline

Introduction

Constraints inPython

Examples

Questions

The End

Thank you!-

Any Questions?

Michael Sioutis Constraint Satisfaction Problems in Python

OutlineIntroductionConstraints in PythonExamplesQuestions