An Introduction to Constraint Programming in JChoco

Constraint satisfaction Constraint satisfaction problem (CSP) is a triple where: –V is set of variables –Each X in V has set of values, D_X Usually assume finite domain {true,false}, {red,blue,green}, [0,10], … –C is set of constraints Goal: find assignment of values to variables to satisfy all the constraints

Di = {1,2,3,4,5} V1 V3 V2 V4 V4  V3 V1  V4  1 V4 + V2 = 5 V1  V2 V2  V3  6 AR33 figure 18, page 35 What can you infer?

Di = {1,2,3,4,5} V1 V3 V2 V4 V4  V3 V1  V4  1 V4 + V2 = 5 V1  V2 V2  V3  6 D1 = {1,2} D2 = {2,3} D3 = {4,5} D4 = {2,3} Do you agree? Was that easy?

A program that models csp6

With print statements and search

Packages used

Can throw an exception

Create a problem

Create variables

Post constraints

Establish AC

Magic code to get all solutions

Code to count solutions

output/trace Problem with no V or C

variables

Variables and constraints

Made AC

All solutions

2 colour K 3 The difference allDifferent makes Just how weak/powerful is AC processing?

Prop0.java Run it Make it AC

allDifferent Prop1.java Run it

X + Y + Z = 20 X,Y,Z  {1..10} See Test.java How many solutions? AF2 assessed exercise One of 5 questions

Test.java Count number of solutions

As a decision problem: is there a glomb ruler with n ticks with length no more than m units?

How many n digit numbers are there where the number must contain at least 0ne number 3 and at least one number 5? n = … See ThreesAndFives.java AF2 assessed exercise

Magic square An example of how to represent a problem An idea from Chris Beck

put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal

put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 1st stab Use sum(x) = sum(y) where x and y are - different rows - different columns - different diagonals Every element of the array is different - represent as a clique of not equals How does it go? For propagation and search?

put a number in each square each number is different a number is in the range 1 to 16 the sum of a column is the same as a sum of a row the same as the sum of a main diagonal 2nd stab But what is k? How does model perform?

Magic square on the web

Thanks to Chris Beck

Thanks to Bouygues