1. G53CLP Constraint Logic Programming
Dr Rong Qu
Solving 8-Queen Puzzle – Demo

2. ILOG OPL Studio CPLEX Optimization software package
Sold via CPLEX Optimization Inc.
Acquired by ILOG Inc in 1997
Acquired by IBM in 2009
Also solves integer programming and large linear programming problems
G53CLP – Constraint Logic Programming Dr R. Qu

3. ILOG OPL Studio OPL Studio One of the modeling systems in ILOG
For both mathematic programming and constraint programming
OPL (Optimization Programming Language) was originally developed by Pascal van Hentenryck
Provide an interpreter
OPL models; A script language
An IDE; An API
G53CLP – Constraint Logic Programming Dr R. Qu

4. Other CP Solvers? Gecode 1.0.1
Java interface for constraint programming
Free for download
Released in Nov 2006
Possible coursework next year?
G53CLP – Constraint Logic Programming Dr R. Qu

5. Solving the 8-Queen Problem
G53CLP – Constraint Logic Programming Dr R. Qu

6. G52AIP – AI Programming A OPL Studio IDE screenshot
Project: model + problem input data
Source code editor
Debug information
Important: Solver, Optimisation, Solutions
G52AIP – AI Programming

7. Solving The 8-Queen Problem – model 2
Variables
x1, x2, …, xn: position of queens on the chessboard
Domain
{0 … n2-1}: tile index of each queen placed
Constraint
R = xi / n + 1
C = xi mod n + 1
Given R1, R2 and C1, C2 of two queens’ positions
One queen each row/column
R1 ≠ R2; C1 ≠ C2
One queen each diagnal
R1 – R2 ≠ C1 – C2
R1 – R2 ≠ C2 – C1
G53CLP – Constraint Logic Programming Dr R. Qu

8. ILOG OPL Studio
G53CLP – Constraint Logic Programming Dr R. Qu

9. Solving The 8-Queen Problem – model 2
//.mod file
//declaration part
var int queens[1..8] in 0..63;
var int r[1..8] in 1..8;
var int c[1..8] in 1..8;
// problem model
solve { … };
x1, x2, …, xn: position of queens on the chessboard
{0 … n2-1}: tile index of each queen placed
R = xi / n + 1
C = xi mod n + 1
R1 ≠ R2; C1 ≠ C2
R1 – R2 ≠ C1 – C2
R1 – R2 ≠ C2 – C1
G53CLP – Constraint Logic Programming Dr R. Qu

10. Solving The 8-Queen Problem – model 2
//.mod file
//declaration part …
//problem model
solve {
forall(ordered i,j in 1..8) {
r[i] = queens[i] / 8 + 1;
c[i] = queens[i] mod 8 + 1;
r[j] = queens[j] / 8 + 1;
c[j] = queens[j] mod 8 + 1; };
R = xi / n + 1
C = xi mod n + 1
R1 ≠ R2; C1 ≠ C2
R1 – R2 ≠ C1 – C2
R1 – R2 ≠ C2 – C1
G53CLP – Constraint Logic Programming Dr R. Qu

11. Solving The 8-Queen Problem – model 2
//.mod file
//declaration part …
//problem model
solve {
forall(ordered i,j in 1..8) {
r[i] <> r[j] ;
c[i] <> c[j] ;
r[i] - r[j] <> c[i] - c[j];
r[i] - r[j] <> c[j] - c[i]; };
R = xi / n + 1
C = xi mod n + 1
R1 ≠ R2; C1 ≠ C2
R1 – R2 ≠ C1 – C2
R1 – R2 ≠ C2 – C1
G53CLP – Constraint Logic Programming Dr R. Qu

12. G52AIP – AI Programming

13. G52AIP – AI Programming

14. Solving The 8-Queen Problem – model 2
G53CLP – Constraint Logic Programming Dr R. Qu

15. Solving The 8-Queen Problem – models 1&3
Lab sessions start next week
I: comparing the 3 models for solving the n-Queen problem
II:
G53CLP – Constraint Logic Programming Dr R. Qu

16. Solving The 8-Queen Problem
To display decision tree
Debug/Display Decision Tree
To run
Execution/Run, or
To stop at a decision point
Debug/Stop at Decision Point
Next solution
All solutions
G53CLP – Constraint Logic Programming Dr R. Qu