1. A novel approach in CSP with GA by Juhos Istvan, Phillip Tann, Toth Attila, Tezuka Masaru

2. EvoNet 2002 - Szeged Contents Constraint Satisfaction Problem: Graph colouring - ”an old friend” Representation GA model Results Conclusion

3. EvoNet 2002 - Szeged Constraint Satisfaction Constraint Satisfaction Problem (CSP) : where X : variables { x 1, …, x n } D : domain { D 1, …, D n } C : constraints { (x, y) | x,y  X }

4. EvoNet 2002 - Szeged X = { x 1, x 2, x 3, x 4, x 5 } D = { red, blue, green,… } C = { (x 1, x 2 ), (x 2, x 3 ), (x 3, x 4 ), (x 2, x 4 ), (x 4, x 5 ) } (x i,x k ) means: != Graph colouring

5. EvoNet 2002 - Szeged Representation: Graph Colouring Each column is a vertex and each row is a colour. Ex: x 1 is colour A (code : 1) x 2 cannot be colour A (code : 0) Goal: minimize the nb of colours. How: merge the rows x1x1 x2x2 x3x3 x4x4 x5x5 A10xxx B0100x Cx010x Dx0010 Exxx01

6. EvoNet 2002 - Szeged Merge operator Merging two rows: 1 and X  1 0 and X  0 0 and 0  0 1 and 1  1 X and X  X 1 and 0  not allowed 0 and 1  not allowed A10xxx Cx010x A+C1010x

7. EvoNet 2002 - Szeged Phenotype : merged matrix = nb of colours Genotype : merging order = permutation of the rows ( D, B, A, E, C ) Fitness function : number of rows in the merged matrix GA Framework

8. EvoNet 2002 - Szeged GA framework cont. Variation Operators: Mutation : swap two members in the permutation Crossover : standard crossover not allowed (doesn’t preserve permutations)

9. EvoNet 2002 - Szeged GA framework cont. Solution: order-based crossover [Syswerda] Select a crossing point; Parent  (Head, Tail); Reorder Parent1 Tail according to Parent2. A B C D E E B C A D B A C D E B E C A D

10. EvoNet 2002 - Szeged The program Novel Genetic algorithm EASEA and EO aided Written in C++ Compiled and running on Linux Uses common input DIMACS format

11. EvoNet 2002 - Szeged Experimental Setting -Problems considered -URL: http://mat.gsia.cmu.edu/COLOR/instances.html - Size of the problems -GA parameters: -Nb of individuals: 100 -Mutation probability: 0.3 -Crossover probability: 0.8 -Nb of fitness evaluations: -Typically 100% known solution is found -How many runs -Computational effort -Compared with previous works

12. EvoNet 2002 - Szeged Results cont. NameOptimaNo Diff. parameter No xover No Diff. parameter With xover With Diff. parameter no xover With Diff. parameter with xover Vertex Edges Flat300_202042 300 21375 Le450_15b1519 450 8169 Queen11_11111514 121 3960 Mychel788888191 2360 Mulsol.i.149 197 3925

13. EvoNet 2002 - Szeged Conclusion What we have done: an algorithm to graph colouring a CSP algorithm the idea seems exciting the results seem good What remains to be done: more intensive tests investigate the mutation and crossover operation improve the fitness function Thanks to EvoNet 2002, special thanks to Michele Sebag and Jano van Hemert

14. EvoNet 2002 - Szeged Perspectives Pheromone-like information about constrained variables Most constrained variables should be put first. What are the most constrained variables ? Learn which variables are the last ones Stored in a global vector: –shared by population, –updated at each generation, –exploited to guide mutation.