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A novel approach in CSP with GA

A novel approach in CSP with GA. by Juhos Istvan, Phillip Tann, Toth Attila , Tezuka Masaru. Contents. Constraint Satisfaction Problem: Graph colouring - ”an old friend” Representation GA model Results Conclusion. Constraint Satisfaction.

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A novel approach in CSP with GA

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

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

  3. Constraint Satisfaction Constraint Satisfaction Problem (CSP) : <X,D,C> where • X : variables{x1,…,xn} • D : domain{D1,…,Dn} • C : constraints{ (x, y) | x,y  X } EvoNet 2002 - Szeged

  4. Graph colouring • X = {x1, x2, x3, x4, x5} • D = {red, blue, green,… } • C = { (x1, x2), (x2, x3),(x3, x4), (x2, x4), (x4, x5) } (xi,xk) means: <xi colour> != <xk colour> EvoNet 2002 - Szeged

  5. Representation: Graph Colouring Each column is a vertex and each row is a colour. Ex: x1 is colour A (code : 1) x2 cannot be colour A (code : 0) Goal:minimize the nb of colours. How:merge the rows EvoNet 2002 - Szeged

  6. 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 EvoNet 2002 - Szeged

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

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

  9. 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 EvoNet 2002 - Szeged

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

  11. 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 EvoNet 2002 - Szeged

  12. Results cont. EvoNet 2002 - Szeged

  13. 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 EvoNet 2002 - Szeged

  14. 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. EvoNet 2002 - Szeged

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