Improving graph colouring with Linear Programming and Genetic Algorithms

A major problem related to combinatorial optimization and population-based algorithms is the functional degeneracy of the search for problems with a high degree of symmetry. The population may in fact present multiple permutations of the same solutions which bound the exploration of the solution space. A genetic algorithm (GA) cannot generally cope with this problem unless additional mechanisms are included. The use of a simple GA together with the linear assignment problem (LAP) for the graph colouring problem has been investigated. The LAP algorithm is embedded in the crossover operator and generates the optimal permutation of colours within a cluster of nodes. This feature prevents oosprings generated by good solutions to be less t than its parents. Simulation results show the successful application of this hybrid technique for the class of random graphs G 1000; 1 2 .