Solution to Graph Coloring Using Genetic and Tabu Search Procedures

Abstract

Some of the engineering applications warrant the solution of Graph Coloring Problem, an NP-hard combinatorial optimization problem. This paper focuses on designing three new evolutionary operators using Tabu searching which are expected to offset the problems in the existing well-known methods in minimal search space and generations, besides maximizing the percentage of successful runs through effectively distributing promising genes for achieving fast stochastic convergence with smaller population size N. In the first method, Single Parent Conflict Gene Extended Crossover and Conflict Gene Mutation with Advanced Local Guided Search operators are designed and employed. These operators have been processed with Conflict Gene Removal constraints in the second method to minimize the search space and to increase the percentage of successful runs of the genetic algorithm. Multipoint Single Parent Conflict Gene Crossover and Multipoint Conflict Gene Mutation with Advanced Local Guided Search operators are employed along with a Conflict Gene Removal constraint in the third method. It has been exhibited that these operators reduce the search space by minimizing $${\bar{g}}$$ to obtain a better near optimal solution. The solution for most of the small and large benchmark graphs has been obtained through multipoint crossover and mutation with reduced $${\bar{g}}$$ whose value lies in a specific interval represented using maximum and minimum degrees of G. Our methods reduce the bound for the minimum colors obtained so far for certain families of graphs using smaller population size.