A New Multi-Objective Optimization In Solving Graph Coloring And Wireless Networks Channels Allocation Problems

Graph coloring problem, a combinatorial optimization problem is being widely applied in solving the channels allocation in wireless networks. This paper exhibits a new evolutionary genetic multi-objective strategy that uses the combined single and multi-parent conflict-gene crossover and combined single and multi-parent conflict-gene mutation operators with clique partitioning to solve the graph coloring and channel allocation problems. The proposed operators minimize problem search space by reducing the expected number of genetic generations. A general fitness function is defined on finding the total conflicting edges in the graph for the initial and particularly the successive generations of individuals in the population. The outcomes of this proposed method are better than the well-known methods and are compared with some of the benchmark graph coloring and channel allocation problems. The devised method of clique partitioning with genetic operators also enhances the successful runs.