A Hybrid Genetic Hill-climbing Algorithm for Four-Coloring Map Problems

We propose a Hybrid Genetic hill-climbing Algorithm (HGA) search algorithm and in this paper, demonstrated for n-region 4-coloring map problems. The HGA incorporates the usual Genetic Algorithm (with reproduction, crossover and mutation genetic operators) and a local hill-climbing algorithm. To effectively reduce the magnitude of the search space by 23 times (equivalent to better than one order of magnitude), in particular where n>6, we propose a group representation that does not result in any loss of generality. We further propose an objective measure as a guide for the search process. To depict the efficacy of the proposed HGA algorithm, we compare its performance against the established standard Genetic Algorithm, Hill-climbing and an artificial neural network optimization algorithm for several n-region 4-color maps. We show that the proposed HGA is the only algorithm that is able to obtain an optimal solution for large maps (n>500). Furthermore, we show that the proposed HGA is the fastest algorithm to yield an optimal solution in all n-region 4-color maps compared.