An ant algorithm for solving the four-coloring map problem

An undirected graph can demonstrate adjacency relationships among regions in a planar map, and the four-coloring map problem is then converted into a graph vertex coloring problem with constraints. In order to solve the graph vertex coloring problem, an ant algorithm hybridized with a greedy algorithm was proposed. In this algorithm, ants in an ant colony with a given size separately move from one vertex to another according to their transition probability, and a greedy algorithm is used to initialize the proposed algorithm for improving its efficiency. Finally, the improved algorithm was tested by coloring the administrative map of Hunan Province, China, and results show that it is good at finding the optimal value, speed and stability.