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Graph coloring is a challenging combinatorial optimization problem with awide range of applications. In this paper, a distribution evolutionaryalgorithm based on a population of probability model (DEA-PPM) is developed toaddress it efficiently. Unlike existing estimation of distribution algorithmswhere a probability model is updated by generated solutions, DEA-PPM employs adistribution population based on a novel probability model, and an orthogonalexploration strategy is introduced to search the distribution space with theassistance of an refinement strategy. By sampling the distribution population,efficient search in the solution space is realized based on a tabu searchprocess. Meanwhile, DEA-PPM introduces an iterative vertex removal strategy toimprove the efficiency of $k$-coloring, and an inherited initializationstrategy is implemented to address the chromatic problem well. The cooperativeevolution of the distribution population and the solution population leads to agood balance between exploration and exploitation. Numerical resultsdemonstrate that the DEA-PPM of small population size is competitive to thestate-of-the-art metaheuristics.utes to its competitiveness to thestate-of-the-art metaheuristics.

A Distribution Evolutionary Algorithm for the Graph Coloring Problem