Graph coloring is a challenging combinatorial optimization problem with a wide range of applications. In this paper, a distribution evolutionary algorithm based on a population of probability model (DEA-PPM) is developed to address it efficiently. Unlike existing estimation of distribution algorithms where a probability model is updated by generated solutions, DEA-PPM employs a distribution population based on a novel probability model, and an orthogonal exploration strategy is introduced to search the distribution space with the assistance of an refinement strategy. By sampling the distribution population, efficient search in the solution space is realized based on a tabu search process. Meanwhile, DEA-PPM introduces an iterative vertex removal strategy to improve the efficiency of $k$-coloring, and an inherited initialization strategy is implemented to address the chromatic problem well. The cooperative evolution of the distribution population and the solution population leads to a good balance between exploration and exploitation. Numerical results demonstrate that the DEA-PPM of small population size is competitive to the state-of-the-art metaheuristics.utes to its competitiveness to the state-of-the-art metaheuristics.

翻译：图着色是一类具有广泛应用的组合优化问题，而本文提出了一种基于概率模型种群的分布进化算法（DEA-PPM）以实现高效求解。与现有的基于分布估计的算法不同，DEA-PPM利用了一种基于新型概率模型的分布种群，引入正交搜索策略，以协助搜索分布空间并通过优化策略进行进一步的细化搜索。通过采样分布种群，利用禁忌搜索方法实现了在解空间中的高效搜索。同时，DEA-PPM引入了迭代顶点删除策略以提高$k$-coloring算法的效率，并实现了继承式初始化策略以很好地解决色差问题。分布种群和解种群的协同进化实现了探索和利用之间的平衡。数值实验表明，即使在规模较小的种群大小下，DEA-PPM也与现有的元启发式算法具有竞争力。