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前景且极具挑战性的组合优化问题。本文提出了一种基于概率模型种群的分布进化算法（DEA-PPM）以高效求解该问题。与现有通过生成解来更新概率模型的分布估计算法不同，DEA-PPM采用基于新型概率模型的分布种群，并引入正交探索策略，在精炼策略的辅助下搜索分布空间。通过对分布种群进行采样，并基于禁忌搜索过程实现解空间的高效搜索。同时，DEA-PPM引入了迭代顶点移除策略以提升$k$-着色的效率，并实现了继承初始化策略以更好地处理色数问题。分布种群与解种群的协同进化在探索与利用之间取得了良好平衡。数值结果表明，采用小种群规模的DEA-PPM相对于当前最先进的元启发式算法具有竞争力。