Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications and, however, are computationally difficult. In this work, a general population-based weight learning framework for solving graph coloring problems is presented. Unlike existing methods for graph coloring that are specific to the considered problem, the presented work targets a generic objective by introducing a unified method that can be applied to different graph coloring problems. This work distinguishes itself by its solving approach that formulates the search of a solution as a continuous weight tensor optimization problem and takes advantage of a gradient descent method computed in parallel on graphics processing units. The proposed approach is also characterized by its general global loss function that can easily be adapted to different graph coloring problems. The usefulness of the proposed approach is demonstrated by applying it to solve two typical graph coloring problems and performing extensive computational studies on popular benchmarks. Improved best-known results (new upper bounds) are reported for several large graphs.

图形着色涉及为图形的顶点分配颜色，以使由边链接的两个顶点接收不同的颜色。图形着色问题是通用模型，对于制定许多相关应用程序非常有用，但是计算困难。在这项工作中，提出了用于解决图形着色问题的基于总体的权重学习框架。与特定于所考虑问题的现有图形着色方法不同，本发明的工作通过引入可应用于不同图形着色问题的统一方法来针对通用目标。这项工作的独特之处在于其求解方法，该方法将求解的搜索公式化为连续权重张量优化问题，并利用了在图形处理单元上并行计算的梯度下降方法。所提出的方法的特征还在于其一般的全局损失函数，可以很容易地适应不同的图形着色问题。通过将其应用于解决两个典型的图形着色问题并在流行的基准上进行大量的计算研究，证明了该方法的有用性。报告了几个大型图形的改进的最佳已知结果（新的上限）。通过将其应用于解决两个典型的图形着色问题并在流行的基准上进行大量的计算研究，证明了该方法的有用性。报告了几个大型图形的改进的最佳已知结果（新的上限）。通过将其应用于解决两个典型的图形着色问题并在流行的基准上进行大量的计算研究，证明了该方法的有用性。报告了几个大型图形的改进的最佳已知结果（新的上限）。