Conventional Boolean computational methods are inefficient in solving complex combinatorial optimization problems such as graph coloring or traveling sales man problem. In contrast, the dynamics of coupled oscillators could efficiently be used to find an optimal solution to such a class of problems. Kuramoto model is one of the most popular mathematical descriptions of coupled oscillators. However, the solution to the graph coloring problem using the Kuramoto model is not an easy task. The oscillators usually converge to a set of overlapping clusters. In this study, we mathematically derive a new coupling function that forces the oscillators to converge to a set of non-overlapping clusters with equal distance between classes. The proposed coupling function shows significant performance improvement compared to the original Kuramoto model.

常规布尔计算方法无法有效解决复杂的组合优化问题，例如图形着色或旅行商问题。相反，可以有效地使用耦合振荡器的动力学来找到这类问题的最佳解决方案。仓本模型是耦合振荡器最流行的数学描述之一。但是，使用仓本模型解决图形着色问题并非易事。振荡器通常会收敛到一组重叠的簇。在这项研究中，我们从数学上推导了一个新的耦合函数，该函数迫使振荡器收敛到类之间具有相等距离的一组非重叠簇。与原始的仓本模型相比，提出的耦合函数显示出显着的性能改进。