Abstract Typically, Graph Coloring Problem (GCP) is one of the key features for graph stamping in graph theory. The general approach is to paint at least edges, vertices, or the surface of the graph with some colors. In the simplest case, a kind of coloring is preferable in which two vertices are not adjacent to the same color. Similarly, the two edges in the same joint should not have the same color. In addition, the same goes for the surface color of the graph. This is one of the NP-hard issues well studied in graph theory. Therefore, many different meta-heuristic techniques are presented to solve the problem and provide high performance. Seemingly, regardless of the importance of the nature-stimulated meta-heuristic methods to solve the GCP, there is not any inclusive report and detailed review about overviewing and investigating the crucial problems of the field. As a result, the present study introduces a wide-ranging reporting of nature- stimulated meta-heuristic methods, which are used throughout the graph coloring. The literature review contains a classification of significant techniques. This study mainly aims at emphasizing the optimization algorithms to handle the GCP problems. Furthermore, the advantages and disadvantages of the meta-heuristic algorithms in solving the GCP and their key issues are examined to offer more advanced meta-heuristic techniques in the future.

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解决图着色问题的元启发式方法的系统研究

摘要 通常，图着色问题（GCP）是图论中图标记的关键特征之一。一般的方法是至少用一些颜色绘制图形的边缘、顶点或表面。在最简单的情况下，一种着色是优选的，其中两个顶点不相邻于相同的颜色。同样，同一关节中的两条边不应具有相同的颜色。此外，图形的表面颜色也是如此。这是图论中深入研究的 NP 难题之一。因此，提出了许多不同的元启发式技术来解决问题并提供高性能。表面上看，不管自然刺激的元启发式方法对解决 GCP 的重要性，没有任何关于概述和调查该领域关键问题的综合报告和详细审查。因此，本研究引入了对自然刺激元启发式方法的广泛报告，这些方法在整个图着色中使用。文献综述包含重要技术的分类。本研究主要旨在强调处理 GCP 问题的优化算法。此外，研究了元启发式算法在解决 GCP 中的优缺点及其关键问题，以在未来提供更先进的元启发式技术。文献综述包含重要技术的分类。本研究主要旨在强调处理 GCP 问题的优化算法。此外，研究了元启发式算法在解决 GCP 中的优缺点及其关键问题，以在未来提供更先进的元启发式技术。文献综述包含重要技术的分类。本研究主要旨在强调处理 GCP 问题的优化算法。此外，研究了元启发式算法在解决 GCP 中的优缺点及其关键问题，以在未来提供更先进的元启发式技术。