图着色问题的模因算法变体
Variations on Memetic Algorithms for Graph Coloring Problems
摘要：
给定颜色数的图的顶点着色问题是一个NP完全问题，求解该问题最有效的方法是混合算法，如模因算法或量子退火算法。这些混合算法在基于种群的算法中使用了强大的局部搜索。本文提出了一种基于最有效算法之一的新模因算法：Galinier和Hao（1999）提出的混合进化算法HEA。所提出的算法，表示为HEAD-Duet中的HEA-仅对两个个体的群体起作用。此外，HEAD带来了一种管理多样性的新方法。这两个主要差异极大地改善了结果，无论是在解质量还是计算时间方面。HEAD已经为流行的DIMACS基准图产生了几个很好的结果，例如\textless{} dsjc 1000.9 \textgreater{}的222种着色、\textless{} flat1000\_76\_0 \textgreater{}的81种着色以及甚至\textless{} dsjc 500.5 \textgreater{}的47种着色和\textless{} dsjc 1000.5 \textgreater{}的82种着色。
英文摘要：
Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for \textless{}dsjc1000.9\textgreater{}, 81-colorings for \textless{}flat1000\_76\_0\textgreater{} and even 47-colorings for \textless{}dsjc500.5\textgreater{} and 82-colorings for \textless{}dsjc1000.5\textgreater{}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
