The k-means problem is one of the most popular models of cluster analysis. The problem is NP-hard, and modern literature offers many competing heuristic approaches. Sometimes practical problems require obtaining such a result (albeit notExact), within the framework of the k-means model, which would be difficult to improve by known methods without a significant increase in the computation time or computational resources. In such cases, genetic algorithms with greedy agglomerative heuristic crossover operator might be a good choice. However, their computational complexity makes it difficult to use them for large-scale problems. The crossover operator which includes the k-means procedure, taking the absolute majority of the computation time, is essential for such algorithms, and other genetic operators such as mutation are usually eliminated or simplified. The importance of maintaining the population diversity, in particular, with the use of a mutation operator, is more significant with an increase in the data volume and available computing resources such as graphical processing units (GPUs). In this article, we propose a new greedy heuristic mutation operator for such algorithms and investigate the influence of new and well-known mutation operators on the objective function value achieved by the genetic algorithms for large-scale k-means problems. Our computational experiments demonstrate the ability of the new mutation operator, as well as the mechanism for organizing subpopulations, to improve the result of the algorithm.

中文翻译：

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具有贪婪遗传算子的K-Means遗传算法

该ķ -means问题是聚类分析中最畅销的车型之一。问题是NP难题，现代文学提供了许多竞争性的启发式方法。有时，实际问题需要在k均值模型的框架内获得这样的结果（尽管不完全精确），而如果不显着增加计算时间或计算资源，将很难通过已知方法进行改进。在这种情况下，带有贪婪凝聚启发式交叉算子的遗传算法可能是一个不错的选择。但是，它们的计算复杂性使得很难将它们用于大规模问题。包含k的交叉运算符-means程序占用了绝大部分计算时间，对于此类算法至关重要，通常会消除或简化其他遗传算子（例如突变）。随着数据量和可用计算资源（例如图形处理单元（GPU））的增加，尤其是通过使用变异算子来维持种群多样性的重要性变得更加重要。在本文中，我们为此类算法提出了一种新的贪婪启发式突变算子，并研究了新的和著名的突变算子对大规模k遗传算法实现的目标函数值的影响-表示问题。我们的计算实验证明了新的变异算子的功能以及组织子种群的机制可以改善算法的结果。