K-Means Genetic Algorithms with Greedy Genetic Operators

Abstract

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.

The color matching design based on polynomial regression

“…It is a computational model built by constantly selecting excellent individual algorithms. 19–21 Like the process of animal inheritance in nature, genetic algorithm also includes steps such as selection, crossover, and mutation, and its implementation process is shown in Figure 4.…”

Hybrid algorithms with alternative embedded local search schemes for the p-median problem

“…Algorithm 1, the Alternate Location-Allocation (ALA) procedure [7,23], is capable of solving both k-means and p-median problems, was introduced by Lloyd [3]. This procedure consistently improves an intermediate solution, which leads to finding locally optimal solutions.…”

“…The mutation operator provides population variability by randomly changing the resulting solutions, and the crossover operator combines new sets of medians from existing ones. The general algorithmic framework for location and clustering problems was presented in [7].…”

“…, 𝐴 𝑁 ∈ 𝑅 𝑑 . The papers [24,25] present parallel (CUDA) versions of algorithms for the discrete problems. For the p-median problem with Euclidean distance, at step 2 of Algorithm 1, at each iteration, the Weiszfeld procedure is performed to solve the Weber problem with a given accuracy 𝜀 1 .…”

“…To solve the p-median problems, we use the algorithmic combinations of the most popular ALA procedure (ALA -Alternate Location-Allocation, Lloyd's algorithm) [7]. The ALA consists of two alternating steps of local search, each of which is aimed at reducing the value of the objective function.…”