Optimization of Clustering of Lindt Truffle Nutrition Data via Genetic Algorithm and PCA: A Comparative Analysis with the K-Means Method

This paper presents a comparative study focused on the mathematical performance of two clustering approaches applied to a dataset of nutritional information of confectionery products. The central problem lies in overcoming the limitations of conventional clustering algorithms, which often require the predetermination of the number of clusters (k) and are sensitive to local minima. The proposed methodology uses a Genetic Algorithm (GA) integrated with Principal Component Analysis (PCA), where the number of clusters is not fixed, but rather a variable optimized by the heuristic itself. The objective function was structured to minimize the ratio of the sum of squares within clusters (WSS) to the sum of squares between clusters (BSS), operating in a search space reduced by the PCA to accelerate convergence. On the other hand, the K-means method was applied using the silhouette method for the selection of the hyperparameter k. The results compare squared error, centroid stability, and computational cost metrics. With this, it was demonstrated that, while K-means has fast execution, AG with parameter optimization eliminates the bias of manual choice of clusters, configuring a different method for grouping data. It is concluded that the evolutionary approach, despite the higher initial computational cost, provides an autonomous and robust clustering solution, validating its application as a good tool for unsupervised classification problems.