optimizing traditional clustering methods using metaheuristic algorithms for joint set identification in copper mines

The assessment of clustering methods is crucial for identifying the primary characteristics of joints in mining and rock engineering. orientation is commonly used to characterize the deformation patterns and mechanical properties of rock formations. this study introduces an enhanced clustering method by integrating the harmony search (hs) and particle swarm optimization (pso) algorithms to classify joint sets based on orientation parameters—namely, dip and dip direction—in the sungun copper mine. first, joint characteristics were clustered using k-means and fuzzy c-means (fcm) techniques. the elbow method was applied to determine the optimal number of clusters, resulting in a four-cluster classification. subsequently, both k-means and fcm were optimized using hs and pso algorithms, and the joint data were evaluated based on three clustering quality criteria: the davies-bouldin index (dbi), the calinski-harabasz index (chi), and the silhouette coefficient (si). the results showed that the fcm-pso method achieved the highest ranking, yielding a dbi of 0.80, a chi of 348.47, and an si of 0.565. in contrast, integrating the hs algorithm with k-means and fcm did not improve clustering performance as expected. furthermore, the k-means-pso method performed worse than the fcm clustering approach, ranking third overall. based on these findings, the fcm-pso method, by effectively optimizing cluster centers, provides a reliable approach for classifying joint sets. the proposed method can be effectively applied in rock mass behavior analysis for large-scale open-pit mines such as the sungun copper mine. the fcm-pso method achieved the best results with dbi=0.80, chi=348.47, and silhouette=0.565.