Optimizing Cluster Centroids using Hybrid Firefly-Genetic Algorithm for Village Development Clustering

Annisa Rahma (Directorate of Services Statistics, Badan Pusat Statistik RI, Jakarta, Indonesia)
Rani Nooraeni (Departement of Statistical Computing, Politeknik Statistika STIS, Jakarta, Indonesia)
Raditya Hizra (Departement of Statistical Computing, Politeknik Statistika STIS, Jakarta, Indonesia)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 22 No. 3 (2026): May 2026

Clustering in the Building Village Index (BVI) offers an alternative approach to identifying village groupings based on numerical and categorical characteristics similarities. K-Prototype (KP) is a popular clustering algorithm for handling . This study proposes the hybridization that combines the exploitation strength of the Firefly Algorithm (FA) with the exploration capability of the Genetic Algorithm (GA) to optimize centroid initialization of KP. The results show that FA-GA hybridization enables the centroid initialization process to be faster with optimal fitness compared to either a single FA or a single GA. FGAKP is the best clustering algorithm in this study because it produces the smallest Total Cost (TC) and the largest Cluster Validity (CV) index with the most efficient centroid initialization time across all training data. The implementation of FGAKP in village grouping based on BVI indicators in North Kalimantan Province in 2024 grouped 484 villages into 5 categories based on their village development potential, achieving an 11.69% reduction in TC and a 16.75% improvement in CV compared to the standard KP without optimization.