Geo-demographic analysis (GDA) is a useful method to analyze information based on location, utilizing several spatial analysis explicitly. One of the most efficient and commonly used method is Fuzzy Geographically Weighted Clustering (FGWC). However, it has a limitation in obtaining local optimal solution in the centroid initialization. A novel approach integrating Gravitational Search Algorithm (GSA) with FGWC is proposed to obtain global optimal solution leading to better cluster quality. Several cluster validity indexes are used to compare the proposed methods with the FGWC using other optimization approaches. The study shows that the hybrid method FGWC-GSA provides better cluster quality. Furthermore, the method has been implemented in R package spatialClust.