Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach - Friansyah Gani; Henny Pramoedyo; Achmad Efendi (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2026)
Understanding spatial disparities in human development is essential for designing equitable development policies. This study examines the spatial variation of the Human Development Index (HDI) in East Java Province using an integrated Geographically Weighted Regression–Flower Pollination Algorithm (GWR–FPA) optimized with a Tricube kernel. The integration of GWR and FPA enables simultaneous spatial weighting and bandwidth optimization using the corrected Akaike Information Criterion (AICc) as the objective function. For standard GWR, the bandwidth was selected using Cross-Validation (CV) to minimize prediction error, while for the GWR–FPA model, bandwidth optimization was performed using the Flower Pollination Algorithm (FPA) with the corrected Akaike Information Criterion (AICc) as the objective function. Three predictors were analyzed: population size (X1), literacy rate (X2), and mean years of schooling (X3). Statistical diagnostics indicated significant spatial autocorrelation and heteroskedasticity in the OLS residuals, justifying the use of a spatial modeling framework. The GWR estimates revealed strong spatial non-stationarity: X1 showed no significant local effect, whereas educational factors (X2 and X3) were significant in all 38 districts and cities. The FPA optimization enhanced bandwidth selection, resulting in improved model fit. Model comparison based on AIC and AICc showed that the GWR–FPA–Tricube model achieved the lowest values (AIC = 135.8821; AICc = 137.0045), outperforming both global OLS and standard GWR. The results highlight the dominant contribution of education-related components to the spatial decomposition of HDI variation across East Java. The optimized model provides a more accurate spatial representation of local development disparities, supporting targeted policy interventions and illustrating the effectiveness of integrating metaheuristic optimization within spatial regression.