Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach

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 metaheuristic-based bandwidth optimization. Three predictors were analyzed: population size ($X_1$), literacy rate ($X_2$), and mean years of schooling ($X_3$). 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: $X_1$ showed no significant local effect, whereas educational factors ($X_2$ and $X_3$) 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. These findings demonstrate that education-related variables are the primary drivers of HDI variation in East Java, while demographic size contributes minimally. 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.