Analysis of Population Growth in Central Lampung Regency Using Exponential and Logistic Models with GRG Parameter Optimization and Model Performance Evaluation - Al Mahkya, Prana; Sutrisno, Agus; Zakaria, La (Desimal: Jurnal Matematika, 2026)
Accurate regional population projection is essential for development planning, infrastructure allocation, public service provision, and long-term resource management. This study analyzes population growth in Central Lampung Regency, Indonesia, by comparing exponential and logistic growth models supported by Generalized Reduced Gradient (GRG) parameter optimization and integrated model performance evaluation. Annual population data from 2016 to 2025 were obtained from official statistics, with 2016 defined as the base year. The exponential model was formulated under the assumption of unlimited proportional growth, whereas the logistic model incorporated a carrying capacity of 2,000,000 people as a modeling assumption to represent bounded demographic growth. The growth-rate parameter was optimized by minimizing Mean Absolute Percentage Error (MAPE), and model performance was evaluated using MAPE, Mean Absolute Error (MAE), and Root Mean Square Error (RMSE). Robustness analysis, direct parameter sensitivity analysis, and paired t-test were also conducted to examine parameter stability and statistical differences between model errors. The results show that the population increased from 1,250,486 people in 2016 to 1,541,429 people in 2025, with a marked structural rise around 2020. Both models achieved very accurate performance, with MAPE values below 10%. However, the logistic model produced slightly lower errors, with MAPE of 2.3227%, MAE of 31,760.57 people, and RMSE of 40,705.66 people. Robustness and sensitivity analyses confirmed stable parameter behavior in both models. The paired t-test indicated no statistically significant difference between their errors. Thus, the logistic model is recommended as the more conceptually appropriate framework for long-term regional population projection.