• An RSM-Entropy Weight Method framework for multi-objective 3E optimization is proposed. • Objective weighting reveals environmental benefit (36.8%) as the dominant factor. • Optimal parameters for a dual-tank solar-electric heating system are identified. • The system's comprehensive score improved by 0.665 after optimization. • The framework provides a reusable paradigm for rural clean heating system design. The promotion of clean heating in rural northern China is hindered by the high costs and performance limitations of existing systems. Most optimization studies rely on one-dimensional objectives or subjective weighting methods, leading to biased and non-generalizable designs. To address this, we propose an integrated Response Surface Methodology (RSM)-Entropy Weight Method (EWM) framework for the multi-objective optimization of a dual-tank solar-electric heating system. The EWM objectively assigns weights to energy, economic, and environmental (3E) indicators based on data dispersion, revealing environmental benefit (36.8%) as the most influential factor. Using RSM, we model and optimize four key parameters: collector tilt angle, collector area, and the volumes of solar storage and heating tanks. The optimal configuration (tilt: 43.52°, area: 59.96 m 2 , storage tank: 2.70 m 3 , heating tank: 2.92 m 3 ) yields a comprehensive system score (CSS) of 0.9386, significantly outperforming the baseline. This study provides not only a specific optimal design but also a robust, objective, and reusable methodological framework, advancing the optimization of rural heating systems from single-dimensional improvement to multi-dimensional synergy.
Wang et al. (Sun,) studied this question.