Energy and daylighting trade-offs in residential window design: multi-objective optimization for hot-arid regions

The relationship between the geometrical parameters of windows and the energy and daylight performance of buildings is inherently complex and requires systematic investigation. This study addresses this challenge by optimizing the geometry of south-facing windows in residential apartments in Yazd, a city with a hot-arid climate. The novelty of this work lies in its holistic integration of a comprehensive set of window parameters, including width, height, sill height, horizontal and vertical position, and subdivision patterns, across eight typical residential room configurations derived from field surveys. Unlike previous studies that focused on isolated parameters or simplified spaces, this research systematically explores the combined influence of window geometry and room dimensions through a generative design approach. The methodology involves parametric modeling in Grasshopper using Python scripting, simulation of energy and daylight performance with Ladybug Tools, and multi-objective optimization through the NSGA-II. Three objectives were considered: minimizing cooling demand, minimizing heating demand, and maximizing average Useful Daylight Illuminance (UDI). Statistical analyses, including correlation and regression, were applied to identify the most influential parameters, and simulation results were validated against actual energy consumption data from residential units in Yazd. The results indicate that window to wall ratio (WWR), window area, and window height have the greatest influence on energy and daylight performance. The optimal configuration is a vertically elongated south-facing window with a WWR of about 20%, a height greater than 2 m, a sill height below 0.5 m, and horizontal centering on the façade. Compared to baseline cases, this configuration achieves a 3.9–5.2% reduction in total energy consumption, a 19.7–23.2% reduction in cooling demand, a 2.3–2.4% reduction in heating demand, and an 8–12% improvement in average UDI, while maintaining acceptable glare levels. These findings confirm that optimized window geometry can simultaneously enhance daylight quality and reduce energy demand, offering evidence-based guidelines for sustainable.