Towards Sustainable Design: A Shape Optimization Framework for Climate-Adaptive Free-Form Roofs in Hot Regions

This study proposes a cross-disciplinary computational framework to advance the sustainable design of free-form grid roofs in hot climates, integrating architectural geometry with building thermal performance to enhance climate adaptability. Numerical analyses systematically explore the impact of thermal objectives, initial configurations, shape control strategies, and boundary constraints. The optimization results demonstrate that targeting indoor temperature under extreme heat yields saddle-shaped, self-shading morphologies, which achieve a measurable improvement in thermal comfort by reducing indoor temperatures by approximately 2 °C. A key practical finding is that symmetric-point control outperforms full-point control. While full-point control may generate forms with complex central depressions that complicate drainage, symmetric-point control consistently yields morphologies that are inherently more regular, symmetric, and constructible. This results in a superior balance among thermal performance, practical design attributes (e.g., drainage feasibility and construction simplicity), and geometric coherence—a combination that aligns closely with real-world engineering requirements. Furthermore, directional boundary constraints are proven to be effective tools for regulating passive shading performance. The proposed framework provides engineers and designers with a systematic and automated method for the climate-responsive and low-carbon design of free-form architectural morphologies, contributing to the development of more sustainable and resilient building infrastructure.