Response Surface Methodology coupled with desirability functions for multi-objective optimization: minimizing indoor overheating hours and maximizing useful daylight illuminance

TL;DR

This paper demonstrates an efficient multi-objective optimization method combining Response Surface Methodology and desirability functions to improve thermal comfort and daylight in tropical housing with minimal simulation runs.

Contribution

It introduces a novel application of RSM and desirability functions for simultaneous optimization of thermal and daylight performance in tropical housing models.

Findings

Optimal window-to-wall ratio and overhang depth improve indoor comfort.

Only 138 simulations needed for effective optimization.

Robustness confirmed with 95% confidence intervals.

Abstract

Response Surface Methodology (RSM) and desirability functions were employed in a case study to optimize the thermal and daylight performance of a computational model of a tropical housing typology. Specifically, this approach simultaneously optimized Indoor Overheating Hours (IOH) and Useful Daylight Illuminance (UDI) metrics through an Overall Desirability (D). The lack of significant association between IOH and other annual daylight metrics enabled a focused optimization of IOH and UDI. Each response required only 138 simulation runs (~30 hours for 276 runs) to determine the optimal values for passive strategies: window-to-wall ratio (WWR) and roof overhang depth across four orientations, totalling eight factors. First, initial screening based on $2_V^{8-2}$ fractional factorial design, identified four key factors using stepwise and Lasso regression, narrowed down to three: roof overhang depth on the south and west, WWR on the west, and WWR on the south. Then, RSM optimization yielded an optimal solution (roof overhang: 3.78 meters, west WWR: 3.76%, south WWR: 29.3%) with a D of 0.625 (IOH: 8.33%, UDI: 79.67%). Finally, robustness analysis with 1,000 bootstrap replications provided 95% confidence intervals for the optimal values. This study optimally balances thermal comfort and daylight with few experiments using a computationally-efficient multi-objective approach.