A Bio-Inspired Approach to Sustainable Building Design Optimization: Multi-Objective Flow Direction Algorithm with One-Hot Encoding

The urgent need for sustainable building design calls for advanced optimization methods that simultaneously address economic and environmental objectives, particularly those involving mixed discrete-continuous variables such as insulation material, heating source, and insulation thickness. While nature-inspired metaheuristics have shown promise in engineering optimization, their application to building envelope design remains limited, especially in handling discrete choices efficiently within a multi-objective framework. Inspired by the natural process of rainwater runoff and drainage basin dynamics, this study presents a novel hybrid approach integrating the Multi-Purpose Flow Direction Algorithm (MOFDA) with One-Hot Encoding to optimize external wall insulation. This bio-inspired algorithm mimics how water seeks optimal paths across terrain, enabling effective navigation of complex design spaces with both categorical and continuous variables. The model aims to minimize total lifecycle costs and CO₂ emissions across Türkiye's six updated climatic regions. Pareto-optimal solutions are created using MOFDA, after which the Complex Proportional Assessment (COPRAS) method, weighted by Shannon Entropy, selects the most balanced designs. The results reveal significant climate-dependent variations: in the warmest region, the cost-optimal thickness is 3.3 cm (Rock Wool), while the emission-optimal reaches 17.3 cm (Glass Wool). In colder regions, emission-driven scenarios consistently require up to 40 cm insulation, indicating a practical limit of current materials. Under balanced weighting, fuel preferences shift from LPG in milder climates to Fuel Oil in harsher climates. Notably, Shannon Entropy assigned a weight of 88-92% to emissions due to their wider variability across the Pareto front, underscoring the environmental priority in data-driven decisions. This study demonstrates that the bio-inspired MOFDA framework, enhanced with One-Hot Encoding, effectively handles mixed discrete-continuous optimization and provides a robust, climate-aware decision tool for sustainable building design, reinforcing the value of translating natural flow processes into engineering solutions.