The database was gathered from several sources including Building Information Modeling (BIM) software like Autodesk Revit and ArchiCAD, smart building sensors, and open-source environmental databases. The dataset consists of 1,500 distinctive building configurations representing both residential and commercial typologies in 5 years (2018–2022) and various climatic zones. The optimization was intended to be versatile in applicability and realistic in outcome.

The data preprocessing phase included.

• Mean imputation for missing numerical values,

Table 1 provides a detailed overview of the dataset features and their relevance to sustainable building design.

To solve the multi-objective optimization problem, this research utilizes seven metaheuristic algorithms, each selected for its strengths in exploring large, complex solution spaces under constrained design scenarios. These include Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), and three additional methods: Firefly Algorithm (FA), Whale Optimization Algorithm (WOA), and NSGA-II.

This study aims to optimize building performance by balancing three key sustainability objectives: minimizing annual energy consumption, maximizing occupant comfort and return on investment (ROI), and reducing carbon footprint. These objectives reflect the architectural, economic, and environmental imperatives central to sustainable urban design.

The multi-objective optimization problem is tackled using a diverse set of metaheuristic algorithms, each designed to explore and exploit the solution space from different perspectives. The following subsections define the objective functions and illustrate how each of the seven algorithms-Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), Firefly Algorithm (FA), Whale Optimization Algorithm (WOA), and NSGA-II—addresses them.

This study uses several performance metrics to evaluate the effectiveness of the metaheuristic algorithms in optimizing sustainable building design. These include both computational indicators and real-world outcome measures. The aim is to provide a clear and structured assessment of how each algorithm performs in terms of processing efficiency and impact on energy consumption, comfort, emissions, and sustainability standards (Pham et al., 2020; Tien et al., 2022; Forootan et al., 2022; Zhang et al., 2023; Wang et al., 2020).

The performance of all seven metaheuristic algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), Firefly Algorithm (FA), Whale Optimization Algorithm (WOA), and NSGA-II—was evaluated using key optimization metrics. These included energy savings, occupant comfort score, return on investment (ROI), carbon footprint reduction, execution time, and convergence rate. The algorithms were applied to optimize 1,500 building configurations across diverse climatic zones and typologies.

As shown in Table 1, PSO achieved the highest energy savings (24.1%) and the fastest execution time (28.5 s), making it the most efficient in terms of computational speed and energy performance. ACO closely followed, showing strong carbon footprint reduction (20.1%) and attaining high occupant comfort scores (84.2). NSGA-II provided the most balanced outcomes across all objectives, particularly excelling in multi-objective trade-off management. GA performed well in occupant comfort (82.3) and ROI, while FA offered moderate energy savings with competitive comfort outcomes. WOA showed significant promise in carbon reduction and design robustness, while SA, though effective in escaping local optima, demonstrated the slowest convergence and lowest energy savings (21.0%).

This initial comparison provides a foundation for deeper analysis in the following sections, where individual metrics and objectives are explored in more detail.

Minimizing energy consumption is the primary objective of sustainable building design optimization. This subsection analyzes how effectively each algorithm reduced total annual energy use across the dataset of 1,500 building configurations. The algorithms were evaluated by calculating the percentage of energy savings relative to the baseline energy consumption.

As illustrated in Figure 1 and further detailed in Table 2, Particle Swarm Optimization (PSO) led all algorithms with the highest energy savings of 24.1%, demonstrating superior exploration capabilities in continuous solution spaces. This was followed closely by Ant Colony Optimization (ACO) at 23.7% and Whale Optimization Algorithm (WOA) at 23.4%, both of which also performed consistently across other metrics. NSGA-II achieved 23.0%, maintaining a good balance while still prioritizing energy efficiency.

Firefly Algorithm (FA) and Genetic Algorithm (GA) produced respectable savings of 22.8% and 22.5%, respectively, benefiting from their population-based search strategies. However, Simulated Annealing (SA) resulted in the lowest savings at 21.0%, indicating its slower convergence toward global minima in this objective.

These results reflect the advantages of swarm- and evolution-based algorithms for energy-related objectives. Algorithms with greater adaptability to multi-dimensional continuous variables, such as PSO, WOA, and ACO, showed more consistent energy reduction across the range of building typologies and climates.

This section considers each algorithm’s optimization of both occupant comfort and return on investment (ROI), both of which are key factors in maintaining a building’s ability to be used effectively and its long-term economic sustainability. A composite score of thermal conditions, air quality, and lighting is used to quantify comfort. ROI indicates the tradeoffs between construction expense and operational savings through energy efficiency.

As can be seen in Table 3, Particle Swarm Optimization (PSO) produced the highest comfort rating of 85.6, with Ant Colony Optimization (ACO) following at 84.2 and NSGA-II at 84.5. These optimizers successfully tuned design variables like HVAC efficiency, window-to-wall ratio, and levels of insulation to maximize internal environmental quality. Firefly Algorithm (FA) and Whale Optimization Algorithm (WOA) had strong comfort ratings of 83.1 and 83.8. Genetic Algorithm (GA) had 82.3, with consistent but lower performance in comfort-oriented scenarios. Simulated Annealing (SA) trailed at 79.9 due to its slow convergence in balancing multiple conflicting variables.

In terms of ROI, PSO again topped the list with a return of 16.8%, leveraging its global best search dynamics to reduce both operational energy costs and capital expenditures on ineffective configurations. ACO and NSGA-II yielded competitive ROI values of 16.5% and 16.3%, respectively. GA and FA followed closely, while SA delivered the lowest ROI, reinforcing its limited capability in dual-objective scenarios.

As illustrated in Figure 2, a scatter plot mapping comfort against ROI reveals that PSO, ACO, and NSGA-II occupy the optimal region, delivering strong trade-offs between human-centric comfort and economic return.

Minimizing the carbon footprint of building operations and materials is a critical objective in sustainable architecture. This section assesses how each algorithm performed in reducing total CO₂ emissions, as calculated from the energy source mix, construction materials, and system efficiency. The outcome corresponds to each of the optimized design configurations’ environmental implications.

As seen in Table 4, ACO realized the greatest carbon footprint reduction of 20.1% due to its capacity to favor configurations encompassing renewable energy sources and low-emission materials on all iterations. WOA was not far behind with 20.0% due to its adaptive mechanism of encircling to optimize against environmental-friendly design variables. NSGA-II and PSO also performed well at 19.8% and 19.7%, respectively, and were highly efficient in balancing environmental concerns and performance.

The Firefly Algorithm (FA) and Genetic Algorithm (GA) realized moderate savings of 18.9% and 18.4%, respectively. These results indicate that both can potentially search for sustainable solutions but have more iterations or need to be hybridized for deeper carbon reductions. Simulated Annealing (SA) realized the least amount of improvement at 17.5% through its low exploration level and slow convergence in the carbon reduction function.

Figure 3 demonstrates the relative carbon reduction performance of the algorithms. The findings confirm that multi-objective optimization-oriented algorithms like ACO, WOA, and NSGA-II can identify low-carbon facility configurations more effectively with little loss of energy efficiency and comfort.

To confirm the applicability of the optimization outcomes in the real-world context, in this section each algorithm’s performance is calculated using LEED certification standards and sustainability indicators. LEED certifications are given in five principal categories: energy efficiency, water efficiency, materials and resources, indoor environmental quality, and innovation. The higher the combined score corresponds to improved levels of certification (e.g., Silver, Gold, Platinum).

As can be seen in Table 5, Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) attained the best overall LEED ratings and were in the Platinum certification category. This was due to their high performance in energy efficiency, indoor environmental quality, and material selection. NSGA-II also attained Platinum rating signifying that its all-around optimization of energy, comfort, and carbon goals resulted in very sustainable structures.

Whale Optimization Algorithm (WOA) trailed just behind it, with efficient use of water and the use of renewable energy standing it in good stead for being awarded a Gold standard. Firefly Algorithm (FA) and Genetic Algorithm (GA) also attained Gold status, evidencing favorable—but not the best—sustainability performance. Simulated Annealing (SA) was lowest in all but one of the categories and attained only a Silver rating on account of low performance in energy and material criteria.

As seen in Figure 4, the LEED certification levels indicate the strength of each algorithm in designing holistically sustainable structures. The high concentration of PSO, ACO, and NSGA-II in the Platinum category emphasizes their applicability in real-world green building projects.

Convergence behavior is an essential indicator of an algorithm’s efficiency in moving towards optimal solutions. Convergence behavior indicates the algorithm’s capacity to stabilize its objective values across iterations and hence signifies both the computational time and optimization stability. In this section, each algorithm’s convergence pattern is examined in terms of iteration number, the rate of convergence, as well as stability over time.

As can be seen from Table 6, Particle Swarm Optimization (PSO) once again demonstrated the quickest convergence, converging within 50 iterations at a rate of 0.93 due to its high exploitation ability and dynamics of the swarm intelligence. NSGA-II was close behind it, converging at 55 iterations at the rate of 0.91 due to its population-based evolutionary mechanism for maintaining Pareto-optimal fronts.

Genetic Algorithm (GA) and Whale Optimization Algorithm (WOA) both had moderate convergence rates of 0.89 and needed approximately 75 and 70 iterations, respectively, to stabilize. Firefly Algorithm (FA) and Ant Colony Optimization (ACO) converged at slightly slower paces with FA stabilizing at iteration 72 and ACO at iteration 65 at respective convergence rates of 0.88 and 0.87. Simulated Annealing (SA) had the slowest convergence with almost 90 iterations to stabilize at a rate of 0.80 due mainly to its probabilistic search procedure accepting inferior solutions during the initial stages.

These are well illustrated in Figure 5, where the convergence curves highlight how quickly and steadily each of the algorithms converged towards optimal solutions for 100 iterations. PSO and NSGA-II curves slope steeply in the initial stages whereas the curve of SA is sloping and gradual reflecting longer times of search and slow adaptation.

In order to guarantee the reliability and stability of the optimization results, the section here gives the statistical error analysis and sensitivity test results. These analyses give insights into the stability and reliability of the algorithms when run repeatedly and also tell us which performance outcomes are most impacted by the designing parameters.

Mean Absolute Percentage Error (MAPE) and Standard Deviation (SD) were evaluated for 10 independent runs of each algorithm to factor in the energy savings’ variation. From Table 7, Particle Swarm Optimization (PSO) had the lowest MAPE of 2.3%, reflecting highly consistent performance in multiple runs. NSGA-II and ACO also performed well with high reliability as evidenced by MAPE results of 2.5% and 2.6%, respectively. Simulated Annealing (SA) demonstrated the highest MAPE of 3.9%, as its more stochastic process and less consistent convergence were reflected.

For Standard Deviation, PSO once again yielded the least variable results (±0.65%), with NSGA-II (±0.72%) and WOA (±0.76%) following next in line. FA and GA had moderate variation, while SA had the largest range of outcome reliability (±1.10%), consistent with the observed trend of its converging behavior.

The sensitivity analysis examined how changes in key input variables—such as HVAC efficiency, window-to-wall ratio, building orientation, and insulation value—affected optimization outcomes. The results, summarized in Figure 6, revealed that HVAC efficiency had the most substantial impact, contributing to 45% of variance in energy savings. Orientation and window-to-wall ratio followed, influencing 30% and 15%, respectively. This highlights the importance of mechanical systems and envelope design in sustainable performance.

These findings confirm that the top-performing algorithms not only deliver superior solutions but also maintain stability across multiple runs and are responsive to the most critical variables in design decision-making.

This section focuses on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and its ability to handle multiple competing objectives by generating a Pareto front. Unlike single-objective optimizers, NSGA-II simultaneously explores trade-offs between energy savings, occupant comfort/ROI, and carbon footprint reduction, providing a set of equally optimal solutions for different stakeholder preferences.

As represented in Figure 7, the Pareto front produced by NSGA-II clearly shows a range of optimal solutions. Designs on the left of the front maximize energy savings as their highest priority, while on the right maximize comfort and ROI, with a balanced middle section being an agreeable solution on all three fronts. The front enables architects and planners to choose the appropriate context solution on the basis of project objectives—either pursuing LEED Platinum, ROI maximization, or minimizing environmental impact.

For example, one NSGA-II solution resulted in 23.0% energy savings, 84.5 comfort score, and 19.8% reduction in carbon footprint, which puts it at par with PSO and ACO. The major strength of NSGA-II is its power to present several such trade-offs without being constrained by a fixed weighting scheme as in weighted-sum models.

This flexibility proves particularly valuable in real-world architectural applications where project constraints vary, and multi-stakeholder input often leads to shifts in design priorities. NSGA-II’s Pareto approach thus enhances decision-making transparency and provides greater design agility in the early stages of sustainable urban planning.

This subsection synthesizes the findings from previous analyses by outlining the core strengths, limitations, and recommended use cases for each of the seven metaheuristic algorithms used in this study. The comparative review aids in selecting the most appropriate algorithm based on specific project priorities such as speed, sustainability, comfort, or balanced trade-offs.

As summarized in Table 8, Particle Swarm Optimization (PSO) emerges as the most well-rounded performer, excelling in energy savings, comfort, execution time, and achieving Platinum LEED certification. Its main limitation lies in slightly less flexibility when handling highly constrained or discrete variables. Ant Colony Optimization (ACO) stands out for its carbon footprint reduction and multi-objective strength, making it ideal for projects emphasizing environmental impact mitigation.

NSGA-II, while not always the absolute best in any single metric, delivers the most balanced solutions across all objectives, particularly in contexts requiring stakeholder-driven trade-offs. It is especially suited for large-scale urban planning where Pareto flexibility is essential. Whale Optimization Algorithm (WOA) offers solid performance in both carbon reduction and comfort but requires slightly more computational time to converge.

Firefly Algorithm (FA) and Genetic Algorithm (GA) show consistent results across most objectives and are preferred when interpretability, modularity, or algorithm simplicity are valued. However, both tend to fall behind in convergence rate and overall LEED scores. Simulated Annealing (SA), though capable of escaping local optima, was the least effective across all key metrics, with slower convergence, higher variation in results, and lower sustainability performance. Nevertheless, SA may still be useful in small-scale design problems or constrained scenarios.

This analysis confirms that no single algorithm is optimal for all use cases, but each offers distinct advantages depending on the design scenario and optimization priorities. As architectural and urban projects continue to embrace data-driven sustainability, understanding the nuanced performance of optimization methods will be critical to informed, context-sensitive design decisions.