## 1 Introduction
These optimization methods principally comprise those grounded in mathematical programming (e.g., Epsilon-Constraint Method, Weighted-Sum Method, and Tchebycheff), evolutionary algorithms (e.g., SPEA2, MOEA/D, NSGA-II, and NSGA-III), swarm intelligence algorithms (e.g., MOPSO, MOGWO, and MOMFO), hybrid algorithms (e.g., NSGA-II+SA), and so forth [14; 15; 16; 17; 18]. Among optimization algorithms, heuristic algorithms, particularly NSGA-II and its variants, are widely employed for multi-objective decision making in energy-saving building renovation [19; 20; 21; 22; 23]. For instance, [PERSON] et al. proposed an enhanced NSGA-III algorithm, incorporating parallel computing and result-archiving mechanisms, significantly boosting its computational efficiency and potential [14]. [PERSON] et al. implemented an archive NSGA-II to optimize building retrofits in a Mediterranean climate, significantly reducing optimization time and substantially decreasing energy expenses, use, and greenhouse gas emissions [24]. [PERSON] et al. implemented NSGA-II in order to identify the initial design parameters for optimal retrofit solutions, aiming to reduce energy consumption and maximize economic performance while improving indoor thermal comfort [25]. [PERSON] et al. employed the NSGA-II algorithm for the multi-objective optimization of the energy performance and indoor thermal environment for rural tourism buildings, marking a substantial advancement in scientifically driven passive design strategies [26]. These studies validate the effectiveness of heuristic algorithms (especially the NSGA-II algorithm and its variants) for a wide range of multi-objective problems, demonstrating their widespread application and continued progress in improving building energy performance, economic efficiency, and occupant comfort across various settings. However, evolutionary algorithms, commonly employed in this context, typically require extensive cost function evaluations to achieve satisfactory outcomes [27]. In recent years, there has been a notable increase in research focusing on the utilization of alternative models for approximating or simulating computationally intensive models, a development precipitated by advancements in artificial intelligence technology [28; 29]. Numerous studies have combined surrogate models (e.g., artificial neural networks (ANNs)) with optimization algorithms [30; 31; 32], particularly NSGA-II [33; 34; 35] or other randomized algorithms [18; 36; 37], in what is commonly known as surrogate model-based optimization. This approach expedites building performance evaluations across various retrofit options, significantly accelerating the search for optimal solutions [38]. Surrogate models leverage diverse machine learning (ML) algorithms, such as random forest (RF), support vector machine (SVM), multivariate linear regression (MVLR), gradient boosting machines (GBMs), response surface methods (RSM), and artificial neural networks (ANNs) [39; 40; 41; 42; 43]. Compared to conventional optimization methods, these approaches analyze simulation data from various renovation options, construct energy performance prediction models, and integrate metaheuristic algorithms for multi-criteria optimization. By overcoming the constraints of a limited solution space, these methods dramatically enhance optimization efficiency. Among the surrogate models, ANNs have been widely employed in building energy optimization studies [38; 44]. However, the reliance on ANNs alone has limitations, including potential inefficiencies, overfitting risks, and a lack of comparative analysis with alternative ML models that may offer better performance. To address this gap, this study incorporates a broader dataset and compares the performance of four different ML models: light gradient boosting machine (LightGBM), fast random forest (FRF), multivariate linear regression (MVLR), and artificial neural network (ANN).