## 2 Research Methods  
### Multi-Objective Optimization Algorithm  
Intelligent optimization algorithms are a category of algorithms inspired by natural and social behaviors, designed to solve complex optimization problems, particularly those that are difficult to address with traditional mathematical methods. These algorithms typically exhibit strong global search capabilities, effectively finding near-optimal solutions within vast search spaces. Key intelligent optimization algorithms include genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), simulated annealing (SA), and others. In the realm of intelligent algorithms, genetic algorithms (GAa) and their improved versions play a dominant role, followed by particle swarm optimization (PSO) [51]. Basic genetic algorithms primarily focus on single-objective optimization, iterating towards optimal solutions through selection, crossover, and mutation processes. The NSGA-II (Non-dominated Sorting Genetic Algorithm II), developed by [PERSON] and [PERSON], is among the most widely used genetic algorithms. It is a rapid, non-dominated, multi-objective optimization algorithm based on Pareto optimal solutions [52; 53]. NSGA-II's elite preservation strategy ensures that high-quality individuals from the parent population are directly carried over to the next generation, preventing the loss of non-inferior solutions. This algorithm is known for its fast performance, high efficiency, and strong convergence, simplifying the complexity of non-inferior quality genetic algorithms [54]. Researchers like [PERSON] have utilized TRNSYS combined with the NSGA-II genetic algorithm for optimizing single-family homes, aiming to reduce energy costs and discomfort times, with results showing more than a 57% reduction in energy consumption [55]. [PERSON], S., has demonstrated the application of the NSGA II algorithm in multi-objective building optimization under operational uncertainties [56]. [PERSON] proposed an optimization solution for automatically identifying the best configurations of windows, envelopes, shading systems, and energy supply systems for an office building in Norway [57]. [PERSON] combined Energy Plus with NSGA-II to optimize the design of residential buildings in Spain, balancing window sizes, types of glass, and external walls and roofs for heating and cooling demands [58]. [PERSON] used the PSO algorithm in GenOpt to optimize buildings for energy, cost, and acoustic performance, while also incorporating analyses with the NSGA-II algorithm [59]. [PERSON], taking buildings in Iran as an example, used Energy Plus and NSGA-II for optimizing building orientation, window area, and window shading, showing a total energy consumption reduction of 23.8-42.2% [60]. As research and the evolution of algorithms progress, scholars are also experimenting with a variety of algorithms like NSGA-III [37, 61], SPEA-II [62], HypE [63], MOPSO, and MOEA/E [41, 64]. [PERSON], [PERSON], and others achieved optimal passive design for single-family homes in different climates by coupling the NSGA-III genetic algorithm with the building energy simulation tool TRNSYS [65]. [PERSON] used an improved version of the NSGA-III algorithm, prNSGA-III, as the research optimization algorithm [61]. From the above, it's clear that researchers have employed various evolutionary algorithms to optimize architectural design. [PERSON] and others used the multi-objective artificial bee colony (MOABC) algorithm to maximize building energy efficiency and indoor thermal comfort in different climate zones of Iran [66]. [PERSON] and his team also used the multi-objective particle swarm optimization (MOPSO) algorithm to evaluate schemes based on annual heating, cooling, and lighting energy consumption standards [67].