Comparative Study on Multi-Objective Optimization Design Patterns for High-Rise Residences in Northwest China Based on Climate Differences

Abstract

As China’s urbanization rate continues to rise, the scale of high-rise residences also grows, emerging as one of the main sources of building energy consumption and carbon emissions. It is therefore crucial to conduct energy-efficient design tailored to local climate and resource endowments during the schematic design phase. At the same time, consideration should also be given to its impact on economic efficiency and environmental comfort, so as to achieve synergistic optimization of energy, carbon emissions, and economic and environmental performance. This paper focuses on typical high-rise residences in three cities across China’s northwestern region, each with distinct climatic conditions and solar energy resources. The optimization objectives include building energy consumption intensity (BEI), useful daylight illuminance (UDI), life cycle carbon emissions (LCCO2), and life cycle cost (LCC). The optimization variables include 13 design parameters: building orientation, window–wall ratio, horizontal overhang sun visor length, bedroom width and depth, insulation layer thickness of the non-transparent building envelope, and window type. First, a parametric model of a high-rise residence was created on the Rhino–Grasshopper platform. Through LHS sample extraction, performance simulation, and calculation, a sample dataset was generated that included objective values and design parameter values. Secondly, an SVM prediction model was constructed based on the sample data, which was used as the fitness function of MOPSO to construct a multi-objective optimization model for high-rise residences in different cities. Through iterative operations, the Pareto optimal solution set was obtained, followed by an analysis of the optimization potential of objective performances and the sensitivity of design parameters across different cities. Furthermore, the TOPSIS multi-attribute decision-making method was adopted to screen optimal design patterns for high-rise residences that meet different requirements. After verifying the objective balance of the comprehensive optimal design patterns, the influence of climate differences on objective values and design parameter values was explored, and parametric models of the final design schemes were generated. The results indicate that differences in climatic conditions and solar energy resources can affect the optimal objective values and design variable settings for typical high-rise residences. This paper proposes a building optimization design framework that integrates parametric design, machine learning, and multi-objective optimization, and that explores the impact of climate differences on optimization results, providing a reference for determining design parameters for climate-adaptive high-rise residences.

1. Introduction

In recent years, China has witnessed rapid urbanization, with the urbanization rate rising from 37.7% in 2001 to 66.2% in 2023. China’s total building area stood at approximately 71.6 billion square meters, with urban high-rise residences reaching 33.1 billion square meters—roughly 46.2%—in 2023 [1]. According to the “China Urban and Rural Construction Sector Carbon Emissions Research Report (2024)”, the national building operation energy consumption stood at 11.9 billion tce in 2022, of which urban high-rise residences accounted for 4.5 billion tce, or approximately 37.8%. Similarly, building operation carbon emissions reached 23.1 billion tCO₂, with urban high-rise residences being responsible for 8.9 billion tCO₂, or approximately 38.5%. Amid growing constraints on urban land and the need for intensive resource utilization, high-rise residences, which boast the advantages of a compact footprint and high land use efficiency, are poised to become the primary form of urban housing in the future, and their role in energy conservation and emission reduction has garnered increasing attention. The World Green Building Council has also issued carbon reduction guidelines, calling for the built environment to achieve net-zero carbon emissions by 2050 [2]. As carbon emissions have become a global concern, a total of 135 countries have pledged to reach net-zero emissions targets, representing 88% of global carbon emissions [3]. In September 2020, China officially announced its dual carbon goals: to reach a carbon peak by 2030 and achieve carbon neutrality by 2060.

As requirements for energy saving and emission reduction in buildings become increasingly stringent, passive design alone cannot achieve near-zero or zero energy consumption (carbon emissions). The full utilization of renewable energy is therefore an inevitable trend, among which solar energy application technology is currently the most well-developed and easiest to implement. The Chinese standard, “GB 55015 General code for energy efficiency and renewable energy application in buildings”, stipulates that new buildings should be equipped with solar systems, with their design being completed in parallel with architectural design [4]. In 2024, the Chinese government issued the “2024–2025 Energy Conservation and Carbon Reduction Action Plan” and the “Opinions on Accelerating the Comprehensive Green Transformation of Economic and Social Development”, both of which propose requirements for promoting the construction of building-integrated photovoltaic systems. The facades of high-rise residence have a large usable area, and adding PV systems to the facades yields significant energy generation benefits [5]. China’s northwestern region is rich in solar energy resources, offering an inherent advantage for solar energy utilization. By reasonably designing architectural parameters, such as building orientation, room dimensions, and window–wall ratio, the capacity of solar photovoltaic power generation can be improved.

When implementing energy-saving and emission reduction measures in buildings, it is essential to consider their impact on economic and environmental performance. For instance, strategies such as incorporating insulation layers in building envelopes, enhancing window thermal performance, and fitting photovoltaic systems can effectively reduce energy costs during the operational phase. However, these measures also increase initial investment costs [6,7]. Therefore, the whole life cycle cost, which integrates operational costs and initial investment costs, should also be a key consideration. Also, reducing the window–wall area ratio and using multi-layer composite exterior windows can help reduce building energy consumption but may also affect natural daylighting [8,9]. Moreover, these objectives are interrelated. Therefore, when optimizing the design of high-rise residences, one should not focus solely on energy conservation and emission reduction but should comprehensively consider the impact of design parameters on several objectives, such as building energy consumption, carbon emissions, life cycle costs, and natural daylighting.

In response to the diverse requirements of architectural design, many scholars have increasingly shifted their focus from single-objective to multi-objective performance optimization in high-rise residences. For example, Wu et al. [10] conducted a multi-objective optimization design using DesignBuilder (V 5.5) software, with a high-rise residence in Tianjin as a case study, to address the issues of summer overheating and excessive incremental costs in passive low-energy buildings. Yu et al. [11] focused on high-rise residence with near-zero energy consumption, optimizing life cycle cost and primary energy consumption by integrating the NSGA-II with the TRNSYS simulation engine. They obtained a “cost–energy consumption” Pareto solution set that included key variables such as the heat transfer coefficients of external walls, roofs, and exterior windows, as well as heat recovery efficiency. Zhu et al. [12] investigated the influence of exterior wall thermal conductivity coefficients on building energy consumption and cost using plate-type and tower-type high-rise residential buildings in Wuhan as case studies. Zhang et al. [13] selected spatial configuration and building envelope parameters as design variables and optimized cooling and heating loads for high-rise residences in Beijing. Tan [14] established building energy consumption, effective natural daylighting illuminance, and thermal comfort as optimization objectives for high-rise residences in severe cold regions, employing the SPEA-2 algorithm within the Rhino–Grasshopper platform to identify the optimal design schemes and parameter values. Liu et al. [15] used a typical high-rise residence in Hong Kong as an example, combining the NSGA-II with the EnergyPlus simulation engine to examine the influence of future climate change on multi-objective decision making, particularly the trade-offs among operational energy consumption, life cycle cost, and carbon emissions. High-rise residences are typically large in scale and contain numerous rooms, which results in slower building performance simulation speeds. In addition to coupling multi-objective optimization algorithms with building performance simulations, several studies have adopted methods such as model simplification and algorithm assistance to enhance optimization efficiency and reduce computation time [16]. For example, Zhang et al. [17] focused on high-rise residences in Wuhan, employing neural networks and genetic algorithms to develop a model with energy consumption, effective daylighting illuminance, and predicted dissatisfaction rate as the optimization objectives. They identified optimal combinations of passive design parameters, including south and north facing window–wall ratios, and U–values of exterior walls, roofs, and windows. Xue et al. [18] applied the ANN and NSGA-II algorithm to optimize high-rise residences in Harbin, obtaining a solution set involving variables, such as insulation layer thickness, window type, window–wall ratio, and building orientation, aimed at minimizing both life cycle cost and carbon emissions. Nan et al. [19] proposed a multi-stage, multi-objective optimization design framework that integrates BPNN and the NSGA-II algorithm, and applied it to the energy consumption and global cost optimization of high-rise residences in Xi’an. Li et al. [20] selected residential buildings in Nanjing as a case study and conducted optimization using four algorithms—NSGA-II, MOPSO, MOGA, and MODE—with sixteen relevant parameters as variables, and life cycle cost, and CO₂ emissions, as well as thermal comfort as optimization objectives.

The influence of climatic characteristics on architectural design schemes should not be underestimated. Most of the aforementioned studies have focused on individual climatic zones, resulting in notable regional limitations [21]. Some scholars have conducted multi-objective optimization design and comparative analyses under different climatic conditions. Harkouss et al. [22] established a synergistic optimization model for building envelopes and renewable energy systems for net-zero energy residential buildings in Lebanon and France, revealing the coupling mechanisms of building energy consumption, cost and energy balance across different climatic zones. Acar et al. [23] employed the NSGA-II algorithm to carry out the multi-objective optimization design for multi-story residences located in both cold and hot climate regions in Turkey. By comparing more than 13 million design schemes, they established an optimal solution set balancing energy demand and investment costs, and proposed control strategies for the life cycle cost of zero-energy residences. Usman et al. [24] integrated the TRNSYS and the NSGA-III algorithms, analyzing 24 residential cases across 20 climate zones worldwide to construct a passive design parameter optimization model. Through the CRITIC–TOPSIS decision-making method, they achieved a balance between thermal load and cost, establishing climate zone-specific benchmarks for energy-efficient design parameters. Rabani et al. [25] coupled the IDA-ICE with GenOpt to compare the life cycle cost and building energy demands of low-energy buildings in three typical cities in Norway’s cold regions, assessing the energy-saving potential and economic viability of optimal solutions across these cities under varying climatic conditions. Saurbayeva et al. [26] developed a multi-stage sensitivity analysis–multi-objective optimization integration method for residential buildings in four sub-climate zones in arid regions, validating the spatial heterogeneity of optimal solutions for total energy consumption and payback period, i.e., different sub-climate zones require distinct optimal solutions. Li et al. [27] conducted optimization research on two-story residences across five climate regions in China. Utilizing the simulation and optimization plugins in the Grasshopper platform, they optimized thermal comfort, energy consumption, and life cycle cost, and identified the optimal design parameters. Baghoolizadeh et al. [28] used the ANN–EnergyPlus–JEPLUS integrated tool to perform multi-objective optimization for residences in six U.S. climate zones, focusing on carbon emissions, electricity costs and thermal comfort, and developed a climate gradient response model. Ascione et al. [29] combined genetic algorithms with EnergyPlus to conduct multi-objective optimization of energy consumption, total energy costs, and discomfort hours, with a focus on the envelope parameters of residential buildings across four climate zones in Italy. Naji et al. [30] combined TRNSYS with the jEPlus+EA tool to optimize the envelope parameters of prefabricated residential buildings across six climate zones in Australia. Through the synergistic optimization of thermal discomfort, daylighting deficiency duration, and life cycle costs, a performance balance was achieved across different climate zones. Abdou et al. [31] integrated energy efficiency retrofits with photovoltaic (PV) systems to carry out the multi-objective optimization of energy consumption, cost, and thermal comfort for multi-story residences in six climate zones in Morocco. They proposed a design paradigm for the retrofit of net-zero energy buildings in hot and humid climate zones. Wu et al. [32] investigated the optimal design for tapping the photovoltaic utilization potential of facades in nearly zero-energy high-rise residences across China’s five climate zones. With the optimization objectives of minimizing heating and cooling loads, maximizing PV power generation, and minimizing investment costs, they derived optimal design solution sets. The methods mainly employ a combination of performance simulation software (e.g., TRNSYS, ENERGYPLUS, and IDA-ICE) or ML-based prediction models (e.g., ANNs and BPNNs) with optimization algorithms (e.g., NSGAs, MOPSO, and MODE). Machine learning can learn from existing data and automatically optimize itself. As it can achieve a good balance between computational accuracy and time costs, ML has become an important method for evaluating building performance in recent years [33]

In summary, although numerous studies have conducted optimization designs based on combinations of different objectives, significant limitations remain. Firstly, existing studies have mostly focused on individual buildings without considering the shading effects of the surrounding environment, thus failing to account for the impact on natural lighting. Secondly, the consideration of carbon emissions has also been insufficient. Thirdly, the potential for energy conservation and carbon reduction through the utilization of solar photovoltaic power has not been explored. However, in the context of China’s “carbon neutrality” goal, the utilization of renewable energy is an inevitable requirement. Furthermore, regarding the consideration of climate differences, existing research has predominantly centered on comparing the effects of different thermal zones (climate zones), but has not incorporated solar energy resources as a distinguishing factor in conjunction with thermal zones.

In response to the aforementioned problems, this paper selects typical cities (Xi’an, Lanzhou, and Xining) in northwestern China with different thermal zones (severe cold region and cold region) and solar resource zones (very rich zone and rich zone) as its research objects. Based on the established optimization design procedure, it carries out a four-objectives optimization design research for high-rise residences. The specific research objectives are as follows: (1) develop a multi-objective optimization model for high-rise residences based on the SVM prediction model and MOPSO algorithm; (2) obtain the Pareto optimal solution set that balances BEI, UDI, LCCO₂, and LCC; (3) establish optimal design patterns for typical high-rise residences in each city and verify their reliability; (4) and analyze the impacts of climate differences on optimization objective values, design parameter sensitivity, optimal design patterns, and corresponding design parameter values.

2. Methodology

2.1. Optimization Design Procedure

This paper proposes a multi-objective optimization design procedure for high-rise residential buildings, which integrates parametric design and simulation, machine learning prediction, algorithm optimization, and multi-attribute decision making, as shown in Figure 1. A parametric model is established using the Rhino–Grasshopper platform, with controllable variables including building orientation, window–wall ratio, sunshade length, bedroom width and depth, the thickness of the exterior wall and roof insulation layers, and window types. Latin Hypercube Sampling (LHS) is employed to generate diverse high-rise residential design schemes. Honeybee, Ladybug, and self-compiled programs are utilized to simulate energy consumption intensity, useful daylight illuminance, and solar radiation, as well as to calculate life cycle carbon emissions and costs. Subsequently, the sample dataset of “design parameters–objective functions” is generated. Based on this dataset, the SVM algorithm is adopted to construct and verify a performance prediction model. Ultimately, the prediction performance is defined as the objective function in the MOPSO algorithm to search for the Pareto optimal solutions, and the TOPSIS multi-attribute decision-making method is utilized to establish an optimized design pattern for high-rise residential buildings. The computer resources utilized are as follows: CPU: 11th Gen Intel(R) Core i7–11800H 2.30 GHz, RAM: 16.0 GB, and GPU: NVIDIA GeForce RTX 3060.

2.1.1. Parametric Modeling and Simulation: Grasshopper

Parametric design is essentially a form of variable design that assigns parameters to design objects and uses functions to link these parameters. Supported by intelligent algorithms, design automation is achieved, thereby generating the desired outcomes [34]. Rhino–Grasshopper is currently the mainstream parametric design platform. Grasshopper is equipped with a wealth of built-in visual programming components, allowing designers to input architectural geometric parameters and build a parametric information model featuring “variable adjustment–model linkage”. In addition, the platform offers high expandability and supports the integration of building performance analysis tools, connecting parametric building models with environmental performance simulation engines to enhance the flexibility of building performance design. For instance, the Honeybee and Ladybug modules within this tool integrate the EnergyPlus and Radiance engines, enabling building environmental performance analysis using the same model in the Rhino interactive interface. This thus realizes parametric building performance simulation characterized by “one model, multiple calculations”.

Building performance simulation primarily encompasses building energy consumption and natural lighting. The EnergyPlus engine is utilized for energy consumption simulation, and when integrated with CSWD meteorological data, it calculates the building energy consumption intensity. Useful daylight illuminance is derived by running the Radiance simulation engine, natural lighting calculator, and test probe distribution calculator. Specific parameter settings are detailed in Section 2.2.3. Life cycle carbon emissions and costs are computed using self-compiled functions based on energy consumption simulation results. Given that parametric performance simulation involves substantial data volume, such simulations typically require considerable computational time. To improve computational efficiency, the study adopts LHS to generate a small set of statistically representative samples for simulation. For each condition, 1000 groups of sample data for the design variables are randomly selected for calculation, resulting in a total of 3000 datasets across the three conditions.

2.1.2. Prediction Model Construction: SVM

The machine learning algorithms employed for developing building performance prediction models include SVM, ANN, MLR, RF, GB, and others. Among these, SVM is an advanced machine learning technique based on the principle of structural risk minimization. It can establish a continuous functional relationship between inputs and outputs using limited training data, and exhibits high effectiveness in addressing nonlinear problems. Notably, SVM effectively resolves issues such as small samples, nonlinearity, high dimensions, and local optima, while maintaining excellent generalization ability [35,36]. Numerous studies have confirmed the high accuracy of the SVM algorithm in predicting residential performance. For instance, Li et al. [37] used four machine learning algorithms, namely SVM, BPNN, radial basis function neural network, and universal regression neural network, to predict residential energy consumption, and found that SVM exhibited higher prediction accuracy. Ma et al. [38] employed a data mining framework that integrates three machine learning algorithms (MLR, ANN, and SVM) and incorporates a geographic information system (GIS), to assess the annual energy consumption intensity of 3640 residential buildings in New York City. The results indicated that the prediction model based on SVM was more accurate than those based on the other two algorithms. Deng et al. [39] compared the predictive capabilities of four algorithms, namely ANN, SVM, Random Forest (RF), and Gradient Boosting (GB), for the energy consumption intensity of office buildings. The results showed that the prediction accuracy of SVM and RF was significantly higher than that of ANN and GB. The core concept of SVM revolves around determining an optimal classification hyperplane, which aims to minimize the error of all training samples relative to this hyperplane. Specifically, there are n sets of input and output indicators that constitute the training samples, as shown in Equation (1). It is assumed that the linear regression function established between the input and output in the high-dimensional feature space is given by Equation (2).

$$T=\{\left(x_1,y_1\right),\left(x_2,y_2\right),\dots ,(x_n,y_n)\}$$

(1)

Therein, T is the training sample, x is the input indicator, and y is the output indicator.

$$f\left(x\right)=W^{T}x+b$$

(2)

Therein, W is the weight coefficient vector; b is the bias term.

To optimize this problem and ensure its solvability, the algorithm introduces non-negative relaxation variables ξi and ξi*, as well as a Lagrange function, to convert the constrained optimization problem into an unconstrained one. Ultimately, the regression function of SVM is obtained as shown in Equation (3).

$$f(x)={\displaystyle \sum _{i=1}^n\left({\alpha }_i-{\alpha }_i^{*}\right)}K(x_i,x)+b$$

(3)

Therein, n is the number of support vectors, ${\alpha }_i$ and ${\alpha }_i^{*}$ are Lagrange multipliers, and $K(x_i,x)$ is the kernel function.

The RBF is used to train the model to learn the inherent relationship between the input variables and output indicators. Existing studies have demonstrated that RBF has excellent fitting capabilities in building performance prediction. By adjusting appropriate parameter settings, the predictive ability of the model can be significantly enhanced [40,41]. The basic process for establishing such a prediction model is as follows:

① Select representative input sample data;

② Simulate the selected input samples to obtain the output data;

③ Train the prediction model using the input and output sample data;

④ Apply error assessment indicators to verify the prediction model’s performance.

2.1.3. Multi-Objective Optimization Algorithm (MOPSO)

The Particle Swarm Optimization (PSO) algorithm, inspired by the collective foraging behavior of birds, was proposed by Eberhart and Kennedy in 1995. It is a promising intelligent optimization algorithm [42]. The algorithm’s success in single-objective optimization has spurred the development of multi-objective particle swarm optimization (MOPSO), which is designed to address multi-dimensional optimization requirements. This algorithm offers the advantages of a simple structure, few parameters, and strong global search capability, with its performance having been validated in practical engineering applications, such as in the study by Moore et al. [43], who were the first to attempt to apply MOPSO to search for multiple optimal solutions. Delgarm et al. [44] coupled EnergyPlus with MOPSO on the MATLAB platform to conduct multi-objective optimization research on the building energy consumption of heating, cooling, and lighting in Iran. The resulting Pareto optimal solution set significantly improved building energy performance, thus confirming MOPSO’s excellent optimization capabilities. The core principle of this algorithm is to determine the individual optimal solution (pBest) and the global optimal solution (gBest) based on Pareto theory. During algorithm execution, particle movement is guided by their pBest and gBest of the entire population, both of which are continuously updated. Therefore, the accurate determination of pBest and gBest is crucial for Pareto-based MOPSO [45]. The basic optimization process of MOPSO is as follows:

① Set the population size and maximum iteration count of the particle swarm;

② Initialize the particle swarm so as to obtain the initial positions of n particles;

③ Input the particle positions into the fitness function to derive the function values for each particle;

④ Determine the pBest and gBest based on the fitness function values of the particles;

⑤ Update the particle’s velocity and position in accordance with Equations (4) and (5).

$$v_{id}^{t+1}=\omega v_{id}^t+c_1{r}_{1d}^t(pBes{t}_{id}^t-x_{id}^t)+c_2{r}_{2d}^t(gBes{t}_{id}^t-x_{id}^t)$$

(4)

$$x_{id}^{t+1}=x_{id}^t+v_{id}^{t+1}$$

(5)

Therein, $\omega$ is the inertial weight; $c_1$,$c_2$ is the learning factor, that is acceleration constants; $r_{1d}$,$r_{2d}$ is the random number within [0, 1]; and t is the iteration count.

⑥ Check whether the termination conditions have been satisfied. If they have, output the optimal value; if not, go back to step 3.

2.1.4. Multi-Attribute Decision-Making Method—TOPSIS

To further screen the optimal design solutions, the technique for order preference by similarity to an ideal solution (TOPSIS), a multi-attribute decision-making method, is introduced. This method quantifies evaluation objects by first constructing “positive ideal solutions” and “negative ideal solutions”, then calculating the relative distance between each alternative and the ideal solutions, and finally ranking these alternatives to identify the optimal one [46]. The calculation steps are as follows:

(1)

Construct an evaluation matrix.

Assume that there are n design schemes, namely $\mathrm{P}=\left\{\left.{\mathrm{P}}_1,{\mathrm{P}}_2,\dots {\mathrm{P}}_{\mathrm{n}}\right\}\right.$, and the set of m optimization objectives for each scheme is $C=\left\{\left.C_1,C_2,\dots C_{\mathrm{m}}\right\}\right.$. $x_{ij}$ is the original value of the i-th indicator in the j-th scheme. The original matrix X for target decision making can be written as Equation (6).

$$\mathrm{X}=\left[\begin{array}{cccc}{\mathrm{x}}_{11}& {\mathrm{x}}_{12}& \cdots & {\mathrm{x}}_{1\mathrm{n}}\\ {\mathrm{x}}_{21}& {\mathrm{x}}_{22}& \cdots & {\mathrm{x}}_{2\mathrm{n}}\\ ⋮& ⋮& ⋮& ⋮\\ {\mathrm{x}}_{\mathrm{m}1}& {\mathrm{x}}_{\mathrm{m}2}& \cdots & {\mathrm{x}}_{\mathrm{mn}}\end{array}\right]$$

(6)

(2)

Standardized evaluation matrix.

To eliminate dimensional discrepancies among different objectives, normalization is performed, that is, all objective values are standardized to the range of [0, 1]. In this paper, each objective is defined as a cost-type objective, where smaller values are more favorable for the results. The normalization method is given in Equation (7).

$${\mathrm{y}}_{\mathrm{ij}}={\displaystyle \frac{\underset{\mathrm{i}}{\max } {\mathrm{x}}_{\mathrm{ij}}-{\mathrm{x}}_{\mathrm{ij}}}{\underset{\mathrm{i}}{\max } {\mathrm{x}}_{\mathrm{ij}}-\underset{\mathrm{i}}{\min } {\mathrm{x}}_{\mathrm{ij}}}}$$

(7)

(3)

Assign weights to the matrix and determine the optimal solution.

To ensure that design proposals are compared under identical conditions, the subjective weighting method is adopted, with a total weight of one assigned to each objective. In this method, the weighting coefficients reflect the preferences of decision makers, and the weighting values can be adjusted to align, with the varying requirements for the four objectives [47]. The empowerment process is shown in Equations (8) and (9), and the ideal solution for the m objectives in matrix Z is finally obtained as ${\mathrm{Z}}_0=\left\{\left.{\mathrm{Z}}_{10},{\mathrm{Z}}_{20},\dots {\mathrm{Z}}_{\mathrm{m}0}\right\}\right.$.

$${\mathrm{Z}}_{\mathrm{ij}}=\omega \cdot {\mathrm{y}}_{\mathrm{ij}}$$

(8)

$$\mathrm{Z}=\left[\begin{array}{cccc}{\mathrm{z}}_{11}& {\mathrm{z}}_{12}& \cdots & {\mathrm{z}}_{1\mathrm{n}}\\ {\mathrm{z}}_{21}& {\mathrm{z}}_{22}& \cdots & {\mathrm{z}}_{2\mathrm{n}}\\ ⋮& ⋮& ⋮& ⋮\\ {\mathrm{z}}_{\mathrm{m}1}& {\mathrm{z}}_{\mathrm{m}2}& \cdots & {\mathrm{z}}_{\mathrm{mn}}\end{array}\right]$$

(9)

Therein, $\omega$ is the weighting coefficient of the j-th scheme, 0 ≤ $\omega$ ≤ 1.

(4)

Evaluate the distance from the ideal solution and rank the design schemes.

After assigning weights, a comprehensive evaluation is performed on each design scheme to assess its proximity to the positive and negative ideal solutions. The schemes are then ranked accordingly, with the optimal design scheme identified ultimately. The proximity degree usually falls within the range [0, 1]. The closer the value is to one, the more optimal the design scheme and the higher its ranking. The positive ideal solution is composed of the optimal values derived from each evaluation criterion, while the negative ideal solution consists of the worst-performing values. The formulae for calculating the distance between the design scheme and ideal solution are shown in Equations (10)–(12).

$${\mathrm{D}}_{\mathrm{j}}^{+}=\sqrt{{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{m}}{\omega }_{\mathrm{i}}\left({\mathrm{Z}}_{\mathrm{i}}^{+}-{\mathrm{z}}_{\mathrm{i}\mathrm{j}}\right)}}^2}$$

(10)

$${\mathrm{D}}_{\mathrm{j}}^{-}=\sqrt{{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{m}}{\omega }_{\mathrm{i}}\left({\mathrm{Z}}_{\mathrm{i}}^{-}-{\mathrm{z}}_{\mathrm{i}\mathrm{j}}\right)}}^2}$$

(11)

$${\mathrm{C}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{j}}}{{\mathrm{D}}_{\mathrm{j}}^{+}+{\mathrm{D}}_{\mathrm{j}}^{-}}}$$

(12)

Therein, ${\mathrm{C}}_{\mathrm{i}\mathrm{j}}$ is the extent to which each solution approximates the ideal one, ${\mathrm{D}}_{\mathrm{j}}^{+}$ is the distance between the j-th solution and ${\mathrm{Z}}_{\mathrm{i}}^{+}$(the positive ideal solution), and ${\mathrm{D}}_{\mathrm{j}}^{-}$ is the distance between the j-th solution and ${\mathrm{Z}}_{\mathrm{i}}^{-}$(the negative ideal solution).

2.2. Case Studies of Three Cities with Different Climatic Characteristics

2.2.1. Climate Characteristics

The climate differences addressed in this paper are mainly reflected in thermal design zoning and solar energy resource zoning. In accordance with the provisions of “GB50176–2016 Thermal Design Code for Civil Building” [48] and “GB/T31155–2014 Classification of Solar Energy Resources—Global Radiation” [49], combined with the regional characteristics of the northwest region and the similarities of high-rise residential building design, Xi’an (Shaanxi Province), Lanzhou (Gansu Province), and Xining (Qinghai Province) were selected as typical cities. The climate differences among cities are shown in

Table 1. Climate differences in three cities.

City	Thermal Design Zoning	Annual Total Solar Radiation	Solar Energy Resource Zoning
Xi’an	Cold Zone B	1201~1300 kW·h/m2	Rich zone
Lanzhou	Cold Zone A	1401~1500 kW·h/m2	Very rich zone
Xining	Severe Cold Zone C	1501~1600 kW·h/m2	Very rich zone

, and the location distribution is shown in Figure 2.

The mean monthly dry bulb temperature and total amount of solar radiation of the three cities are presented in Figure 3 and Figure 4. The monthly average temperature changes are similar in each city, with the minimum value occurring in January and the maximum value in July. The annual average temperatures of Xi’an, Lanzhou, and Xining are 14.1 °C, 10.2 °C, and 5.9 °C, respectively, while their corresponding annual total solar radiations are 4262.1 MJ/m², 5041.9 MJ/m², and 5601.0 MJ/m² (1 kW·h/m² ≈ 3.6 MJ/m²). It can be seen that the three cities exhibit significant differences in temperature, solar radiation, etc. Therefore, in the design process, the impact of climatic differences on building performance and the values of design parameters should be fully considered.

2.2.2. Parametric Model

To ensure the representativeness of the established model, a survey was first conducted in high-rise residential areas across three cities. The survey contents cover morphological design parameters such as the land area and layout form of residential areas, building height etc., as well as unit type design parameters including floor plan layout, areas, and dimensions etc., and the building envelope construction. Newly built high-rise residential buildings constructed over the past five years (from 2019 to 2023) were selected, and a combination of online and on-site investigation methods was adopted. For the online survey, Gaode Map and the National Geographic Information Public Service Platform (Tian map) were used as the primary data sources, with Tencent Map and Baidu Map serving as supplementary data sources. The on-site investigation was carried out by contacting the property department of the residential areas to obtain design drawings and relevant data. Finally, data were collected for 62 high-rise residential areas (including 821 high-rise residences) and 284 unit types. Through statistical analysis of residential area form (land area, floor area ratio, layout form, and building height), unit type attributes (plan layout, area, and dimensions) and enclosure structures (exterior wall, roof, and windows), the spatial form and design features of typical high-rise residences were extracted, thus identifying several typical spatial patterns. Taking one typical pattern as an example, parametric models were established using the Rhino–Grasshopper platform, which serve as the foundation for subsequent building performance simulation and optimization.

High-rise residences are usually presented in a cluster layout form. Surrounding buildings can affect sunlight access, natural lighting, etc. Therefore, the surrounding spatial patterns of high-rise residences were first analyzed and extracted. According to the analysis of land use scale and floor area ratio of high-rise residential area, a parallel layout consisting of six buildings arranged in two rows and three columns is adopted, as illustrated in Figure 5. The high-rise residence (yellow blocks) located at the most disadvantageous position is selected as the research object to ensure the resulting design scheme has broader applicability. Combined with the building spacing requirements for residential buildings specified in “GB 50180-2018 Standard for Urban Residential Area Planning and Design” [50], and through sunlight simulation analysis, the north–south spacing is determined to be 40 m, with the east–west spacing set at 20 m. In line with the survey results, the high-rise residences are defined as 26-story buildings with a south-facing orientation.

For single-building high-rise residence, the two-elevator, four-unit layout is the predominant floor plan form, accounting for 85% of the survey samples. Accordingly, this layout is designated as the typical floor plan configuration for high-rise residences, with the standard floor plan shown in Figure 6, where it integrates a three-bedroom, two-living room layout with a two-bedroom, two-living room layout. The specific design parameters are presented in

Table 2. Design parameters for typical high-rise residence.

Design Parameter		Typical Residential Building
Number of stories		26 story
Building height		3.0 m
Building orientation		South
Combination type		A: three-bedroom, two-living room B: two-bedroom, two-living room
Floor area		A 109.24 m2 B 83.43 m2
Window–wall area ratio	North	0.25
	East, West	0.10
	South	0.45

, the building envelope construction and heat transfer coefficients are detailed in

Table 3. Building envelope construction and heat transfer coefficient of typical high-rise residence.

Parts	Construction	Heat Transfer Coefficient
External window	5 mm clear glass + 12 air + 5 mm clear glass + 12 air + 5 mm clear glass	1.7 W/m2·K
External wall	20 mm mixed mortar + 200 mm reinforced concrete + 20 mm cement mortar + 80 mm XPS + 20 mm cement mortar	0.4 W/m2·K
Roof	30 mm fine aggregate concrete + 30 mm expanded clay aggregate concrete + 100 mm XPS + 100 m reinforced concrete + 20 mm cement mortar	0.3 W/m2·K

, and the parametric model is depicted in Figure 7.

The installation of solar photovoltaic systems in high-rise residences should comply with the provisions of “CECS 418: 2015 Technical specification for integration of building and solar photovoltaic system”. The installation location must ensure that there is more than 3 h of sunlight throughout the day on the winter solstice [51]. By simulating solar radiation on building facades with different orientations, and ensuring an effective comparison of BEI across three cities, the following uniform settings are adopted: photovoltaic panels are installed on building rooftops and the south-facing exterior wall surfaces above the 16th floor (excluding window areas). Rooftop photovoltaic panels are mounted at a 30° inclination angle, while wall-mounted panels are installed vertically.

2.2.3. Objective Function

This section defines the calculation methods for four optimization objectives (building energy consumption intensity, useful daylight illuminance, life cycle carbon emissions, and life cycle cost), converting these objectives into quantifiable objective functions to ensure the accuracy of performance evaluation in the subsequent optimization process.

(1)

Building energy consumption intensity (BEI)

Operational energy consumption refers to the external energy introduced during a building’s service life, encompassing energy expended on maintaining the building’s environment (e.g., heating, cooling, and lighting) and that consumed by various in-building activities, such as the operation of electrical appliances and the preparation of domestic hot water. Relevant studies have indicated that operational energy consumption accounts for over 80% of a building’s life cycle energy use [52], with heating and cooling energy consumption constituting the largest proportion. This paper focuses on the scheme design phase, emphasizing the energy consumption of building itself in maintaining its environment, excluding energy used for electrical appliances, domestic hot water, etc., where energy consumption for heating and cooling account for the dominant share.

China’s national standard “GB 55015-2021 General code for energy efficiency and renewable energy application in buildings” [4] stipulates that new buildings shall be equipped with solar energy systems to improve energy efficiency. Owing to their height advantage, high-rise residences are more suitable for photovoltaic systems, which helps to enhance the utilization rate of renewable energy. Therefore, photovoltaic systems should be incorporated into the building design stage. In accordance with the provisions of “GB/T 51366-2019 Standard for building carbon emission calculation” [53], the annual electricity output of a photovoltaic system can be calculated using Equation (13).

$$E_{pv}=I\times K_E\left(1-K_S\right)A_p$$

(13)

Therein, E_pv is the yearly electricity output of photovoltaic system, kWh; I is the yearly solar irradiance on the surface of photovoltaic cells, kWh·m⁻²; K_E is the energy conversion rate of photovoltaic cell, taken as 15%; K_S is the efficiency loss of photovoltaic system, taken as 25%; and A_p is the net surface area of photovoltaic modules, m².

This paper designates building energy intensity (BEI) as one of the optimization objectives, defined as the annual energy consumption per unit of building floor area. It is calculated by subtracting the annual electricity generation of photovoltaic system from the total annual building energy consumption, where the latter can be extracted from the output results of the EnergyPlus simulation engine. The method used to calculate BEI is illustrated in Equation (14).

$$\mathrm{BEI}={\displaystyle \frac{1}{A}}\left[{\displaystyle \frac{E_{\mathrm{H}}}{{\eta }_{\mathrm{H}}}}+{\displaystyle \frac{E_C}{{\eta }_{\mathrm{C}}}}+E_L-E_{pv}\right]$$

(14)

Therein, BEI is the building energy consumption intensity, kWh·m⁻²; A is the building area, m²; E_H is the heating energy consumption, kWh; η_H is the heating system efficiency, taken as 0.8 [18]; E_C is the cooling energy consumption, kWh; η_C is the cooling system efficiency, taken as 3.0 [54]; E_L is the lighting energy consumption, kWh; and E_pv is the yearly power output of photovoltaic systems, kWh.

The parameters related to energy consumption simulation are specified as follows: the heating period in Xi’an spans from 15 November through to 15 March of the next year; in Lanzhou, it runs from 1 November to 31 March; and in Xining, it extends from 15 October to 15 April. The indoor heating and cooling set temperatures are 18 °C and 26 °C, respectively. Bedrooms, living rooms, kitchens, and bathrooms are designated as heating and air conditioning zones, while other auxiliary rooms are classified as non-heating and non-air conditioning zones. The heating system operates 24 h a day. The cooling demands in the three cities are mainly concentrated in the summer. The cooling period is set from 15 June to 15 September, and the air conditioning system is set to the ideal mode. Relevant studies have shown that different control strategies can affect the simulation results of building energy consumption [55]. To accurately reflect real-world usage scenarios and achieve better energy-saving effects, a natural ventilation control method is utilized to optimize the operation time of the air conditioning system. That is, based on the set cooling temperature, window opening and air conditioning system activation are controlled by comparing indoor and outdoor temperatures. The control strategy is shown in

Table 4. Control strategies of air conditioning systems and natural ventilation.

Outdoor Temperature, ℃	Indoor Temperature, ℃	Air Conditioning System	Natural Ventilation
>26	≥26	on	off
≥26	<26	off	off
<26	≥26	off	on
<26	≤26	off	off

.

The occupancy rate, lighting, and electrical equipment usage time are set according to the recommended values in the energy-saving design specifications [4]: the occupancy density is 0.25 people/m², the lighting power density is specified as 5.0 W/m², the power density of electrical devices is configured to be 3.8 W/m², and the rate of air exchange is set as 0.5 h⁻¹.

(2)

Useful daylight illuminance (UDI)

UDI is adopted as the evaluation index for the daylighting performance. This index was first proposed by Nabil and Mardaljevic in 2005 [56], and is used to assess the effective utilization of natural daylight in building spaces, as it accounts for both excessively high and low illuminance levels. The illuminance level is divided into three intervals: below 100 lx, between 100 lx and 2000 lx, and above 2000 lx, while considering the visual comfort at each level. When indoor illuminance is less than 100 lx, basic visual needs cannot be met, and artificial lighting is therefore required to ensure the basic space lighting requirements. When illuminance exceeds 2000 lx, glare may occur, leading to visual discomfort. In this case, shading measures or adjusting to exterior window design should be implemented to reduce illuminance value and improve visual comfort [57]. It is more appropriate to maintain the illuminance between 100 lx and 2000 lx. This not only meets lighting requirements but also avoids increased lighting energy consumption and visual discomfort.

Therefore, taking UDI_{100~2000 lx} as the optimization objective, the higher the value, the better the lighting performance. The UDI calculation for a single measurement point is shown in Equation (15). The UDI of the entire building is the arithmetic mean of all measurement points.

$${\mathrm{UDI}}_{100-2000\mathrm{lx}}={\displaystyle \frac{T_{\mathrm{UDI}}}{8760}}\times 100\%$$

(15)

Therein, UDI_{100~2000 lx} is the useful daylight illuminance at one measurement point, %; T_UDI is the number of hours in a year when the natural lighting is between 100 and 2000 lx, hours.

Using the Honeybee plugin in Rhino–Grasshopper platform, and invoking the Daysim and Radiance simulation engines, an hourly daylighting performance simulation was conducted, with directly output of UDI_{100~2000 lx} value. Lighting grid points were divided at a spacing of 0.5 m, and the working surface height was defined as a horizontal plane 0.75 m above the ground. The optical parameters of the building envelope and materials were set in accordance with the “GB 50033-2013 Standard for Daylighting Design of Buildings” [58], as follows: the reflectivity of exterior walls and roofs was 0.32; the interior walls and ceilings were painted with white plaster, with a reflectivity of 0.75; the floor adopted light-colored wooden flooring, with a reflectivity of 0.58; the shading panel has a reflectivity of 0.2; and the roughness of all materials was set to 0.05. The visible light transmittance of exterior window was set according to the window types.

(3)

Life cycle carbon emission (LCCO2)

LCCO₂ is mainly used to assess carbon dioxide emissions generated by buildings throughout all phases of the life cycle [59]. Research indicates that carbon emissions from building operation, as well as the production and transportation of materials, account for approximately 90% of total LCCO₂ [60,61]. Therefore, in this paper, the scope of LCCO₂ is confined to emissions produced during material production and building operation stages, excluding the construction and demolition stages. In addition, since this optimization design does not involve any changes in the materials transportation, emissions associated with this stage are not included in the calculation. China’s national standard “GB/T 51366-2019 Standard for building carbon emission calculation” [53] stipulates the use of carbon emission factors (CEF) for calculating building carbon emissions. As high-rise residences are equipped with photovoltaic systems, the carbon reduction achieved through photovoltaic power generation must be incorporated into the calculation. To more intuitively demonstrate the differences between schemes and the carbon reduction potential of optimized schemes, domestic hot water systems and carbon sinks, etc., are not included in the calculation. This study adopts a 30-year life cycle period. It is assumed that insulation materials, windows, and shading devices, etc., will not be replaced during this period; hence, the carbon emissions generated during materials production are calculated on a one-time basis.

The calculation method of LCCO₂ is shown in Equation (16). Among them, carbon emissions during the operation stage mainly originate from building energy consumption. The intensity values of heating, cooling, and lighting energy consumption need to be converted into energy values with the same unit as the supplied energy, and then multiplied by the corresponding energy carbon emission factors [62].

$${\mathit{LCCO}}_2=\sum _{i=1}^m{Q}_i\cdot f_i+n\cdot \left[{\displaystyle \frac{E_H}{H\cdot {\eta }_H}}\cdot f_c+\left({\displaystyle \frac{E_C}{{\eta }_C}}+E_L-E_{PV}\right)\cdot f_e\right]$$

(16)

Therein, LCCO₂ is the carbon emissions per unit building area over the life cycle, kgCO₂·m⁻²; i refers to the building materials; Q_i is the quantity of i; f_i is the carbon emission factor of I; n is the life cycle years, set as 30; H is the conversion coefficient between thermal energy and coal, kWh·(kg)⁻¹, set as 8.14 [63]; f_c is the carbon emission factor of coal, kgCO₂·(kg)⁻¹, set as 2.77 [53]; and f_e is the carbon emission factor of local power grid, kgCO₂·(kWh)⁻¹, set as 0.6671 [53].

(4)

Life cycle cost (LCC)

LCC analysis is a method for evaluating the economic benefits associated with project costs, and serves as a key indicator for measuring the economic feasibility of design schemes. It enables a comprehensive assessment of design decisions from the perspective of long-term economic efficiency [22,64]. According to the international standard ISO 15686-5: 2017 [65], the life cycle cost includes design and construction costs, operation costs, maintenance costs, and dismantling costs. The life cycle is also set at 30 years, with the assumption that the building envelope and components do not require replacement or maintenance during this period. In terms of investment cost, given that the main structures, labor costs, and transportation costs are largely identical across different design schemes, there is no need to calculate the absolute value of the initial investment cost. Only the incremental cost resulting from changes in design parameters need to be calculated. Therefore, the LCC in this paper contains the additional cost of the optimized design and the energy cost during operation (including the cost of energy savings from photovoltaic system). The calculation method is shown in Equation (17).

$$\mathrm{LCC}=dIC+{\displaystyle \sum _{i=1}^{n}a(r_e,i)\cdot EC}$$

(17)

Therein, dIC represents the investment cost difference between reference building and optimized scheme, ¥·m⁻²; a is the present value factor; r_e is the actual interest rate, %; i is the number of years after the cost occurs (after the starting year); and EC is the yearly energy cost, ¥·m⁻².

The present value factor (a) depends on the r_e and i, and its calculation is shown in Equations (18)–(20).

$$a={\displaystyle \frac{1-{(1+r_e)}^{-i}}{r_e}}$$

(18)

$$r_e={\displaystyle \frac{r-e}{1+e}}$$

(19)

$$r={\displaystyle \frac{r_i-f}{1+f}}$$

(20)

Therein, r is the market interest rate adjusted for inflation rate, %; e is the increase rate of energy price throughout the life cycle, %, set as 1.2% [10]; r_i is the benchmark interest rate, %, set as 4.9% [66]; and f is the inflation rate, %, set at 2% [18].

The annual energy cost (EC) is defined as the total expenditure of heating, cooling, and lighting energy consumption minus the revenue generated from photovoltaic power generation. The calculation method is given in Equation (21).

$$EC={\displaystyle \frac{E_{\mathrm{H}}}{H\cdot {\eta }_{\mathrm{H}}}}\cdot P_{\mathrm{c}}+({\displaystyle \frac{E_{\mathrm{C}}}{{\eta }_{\mathrm{C}}}}+E_{\mathrm{L}}-E_{\mathrm{pv}})\cdot P_{\mathrm{e}}$$

(21)

Therein, P_c is the price of coal, ¥·kg⁻¹; P_e is the price of electricity energy, ¥·kWh⁻¹.

2.2.4. Optimization Design Variables

The rational selection of design variables directly impacts the achievement of the final objectives. In the schematic design stage, the design parameters controllable by architects are first screened out, then categorized into spatial form parameters and building envelope parameters, and the value ranges of the design variables are determined based on the survey results of high-rise residences. This paper selects thirteen design parameters as optimization variables, including ten spatial form parameters (e.g., building orientation, sunshade design, window−wall ratio, and main room dimensions) and three building envelope parameters (e.g., insulation layer thickness and window type).

Building orientation refers to the angle between the normal of a building’s main facade and the south direction. It exerts a notable influence on solar radiation reception and serves as a key factor during the building scheme design stage. In cold and severe cold regions, the orientation of high-rise residences directly affects heating, cooling, and lighting performance, thereby determining energy consumption efficiency, indoor light environment quality, and carbon emission levels. The window−wall ratio is one of the core parameters for controlling windows size, defined as the ratio of the total exterior window area to the total wall area of a specific orientation. As a key factor affecting building energy consumption, it is closely associated with environmental requirements such as indoor lighting. In high-rise residences, east- and west-facing windows are relatively small or even absent. Therefore, the window−wall ratios of the south and north facades are key aspects to be optimized. High-rise residences usually adopt horizontal overhang sun visors, which are installed at the upper edge of exterior windows and can not only enhance the layering effect of facade design but also ensure pleasant visual comfort within the residential building. Since the south facade receives the most solar radiation and typically has the largest window area, sun visors are installed on the south facade, with the overhang length selected as the design variable for optimization.

The bedroom, as a fundamental functional space in a residence, is also the room type accounting for the largest area proportion. Its size directly affects living comfort. Currently, the bedroom space in high-rise residence is gradually expanding, with each unit type equipped with at least two bedrooms, as shown in Figure 8. Based on the room location and orientation, bedrooms are divided into the main bedroom, south-facing secondary bedroom, and north-facing secondary bedroom. Six design parameters are established, including the main bedroom width, main bedroom depth, south-facing secondary bedroom width, south-facing secondary bedroom depth, north-facing secondary bedroom width, and north-facing secondary bedroom depth. To meet actual usage requirements and avoid affecting the normal spatial scale of other rooms, extreme design scenarios (e.g., overly long or narrow rooms) are excluded. During the adjustment of design parameters, the following rule was maintained: the main bedroom area > south-facing secondary bedroom area > north-facing secondary bedroom area.

The thermal insulation performance of exterior walls and roofs, as the primary components of non-transparent envelopes, is determined by the heat transfer coefficient. At present, the predominant approach to improve this indicator in engineering practice is to incorporate an insulation layer. Since the load-bearing structure remains unchanged during the optimization process, the thickness of the exterior wall and roof insulation layers are selected as optimization variables, with extruded polystyrene board (XPS) adopted as the insulation material. Based on the limit values of heat transfer coefficients for exterior walls and roofs [4], the range of the insulation layer thickness is determined. The exterior windows consist of window frames and glass, which are composed of glass plates, gas fillers, and spacers, and the thermal performance of exterior windows is jointly determined by these materials. Combining relevant standards with survey results, five types of exterior windows are selected as optimal design variables. The specific types and parameters are illustrated in

Table 5. Exterior window types and physical properties.

Window Types and Materials	Heat Transfer Coefficient, W/m2·K	Sun Shading Coefficient	Visible Light Transmittance
1. Broken bridge aluminum window 5 + 12 A + 5 + 12 A + 5	1.70	0.78	0.737
2. Broken bridge aluminum window 5 + 12 Ar + 5 + 12 Ar + 5 Low-E	1.50	0.51	0.590
3. Broken bridge aluminum window 5 + 12 A + 5 + 12 A + 5 Low-E	1.30	0.70	0.667
4. Broken bridge aluminum window 5 + 12 Ar + 5 Low-E + 12 Ar + 5 Low-E	0.90	0.62	0.581
5. Aluminum–wood composite window 5 + 12 A + 5 + 12 A + 5	0.80	0.62	0.664

. Room dimensions, shading size, and other relevant parameters are determined based on surveys and building design datasets [67].

In summary,

Table 6. Optimization design variables and parameters of a typical high-rise residence.

Optimization Design Variables	Symbol	Type	Range	Step
Building orientation	O	Continuous variable	[−45°, 45°]	5°
South window–wall ratio	Swwr	Continuous variable	[0.25, 0.50]	0.05
North window–wall ratio	Nwwr	Continuous variable	[0.10, 0.30]	0.05
Horizontal overhang sun visor length	SD	Continuous variable	[0, 1.5]	0.1
Main bedroom width	MW	Continuous variable	[3.0, 3.9]	0.1
Main bedroom depth	ML	Continuous variable	[3.6, 4.5]	0.1
South secondary bedroom width	SW	Continuous variable	[2.7, 3.3]	0.1
South secondary bedroom depth	SL	Continuous variable	[3.6, 4.2]	0.1
North secondary bedroom width	NW	Continuous variable	[2.7, 3.5]	0.1
North secondary bedroom depth	NL	Continuous variable	[2.8, 3.6]	0.1
Wall insulation layer thickness	WT	Continuous variable	[0.08, 0.30]	0.02
Roof insulation layer thickness	RT	Continuous variable	[0.10, 0.32]	0.02
Window type	W	Discrete variable	W1~5	/

summarizes the optimization variables and parameters for high-rise residences. The cost information and carbon emission factors of related materials and energy are displayed in

Table 7. Cost and carbon emission factors of materials.

Name	Material	Price	c
Sun visor	60 mm concrete slab	120 ¥/m2	295 kgCO2/m2
Insulation layer thickness	Extruded polystyrene board (XPS)	650 ¥/m3	5020 kgCO2/t
Exterior window	W1	920 ¥/m2	194 kgCO2/m2
	W2	1200 ¥/m2
	W3	1500 ¥/m2
	W4	1900 ¥/m2
	W5	2300 ¥/m2	122.5 kgCO2/m2
Photovoltaic panel	Monocrystalline silicon solar panels	630 ¥/m2	30 kgCO2/m2

and

Table 8. Cost and carbon emission factors of energies.

Energy Type	Price	Monocrystalline Silicon Solar Panels
Coal	2.2 ¥/kg	2.19 kgCO2/kg
Electricity	Xi’an: 0.50 ¥/m2	0.6671 kgCO2/kWh
	Lanzhou: 0.51 ¥/m2
	Xining: 0.38 ¥/m2

.

2.2.5. Establishment of Prediction Model

By integrating the parameterized model, objective functions, and design variables, the Grasshopper plugin DSE was employed to couple with the performance model of high-rise residences for LHS of the design variables, and to complete the calculation of four objective functions. Using the generated “design variables–objective function” sample dataset, a multi-objective prediction model was established on the MATLAB R2021b platform. The sample data were split into a training set and a test set at a ratio of 8:2 [57]. That is, 800 groups were used as the training set to develop the SVM prediction model, while 200 groups served as the test set to verify the model’s accuracy. The cross-validation method was applied to find the optimal parameters of the kernel function RBF: c (the penalty factor) and g (the variance of kernel function) Subsequently, the model was trained using the optimal parameters.

Two error evaluation indicators, R² and MSE, are employed to assess the predictive performance of the model. R² (coefficient of determination) serves as an indicator for measuring the overall fitting error. The calculation method is presented in Equation (22). Generally, a model with R² > 0.9 is considered reasonable, one with R² > 0.95 is regarded as precise, and with R² > 0.99 can be deemed nearly perfect [34].

$${\mathrm{R}}^2=1-{\displaystyle \frac{{{\displaystyle \sum _{i=1}^n\left(y_i-{\widehat{y}}_i\right)}}^2}{{{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}}^2}}$$

(22)

Therein, n is the sample count of test set, $y_i$ is the true value, $\widehat{y_i}$ is the predicted value, and $\overline{y}$ is the average of true values.

The mean squared error (MSE) is a metric used to quantify the discrepancy between predicted values and actual values, and its calculation is expressed in Equation (23). This metric evaluates a model’s predictive performance by computing the average of the squared difference between the predicted values and true values. MSE is particularly sensitive to larger errors; if a model yields prediction with significant deviations, the MSE will rise substantially, thereby indicating the model requires further refinement.

$$\mathrm{MSE}={\displaystyle \frac{1}{n}}{{\displaystyle \sum _{i=1}^n\left(y_i-{\widehat{y}}_i\right)}}^2$$

(23)

In this paper, SVM prediction models were established for typical high-rise residences in Xi’an, Lanzhou, and Xining, respectively. The input parameters of the models include thirteen optimization design variables, while the output parameters consist of four objective functions. Through validation tests, the optimal parameters for RBF were determined as c = 4.0 and g = 0.8. Using these parameters, 800 sets of data were trained to develop SVM prediction models for each objective with respect to the design variables. Then, 200 sets of data from the test set were used for verification. Taking Xi’an City as an example, the test results are shown in Figure 9. Specifically, for BEI, MSE = 0.0519, R² = 0.9977; for UDI, MSE = 0.0229, R² = 0.9971; for LCCO₂, MSE = 2.077, R² = 0.9967; and for LCC, MSE = 4.1645, R² = 0.9970. It indicates that the discrepancy between the simulated values and predicted values is extremely small, and the predicted results are reliable. Notably, the R² of all prediction models exceed 0.95. Similarly, the performance of the prediction models for the other two cities also meets the required standards and detailed results are provided in Appendix A.

2.2.6. Development of Optimization Model

A multi-objective optimization model is established by developing the MOPSO algorithm on the MATLAB platform and coupling it with the SVM prediction model. The MOPSO algorithm can directly invoke the prediction model of each optimization objective, which is adopted as the fitness function for optimization calculations. For the optimization objective of the UDI value, a larger value indicates better performance. Regarding other objectives, the minimum value is regarded as the optimal solution. To ensure all objectives are optimized in the same direction, the negative value of the UDI is set as the objective, as shown in Equation (24).

$$\min \left\{\left.f_1(x)=\mathrm{BEI},f_2(x)=-\mathrm{UDI},f_3(x)={\mathrm{LCCO}}_2,f_4(x)=\mathrm{LCC}\right\}\right.$$

(24)

The setting of algorithm parameters exerts a significant impact on the convergence speed, operational efficiency, and solution set quality. The main parameters to be determined in the MOPSO algorithm include population size (N), learning factor (c₁, c₂), inertia weight (ω), and maximum number of iterations (MaxIt), etc. Based on the influence analysis of algorithm parameters on the optimization results in relevant studies, combined with the suggested value ranges provided in references [68,69,70], the parameter values were determined through comparative analysis, as shown in

Table 9. Parameters setting for the MOPSO algorithm.

Name	Parameter Value
Population size, N	50
Learning factor, c1 and c2,	1.8
Inertia weight, ω	0.9
Maximum number of iterations, MaxIt	1500

. A total of three multi-objective optimization models were established, which are suitable for the typical high-rise residences in three cities, respectively.

3. Results and Discussion

3.1. Pareto Optimal Solution Set Analysis

Multi-objective optimization differs from single-objective optimization. The fundamental difference lies in the fact that in multi-objective optimization, there is no unique solution capable of optimizing all objectives simultaneously. A solution may perform optimally for one objective yet poorly for others. Instead, one or more satisfactory solutions need to be sought to balance these objectives, and such solutions are termed Pareto optimal solutions. Through iterative calculations of the MOPSO model integrated with the SVM surrogate model, 50 Pareto optimal solutions were screened for each condition. The ranges of the four objectives for each city are shown in

Table 10. The range of four objectives in Pareto optimal solution sets.

Optimization Objective	Xi’an	Lanzhou	Xining
BEI, kWh/m2	30.85~42.82	15.40~31.04	21.16~35.79
-UDI, %	−63.24~−52.73	−76.94~−66.37	−75.68~−60.16
LCCO2, kgCO2/m2	437.28~540.77	213.32~355.37	304.43~412.65
LCC, ¥/m2	367.03~670.08	385.71~640.96	407.45~763.11

. The objective value distribution of each condition can be seen in the figures in Section 3.4.

As shown in Table 10, the dispersion degree of objective values differs across various cities. To quantify the dispersion degree of each objective, the entropy weight method (a mathematical approach for evaluating the dispersion of indicators, primarily used to measure information uncertainty) was adopted. Generally, a lower entropy value indicates a higher degree of dispersion, implying that adjustments to the design variables have a more significant impact on the corresponding objective. Conversely, a higher entropy value reflects a lower degree of dispersion.

Table 11. The entropy value of each objective for a typical high-rise residence.

Optimization Objective	Xi’an	Lanzhou	Xining
	Entropy Value	Entropy Value	Entropy Value
BEI	0.977	0.990	0.976
UDI	0.958	0.969	0.969
LCCO2	0.985	0.987	0.970
LCC	0.984	0.963	0.975

shows the entropy values of the optimization objectives for the three cities. The ranking of objectives as follows, Xi’an: UDI > BEI > LCC ≈ LCCO₂, Lanzhou: LCC > UDI > LCCO₂ > BEI, Xining: UDI > LCCO₂ > LCC ≈ BEI. Overall, the entropy values of the four objectives do not exhibit significant differences, indicating that the solution set derived from the optimization achieves a favorable balance among the four objectives. The subsequent step will involve analyzing the optimization potential.

The optimization potential is defined as the improvement rate of objective performance relative to the baseline scenario, with the calculation results shown in

Table 12. Comparison of objective performance between Pareto optimal solution set and baseline scheme for typical high-rise residence.

Optimization Objective	Xi’an		Lanzhou		Xining
	Baseline Scheme	Improvement Rate	Baseline Scheme	Improvement Rate	Baseline Scheme	Improvement Rate
BEI, kWh/m2	56.19	23.8%~45.1%	52.15	40.5%~70.5%	63.84	43.9%~66.8%
-UDI, %	−58.43	−9%~8.2%	−69.17	−4.1%~11.2%	−70.12	−14.2%~7.9%
LCCO2, kgCO2/m2	699.17	22.7%~37.5%	691.45	48.6%~69.1%	762.23	45.9%~60.1%
LCC, ¥/m2	602.33	−11.2%~39.1%	633.79	−1.1%~39.1%	634.24	−20.3%~35.8%

. When ranked by the maximum improvement rate for each objective, the order of Xi’an is BEI > LCC > LCCO₂ > UDI, whereas for all other cases, the order is BEI > LCCO₂ > LCC > UDI. A comprehensive comparison indicates that Lanzhou exhibits the greatest optimization potential for high-rise residences, with the maximum improvement rates for all objectives being the highest among high-rise residences of the same type across different cities. There are slight differences for Xining and Xi’an depending on the objective performance.

In terms of detailed analysis, for Lanzhou, the maximum improvement rates of the Pareto optimal solution set in terms of BEI, LCCO₂, LCC, and UDI are 70.5%, 69.1%, 39.1%, and 11.2%, respectively. Xi’an can achieve a maximum LCC improvement of 39.1%, which is on par with that of Lanzhou. However, it exhibits a significant disadvantage in BEI and LCCO₂, with maximum improvement rates of only 45.1% and 37.5%, respectively. Xining’s optimization potential for BEI and LCCO₂ is close to that of Lanzhou, reaching 66.8% and 60.1%, respectively, demonstrating excellent energy-saving and carbon reduction potential. However, it lags behind the other two cities in terms of UDI and LCC performance.

It is worth noting that within the Pareto optimal solution set, the values of UDI and LCC occur as lower than those of the baseline scheme. However, the values of the other objectives corresponding to these solutions are either equal to or close to optimal performance. In other words, when UDI decreases or LCC increases, the other objectives show significant optimization compared with the baseline scheme. Given that the baseline scheme was designed without considering multi-objective trade-offs, the Pareto solution set obtained through multi-objective optimization explores a broader range of possibilities for scheme design and further clarifies the constraints among energy efficiency, carbon reduction, environmental comfort, and economic feasibility.

The objective values and corresponding design parameter values of the Pareto optimal solution set are displayed in Figure 10. Each combination represents a feasible design scheme. It is evident from the figure that the values of some design parameters are distributed within the given range, but the concentrated values are different. In contrast, the value ranges of other design parameters are narrowed through optimization. Specifically, in Xi’an, the value range of living space scale is narrowed, such as the lower limits of MW, ML, SW, and NL are all higher than the given range, while the upper limit of SL is lower. In Lanzhou, changes are observed in building form, space scale, and building envelope; for example, the lower limits of SD, MW, WT, and W are higher than the given range, whereas the upper limits of Nwwr, SL, and RT are lower. For Xining, the primary changes relate to space scale and building envelope, such as the lower limits of MW, SL, WT, RT, and W are higher than the given range, the upper limit of ML is lower, and both the upper and lower limits of SW are altered. Furthermore, the absence of parallel lines in the figure indicates that the design parameters exert interactive impacts on multi-objective performance rather than having isolated effects on individual objectives.

3.2. Sensitivity Analysis of Design Parameters

When each design parameter changes, the magnitude of its impact on the optimization objective varies. Some exert a significant effect, while others may play a relatively minor role. Understanding this characteristic helps designers identify the most critical parameters. Sensitivity analysis enables the identification of input factors that have the greatest impact on output variations by quantitatively comparing changes in outputs and inputs. Based on 1000 sampled data for each city, Spearman correlation analysis and significance testing were first conducted. The results showed that all design variables had a significant impact on at least one optimization objective at the 0.05 significance level, but the linear correlation was relatively weak. Therefore, sensitivity was analyzed by calculating the Partial Rank Correlation Coefficient (PRCC) between design parameters and optimization objective. As a global sensitivity analysis method, PRCC is applicable when there is a nonlinear relationship between input variables and output objectives. By evaluating the rank correlation between a single input and output objective while controlling for other variables, it can accurately reflect the sensitivity relationship between a single input and the output. The range of PRCC values is from −1 to 1. A positive value indicates a positive correlation, and the reverse is also true. The larger the absolute value, the more significant the impact of the design parameter on the objective. When the absolute value is less than 0.2, the parameter has a relatively minor impact on the objective. Thus, we focus on analyzing design parameters with sensitivity coefficients greater than 0.2. By writing codes in Python 3.13 to call the PRCC function in the SALib library, three solution sets were analyzed.

The calculation results are shown in Figure 11, Figure 12, Figure 13 and Figure 14. As illustrated in Figure 11, the sensitivity ranking of design parameters for building energy consumption intensity is as follows: Xi’an: WT > W > SD > NW > RT > O > Swwr > MW > SW > Nwwr > NL > SL > ML, where the sensitivity of five parameters exceeds 0.2; Lanzhou: WT > W > ML > O > SD > SW > NW > Nwwr > RT > SL > Swwr > NL > MW, with the sensitivity of five parameters also exceeding 0.2; and Xining: WT > W > NL > SW > RT > SL > Nwwr > Swwr > NW > MW > SD > O > ML, where eight parameters have a sensitivity exceeding 0.2. The ranking indicates that the thickness of the exterior wall insulation layer and windows type are highly sensitive across all three conditions and are negatively correlated with building energy consumption. The remaining design parameters exhibit significant discrepancies. For example, building orientation is highly sensitive in Xi’an and Lanzhou, but less so in Xining. This is primarily because building orientation has a minimal impact on heat gain when solar radiation is abundant. In Lanzhou, a negative correlation is observed, indicating that its optimal orientation range differs from that of the other two cities. The horizontal overhang sun visor length also demonstrates high sensitivity in Xi’an and Lanzhou; while its sensitivity is lower in Xining, it remains positively correlated, mainly due to climatic difference. As the air temperature decreases, the demand for sunshades gradually diminishes. The sensitivity of roof insulation layer’s thickness is high in Xi’an and Xining, but lower in Lanzhou, indicating that under this climatic condition, changes in insulation layer thickness have a relatively minor impact on energy consumption when energy-saving requirements are met.

As shown in Figure 12, regarding the natural lighting performance, the sensitivity ranking of design parameters is as follows: Xi’an: Nwwr > Swwr > SW > W > SL > O > ML > RT > WT > NL > MW > NW > SD, with the sensitivity of eight parameters greater than 0.2; Lanzhou: Nwwr > Swwr > NL > O > W > SW > MW > ML > SD > WT > RT > SL > NW, also with the sensitivity of eight parameters exceeding 0.2; and Xining: Swwr > Nwwr > NW > W > SD > ML > NL > SL > O > MW > SW > RT > WT, with six parameters having a sensitivity above 0.2. It can be observed from the rankings that the south and north window–wall ratios and window types have relatively high sensitivity under all three conditions, and all are positively correlated with -UDI. Additionally, significant differences exist in the sensitivity of certain design parameters. For instance, the sensitivity of building orientation is higher in Xi’an and Lanzhou, and lower in Xining. However, all three cases present a negative correlation with -UDI. The sensitivity of SW is higher in Xi’an and Lanzhou, and lower in Xining; the sensitivity of NL is higher in Lanzhou, and lower in Xi’an and Xining; and the sensitivity of NW is higher in Xining, and lower in Xi’an and Lanzhou. Meanwhile, the correlation directions of these parameters are not entirely consistent.

The sensitivity analysis of design parameters to LCCO₂ is shown in Figure 13, with the ranking results as follows: Xi’an: W > NW > SD > O > WT > NL > Swwr > SW > Nwwr > SL > RT > ML > MW, and among them, eight parameters exhibit a sensitivity coefficient greater than 0.2; Lanzhou: Swwr > Nwwr > O > NL > SW > ML > W > NW > WT > SD > MW > SL > RT, where the sensitivity of eight parameters is greater than 0.2; and Xining: Nwwr > Swwr > NW > NL > SW > WT > SD > O > W > SL > ML > MW > RT, with the sensitivity of six parameters exceeding 0.2. As is indicated by the ranking results, there is no obvious consistency among the three conditions. Among the design parameters with a sensitivity coefficient > 0.2, common ones include NW, NL, Swwr, and SW, but their correlation directions are not completely consistent. For Lanzhou and Xining, the sensitivity of the south and north window−wall ratio is higher, and both are positively correlated.

The sensitivity analysis of design parameters on LCC is shown in Figure 14, with the sensitivity ranking as follows: Xi’an: Swwr > W > Nwwr > WT > O > SW > RT > SD > NL > ML > SL > NW > MW, where eight parameters exhibit a sensitivity coefficient greater than 0.2; Lanzhou: Swwr > W > WT > Nwwr > NL > SD > SW > RT > MW > O > ML > NW > SL, where eight parameters also have a sensitivity coefficient exceeding 0.2; and Xining: W > Swwr > Nwwr > ML > WT > SD > NW > MW > NL > SL > SW > RT > O, where seven parameters show a sensitivity coefficient greater than 0.2. From the ranking results, Swwr, W, Nwwr, WT, and SD demonstrate higher sensitivity under all three conditions, and all are positively correlated with LCC. The sensitivity of other design parameters varies across regions. For example, the sensitivity of O, SW, and RT is higher in Xi’an and Lanzhou, but have lower sensitivity in Xining, with the correlation direction being the opposite.

Though comparative analysis, it can be revealed that the sensitivity ranking of design parameters varies under the four objective orientations, and the parameters that play a dominant role also show significant differences. For example, the two design parameters of WT and W are more sensitive to building energy consumption; in contrast, for natural lighting and LCC, the most sensitive parameters are Nwwr and Swwr, as well as W and Swwr, respectively. However, under the impact of LCCO₂, the two most sensitive parameters are inconsistent with the above combinations. This indicates that there is an interactive influence between design parameters and multiple objectives, and their correlation directions with different objectives are also differ. It is necessary to consider these parameters and objectives collaboratively to derive a more comprehensive optimal design scheme. Moreover, even for the same design parameter under the influence of the same objective, its sensitivity to this objective varies significantly across the three climate conditions (cities).

3.3. Comprehensive Optimal Design Pattern Decision and Verification

The schemes within Pareto optimal solutions may have better performance in each objective compared to most other solutions in the design space, yet not all objectives achieve their optimal values. Consequently, the relative merits of these schemes cannot be directly compared, requiring designers to further balance trade-offs based on personal preferences or practical requirements. The comprehensive optimal design scheme refers to a pattern where all objectives are treated as equally important (without prioritization). This section mainly constructs this pattern and elaborates on the balance among its four objectives. Firstly, using the IBM SPSS 30.0 platform, combined with the TOPSIS method and subjective weighting approach, the Pareto optimal solution sets are weighted for decision making. That is, when equal weights (0.25 each) are assigned to all objectives in the TOPSIS method, the top-ranked scheme is obtained as the comprehensive optimal design pattern (ODP_comp). To verify its reliability, single-objective optimal decisions are conducted separately using BEI, −UDI, LCCO₂, and LCC, resulting in four single-objective optimal design patterns (ODP_BEI, ODP_-UDI, ODP_LCCO2, ODP_LCC). Together with the ODP_comp, these patterns constitute typical residential optimization design schemes tailored to different decision-making requirements, and their performance differences across objectives are subsequently compared. It should be noted that the single-objective optimal solutions discussed herein are also selected from the Pareto optimal solution set. All of them are viable as optimization schemes, differing only in their emphasis on one or some objectives.

The comparison of objective values for the optimization design pattern in Xi’an is shown in Figure 15. For the three design patterns of ODP_BEI, ODP_-UDI, and ODP_LCCO2, although their individual single-objective optimal indicator values and LCC values are slightly superior to those of ODP_comp, the other two indicators still exhibit certain gaps compared with ODP_comp. As for ODP_LCC, only its LCC value is lower than that of ODP_comp. That is, this pattern prioritizes the best economic performance at the expense of the optimization of other performance aspects. The BEI, -UDI, and LCCO₂ values of ODP_comp all fall within the middle range of the corresponding values across all optimization design patterns and are close to the optimal values. Only the LCC value performs poorly, being the highest among all optimized design patterns, but it does not differ significantly from the values of other optimization design patterns except ODP_LCC, thus maintaining a good balance of performance.

As shown in Figure 16, in Lanzhou, although the BEI, -UDI, and LCCO₂ values of the ODP_BEI are all superior to those of the ODP_comp, its LCC value has significantly increased and ranks the highest among all optimization design patterns. For the ODP_-UDI, only the -UDI value outperforms that of ODP_comp. Moreover, its BEI and LCCO₂ values are the highest among all optimization design patterns, resulting in relatively underwhelming performance in energy conservation and carbon emission reduction. The LCCO₂ and LCC values of ODP_LCCO2 and ODP_LCC are all better than those of ODP_comp. However, their other two performances have deteriorated, with their natural lighting performance showing a particularly noticeable decline. By comparison, ODP_comp exhibits intermediate values across all objectives without any significantly deviations, indicating its reliability in realizing multi-objective balance.

The comparison results for Xining are displayed in Figure 17. Compared with the ODP_comp, the daylighting performance of ODP_BEI deteriorates significantly, whereas other objective values decrease slightly. The ODP_-UDI outperforms other schemes only in terms of lighting performance, while all other objective values reach the highest ones within optimization design patterns. For ODP_LCCO2 and ODP_LCC, although their LCCO₂ and LCC values are superior to those of ODP_comp, the other objective values are inferior, especially in daylighting performance. Overall, each objective value of ODP_comp still falls within the middle range of all optimization design patterns, which effectively achieves a balanced improvement in multi-objective performance.

3.4. Comprehensive Optimal Design Pattern Comparison

This section mainly compares the differences in objective values and design parameter values of the ODP_comp in three cities, aiming to clarify the impacts of thermal zoning and solar resources. Firstly, by comparing with the baseline scenario, the optimization improvement rate of ODP_comp is explored, and the influence of design parameter variations on multi-objective performance is analyzed. Then, through cross-city comparisons of ODP_comp, the performance optimization potential and characteristics of design parameter values for each city is investigated. To more intuitively illustrate the position and performance of ODP_comp within the Pareto optimal solution set, the optimization objectives are combined in pairs, and two-dimensional scatter plots between each pair objectives are drawn, as shown in Figure 18, Figure 19 and Figure 20, where the solid dots represent ODP_comp.

Compared with the baseline scenario, the ODP_comp for typical high-rise residences in Xi’an shows varying degrees of improvement in all objectives, specifically 42.5% energy savings, a 5.7% improvement rate in the natural lighting performance, a 36.3% reduction in LCCO₂, and a 12.9% reduction in LCC. The detailed results are presented in Figure 18 and

Table 13. Comparison of the objective values between ODP_comp and baseline scenario in Xi’an.

	BEI, kWh/m2	-UDI, %	LCCO2, kgCO2/m2	LCC, ¥/m2
Baseline scenario	56.19	−58.43	699.17	602.33
ODPcomp	32.32	−61.77	445.21	524.75
Improvement rate	42.5%	5.7%	36.3%	12.9%

.

Table 14. Comparison of the design parameter values between ODP_comp and baseline scenario in Xi’an.

	O	Swwr	Nwwr	SD	MW	ML	SW	SL	NW	NL	WT	RT	W
Baseline scenario	0	0.40	0.20	0	3.3	4.5	2.9	3.9	3.3	3.6	0.08	0.10	1
ODPcomp	−15	0.50	0.20	0.6	3.6	4.5	3.3	3.6	3.4	3.4	0.24	0.20	3

lists the design parameter values for both the ODP_comp and baseline scenario. In terms of spatial form, the building orientation is optimized from the baseline scenario’s southward orientation to 15° southwest. The Swwr is increased from 0.40 to 0.50, whereas the Nwwr remains unchanged, thereby enhancing indoor natural lighting. For sunshade components, the installation of a horizontal overhang sun visor with a length of 0.6 m is recommended. The dimensions of main living space are slightly adjusted, such as the MW of the ODP_comp is increased by 0.3 m, reaching 3.6 m, while the ML remains consistent with the baseline scenario. The SW is increased by 0.4 m, and the SL is reduced by 0.3 m. The NW is increased by 0.1 m, while the NL is decreased by 0.2 m. Overall, these changes are relatively small. Regarding the building envelope, the WT and RT are significantly increased by 0.16 m and 0.10 m, respectively, compared to the baseline scenario, reaching 0.24 m and 0.20 m. The window type is replaced from the type 1 (K = 1.70 W/m²·K) of the baseline scenario to type 3 (K = 1.30 W/m²·K). In summary, the design parameter values for the ODP_comp are generally higher than those in the baseline scenario, which aligns with the requirements for multi-objective trade-offs and performance improvement.

Based on the data shown in Figure 19 and

Table 15. Comparison of the objective values between ODP_comp and baseline scenario in Lanzhou.

	BEI, kWh/m2	-UDI, %	LCCO2, kgCO2/m2	LCC, ¥/m2
Baseline scenario	52.15	−69.17	691.45	633.79
ODPcomp	17.46	−72.98	272.16	446.88
Improvement rate	66.5%	5.5%	60.6%	29.5%

, the ODP_comp for typical high-rise residences in Lanzhou demonstrates greater potential for energy saving and carbon emission reduction. Compared with the baseline scenario, the energy-saving rate reaches 66.5%, LCCO₂ is reduced by 60.6%, LCC is saved by 29.5%, and the natural lighting performance is improved by 5.5%. The optimized design parameter values are compared in

Table 16. Comparison of the design parameter values between ODP_comp and baseline scenario in Lanzhou.

	O	Swwr	Nwwr	SD	MW	ML	SW	SL	NW	NL	WT	RT	W
Baseline scenario	0	0.40	0.20	0	3.3	4.5	2.9	3.9	3.3	3.6	0.08	0.10	1
ODPcomp	0	0.35	0.20	1.0	3.6	3.8	3.2	3.8	3.2	3.5	0.26	0.20	3

. In terms of spatial form, the building orientation remains consistent with the baseline scenario, the Swwr is reduced to 0.35, while the Nwwr remains unchanged, and a horizontal overhang sun visor with a length of 1.0 m is added, which can effectively reduce heat loss and enhance daylighting effects. Regarding the scale adjustments of main living spaces: the MW of ODP_comp is increased by 0.3 m, and the ML is reduced by 0.7 m, resulting in a slight decrease in floor area. The SW is increased by 0.3 m, and the SL is reduced by 0.1 m. Both the NW and NL are reduced by 0.1 m. For the building envelope, the WT and RT are also significantly increased by 0.18 m and 0.10 m, respectively. The exterior windows are upgraded to type 3 (K = 1.30 W/m²·K).

As shown in Figure 20 and

Table 17. Comparison of the objective values between ODP_comp and baseline scenario in Xining.

	BEI, kWh/m2	-UDI, %	LCCO2, kgCO2/m2	LCC, ¥/m2
Baseline scenario	63.84	−70.12	762.23	634.24
ODPcomp	22.75	−70.28	330.42	506.19
Improvement rate	64.4%	0.2%	56.7%	20.2%

, the natural lighting performance of ODP_comp is close to that of the baseline scenario, with an improvement of only 0.2%. However, its energy-saving rate and carbon reduction rate have increased significantly, reaching 64.4% and 56.7%, respectively. Meanwhile, it can reduce the LCC by 20.2%. The differences in design parameter values between the two conditions are shown in

Table 18. Comparison of the design parameter values between ODP_comp and baseline scenario in Xining.

	O	Swwr	Nwwr	SD	MW	ML	SW	SL	NW	NL	WT	RT	W
Baseline scenario	0	0.40	0.20	0	3.3	4.5	2.9	3.9	3.3	3.6	0.08	0.10	1
ODPcomp	−20	0.30	0.20	0.4	3.6	4.3	3.2	3.7	3.0	3.3	0.28	0.22	3

. Compared with the baseline scenario, the building orientation of ODP_comp shifts from south to 20° west of south. The Swwr is decreased to 0.3, and the Nwwr also remains unchanged. A horizontal overhang sun visor with a length of 1.0 m is added. These changes may result in a relatively small potential for improving daylighting performance. The scale changes in the main living spaces are as follows. The MW and SW are increased by 0.3 m, and both the ML and SL are decreased by 0.2 m. The change in floor area is relatively small. The NW and NL are reduced by 0.3 m, resulting in a significant decrease in their floor areas. The heat transfer coefficient of the building envelope is further reduced. The WT and RT are increased by 0.20 m and 0.12 m, respectively, reaching 0.28 m and 0.22 m. The window type is the same as those in Xi’an and Lanzhou. It is changed from type 1 to type 3 (K = 1.30 W/m²·K).

A comparative analysis of the objective performance of three cities reveals that the ODP_comp in Lanzhou achieved the greatest improvement compared to the baseline scenario, followed by Xining and Xi’an. Figure 21 displays the objective values and improvement rates of ODP_comp across the three cities. In terms of the improvement rates of the BEI, LCCO₂, and LCC, the three cities follow the same descending order: Lanzhou > Xining > Xi’an, with a relatively narrow gap observed between Lanzhou and Xining. By contrast, the improvement rate of -UDI follows a different ranking: Xi’an > Lanzhou > Xining, where the improvement effect of natural lighting in Xining is very minor.

By comparing the design parameter values of ODP_comp (as shown in

Table 19. Comparison of the design parameter values of ODP_comp.

ODPcomp	O	Swwr	Nwwr	SD	MW	ML	SW	SL	NW	NL	WT	RT	W
Xi’an	−15	0.50	0.20	0.6	3.6	4.5	3.3	3.6	3.4	3.4	0.24	0.20	3
Lanzhou	0	0.35	0.20	1.0	3.6	3.8	3.2	3.8	3.2	3.5	0.26	0.20	3
Xining	−20	0.30	0.20	0.4	3.6	4.3	3.2	3.7	3.0	3.3	0.28	0.22	3

), its key characteristics based on the difference in thermal zoning and solar resource were analyzed. Firstly, in terms of spatial form, the building orientation of ODP_comp differ across different cities. Among them, the best orientations for Xi’an, Lanzhou, and Xing are 15° south by west, south, and 20°south by west. The Swwr decrease successively, being 0.5, 0.35, and 0.3, respectively, which, in Lanzhou and Xining, falls within the middle to lower range. This is attributed to the abundant solar resources and lower temperatures in the two cities, and the Swwr is reduced by trade-off. The Nwwr of the three cities is uniformly 0.20. Since the north side is less affected by solar radiation, increasing the window area would be detrimental to energy conservation. However, to ensure adequate daylighting performance, the Nwwr is set at a middle to lower value range. The SD varies significantly among the cities. For instance, the SD in Lanzhou is the longest, possibly due to its abundant solar resources; while in Xining, the SD is the shortest, although this region has the richest solar resources. It may result from its relatively small Swwr and the colder climate, which led to a reduction in shading requirement to ensure sufficient daylighting and acquisition of solar radiation.

Secondly, in terms of living space dimensions, the MW of ODP_comp is uniformly set at 3.6 m. The ML becomes the main optimization design parameter. The rank in descending order is Xi’an, Xining, and Lanzhou. Among them, the ML of Xi’an reaches the upper limit, while that of Xining takes a relatively large value; by contrast, the ML of Lanzhou is close to the minimum value. The scale of the south secondary bedroom varies slightly among different ODP_comp; for instance, the SW in Xi’an is marginally larger, whereas the SL in Lanzhou and Xining is a little larger. Regarding the dimensions of north secondary bedroom, both the NW and NL in Xining are smaller than those in the other two cities. This may be related to the colder climate there, which prompts the optimization of north-facing rooms to a relatively smaller size.

Finally, the design parameter values of the building envelope differ only in terms of the insulation layer thickness. Owing to the higher insulation requirements under severe cold climates, the WT and RT of the ODP_comp in Xining are the highest, followed by those in Lanzhou and Xi’an. This trend is consistent with the variation in outdoor temperatures. The window types are the same, all being type 3, which represents the intermediate performance among the alternative solutions. This indicates that this type of exterior window exhibits good adaptability to the three climate conditions under multi-objective trade-offs. As can be seen from the above analysis, due to the influences of climate and solar energy resources, the optimization potential for objective performance and the design parameter values of typical high-rise residences in each city are not exactly the same. The design parameter values of ODP_comp are input into the parametric model, yielding the design schemes for typical residences in each city, as shown in Figure 22.

It is worth noting that the comprehensive optimal design pattern is derived under the assumption of equal weights assigned to the four objectives. However, in practical design processes, all solutions within the Pareto optimal solution set are feasible. We can select the appropriate solution from the perspective of optimization objective. If the four objectives are of equal importance, the scheme shown in Figure 22 (ODP_comp) is recommended. If a specific objective is prioritized for optimization to achieve the best performance, the single-objective optimal design schemes presented in Section 3.3 (ODP_BEI, ODP_-UDI, ODP_LCCO2, and ODP_LCC) can be selected. For other scenarios, screening can be conducted by sequentially restricting the optimization objectives layer by layer. Firstly, define a value range for the first optimization objective, which helps filter out some solutions. If no further restrictions on other optimization objectives are defined, the TOPSIS method can be used to make further decisions among the remaining solutions. If additional optimization objectives still need to be constrained, set a value range for the second optimization objective and repeat the filtering process to support decision making. In addition, the values of design variables can also be restricted to filter schemes. For instance, in practical design, based on the ranking from sensitivity analysis, parameters with greater impact should be controlled first, and their value ranges can be defined initially. Then, schemes in the Pareto solution set that meet the conditions can be selected for design decision making.

4. Conclusions

This paper proposes a framework for constructing the optimal design pattern of urban high-rise residences, integrating parametric design, machine learning, and multi-objective optimization. Subsequently, typical high-rise residences in cities with distinct solar resources in the severe cold region and cold region (Xi’an, Lanzhou, and Xining) are chosen as research objects to conduct multi-objective optimization design. Based on the obtained Pareto optimal solution sets, the optimization potential of objective performances and the sensitivity of design parameters in different cities are analyzed. By establishing the comprehensive optimal design pattern for typical high-rise residences, the influence of climatic differences on objective values and design parameters values is explored. The primary conclusions are summarized as follows.

By integrating Grasshopper’s parametric modeling and performance simulation, the SVM algorithm, MOPSO algorithm, and TOPSIS method, a multi-objective optimization design framework for urban high-rise residences is established. The optimization objectives encompass building energy consumption intensity (BEI), useful daylight illuminance (UDI), life cycle carbon emission (LCCO₂), and life cycle cost (LCC), while the optimization variables include building orientation, south and north window−wall ratio, horizontal overhang sun visor length, main bedroom width and depth, south secondary bedroom width and depth, north secondary bedroom width and depth, wall and roof insulation layer thickness, and window type. This approach reduces the computational cost of high-dimensional multi-objective optimization problems through the introduction of a surrogate model, and enhances search efficiency and solution space stability. Furthermore, it can also provide optimized design methods and practical references for applications in other cities or different building types.

Through the investigation and analysis of the spatial forms, plan layouts, and building envelope characteristics of high-rise residences in three cities, their typical design features are extracted. Parametric models of typical high-rise residences are established on the Rhino–Grasshopper platform. Based on the predefined objective functions and design variables, 3000 sets of data are sampled using LHS, and the corresponding objective function values are calculated. The generated sample datasets are used to construct the SVM prediction model. Verified by error indicators, the prediction results exhibit high credibility. Taking the SVM model as the fitness function and the design parameters of high-rise buildings as optimization variables, multi-objective optimization models based on the MOPSO algorithm are constructed. Through iterative calculations, the Pareto optimal solution sets for typical high-rise buildings in different cities are obtained. Compared with the baseline scenario, the performance of each objective has achieved a certain degree of improvement; however, the influence degree of each objective varies across different climates conditions. The analysis via the entropy method yields the following priority rankings: in Xi’an, UDI > BEI > LCC ≈ LCCO₂; in Lanzhou, LCC > UDI > LCCO₂ > BEI; and in Xining, UDI > LCCO₂ > LCC ≈ BEI. Meanwhile, the sensitivity of the design parameters is analyzed using the Partial Rank Correlation Coefficient (PRCC). The results indicate that due to differences in climate and optimization objectives, the sensitivity rankings of design parameters differ across the three cities. This clarifies the design parameters that exert a significant effect on the optimization objectives, and these parameters should be prioritized during the design process.

By adopting the TOPSIS multi-attribute decision-making method combined with subjective weighting, the comprehensive optimal design patterns with equal weights for four objectives is identified from the Pareto solution set. Meanwhile, single-objective optimal design patterns are selected separately and compared with the comprehensive optimal design pattern to verify its balance across objectives. On this basis, the objective values and design parameter values of the comprehensive optimal design pattern and the baseline scenario are compared for each city, respectively. The multi-objective improvement effects and design parameter value characteristics of the comprehensive optimal design mode are then evaluated. Furthermore, differences in the objective performance and design parameter values of the comprehensive optimal design patterns among various cities are analyzed, and the ranking of optimization potential for multi-objective is derived. Among these cities, the typical high-rise residence in Lanzhou exhibits the greatest optimization potential, which also reflects the impact of climate conditions and solar resource differences on building performance optimization. Finally, the optimized design scheme for typical high-rise residences is proposed.

Shortcomings and Prospects: (1) Expand the types of research object. This paper is limited to typical high-rise residences. In future studies, it can be further extended to more types of residences to improve the applicability and universality of the findings. Additionally, this paper only conducts optimization design for high-rise residences in severe cold regions and cold regions. Subsequent research may apply the proposed optimization design method to other climate zones and building types, exploring its feasibility in a broader range of scenarios. (2) Supplement optimization objectives and design variables. The optimization objectives of this paper focus on energy saving, natural daylighting, carbon reduction, and economic benefits. However, other performance indicators such as indoor ventilation should also be incorporated into the design of high-rise residences. Regarding the setting of design variables, the differences among floors are not taken into account. The study treats the entire building as the research object. In addition, although solar photovoltaics utilization is considered in this paper, the relevant parameters are not included as optimization design variables. In subsequent research, it would be valuable to integrate more detailed and granular design variables.