Multi-Objective Optimization of Residential Block Space Morphology in Xingtai City Under Energy-Saving Orientation

Abstract

Studies have shown that the morphology of residential blocks has a significant impact on the buildings’ energy use intensity (EUI), solar energy utilization potential (SEUP), and average sunlight hours (ASH). This paper utilizes the Rhino and Grasshopper platforms, employing the Wallacei multi-objective optimization algorithm, to study the relationship between the morphology of residential blocks in Xingtai City, EUI, SEUP, and ASH. First, 108 residential blocks in Xingtai City were surveyed, based on varying design criteria, they were classified into three categories: multi-story, high-rise Type I, and high-rise Type II. Next, after integrating microclimatic factors, the Wallacei multi-objective optimization algorithm was employed to optimize three objectives: EUI, SEUP, and ASH. Finally, the simulation results were subjected to a quantitative analysis using statistical methods, such as K-means clustering. The spatial morphology of residential blocks had a maximum impact of 11.69% on EUI, 39.8% on SEUP, and 36.85% on ASH. Therefore, energy saving can be achieved by controlling the building density, average number of floors, building shape factor and other morphological indicators of residential blocks.

1. Introduction

1.1. Background

With the continuous development of the economy, the demand for energy has been increasing [1]. Urban expansion has significantly contributed to the growth in EUI [2]. Chen et al. found that from 2005 to 2008, urban expansion in the Pearl River Delta region of China led to a doubling of EUI per capita [3]. In 2021, buildings accounted for 30% of global final EUI [4]. In China, as urbanization enters a relatively stable phase, reducing EUI in urban buildings and improving the utilization of renewable energy have become the key areas of focus.

With this background, researchers have investigated the factors influencing building energy use intensity and renewable energy utilization. Based on these studies, this paper focuses on spatial morphology and, utilizing the Rhino and Grasshopper platforms, proposes spatial morphology optimization strategies for residential blocks in cold regions.

1.2. Review

1.2.1. Energy Use Intensity Research

Meanwhile, urban morphology and block morphology play important roles in reducing the building EUI [5]. Wong et al., through their research on urban morphology in Singapore, concluded that if urban morphological elements are effectively managed, EUI can be reduced by 4.5% [6]. Masson et al., from the perspective of urban planning, found that urban morphology can reduce building cooling loads by nearly 20% in Paris [7].

Additionally, when researching the factors related to urban morphology and block morphology, it was found that the mainstream research methods are mainly empirical and simulation approaches, each with its own distinct tendencies in the selection of influencing factors.

The former generally combines morphological elements with social factors in research. Ko et al., using geographic information systems and LiDAR data (higher resolution 3D spatial information can be obtained), collected data on property conditions and demographic characteristics while studying urban morphology. They explored the relationship between these factors and electricity consumption data from Sacramento [8]. Ahn et al. utilized the 2016 Seattle Building Energy Benchmarking dataset and the GIS data to investigate the relationship between horizontal compactness, vertical density, and variations in building height with annual EUI [9].

The simulation school focuses more exclusively on urban morphological elements, relying heavily on EUI simulation software to evaluate building energy performance. Among these tools, EnergyPlus has been proven to be a reliable energy simulation software and is widely applied in EUI modeling [10].

However, there are some differences in model selection, primarily categorized into actual models and typical models. Among the studies using actual models, Ahmadian et al. examined the relationship between urban building morphology, density, orientation, floor plan layout, and EUI, in London [11]. Similarly, Leng et al. explored the correlation between heating EUI and urban block morphological factors in 73 office buildings in Harbin. In the studies utilizing typical models [12], Deng et al. identified three representative urban block types in Jinan—linear arrangement, staggered layout, and courtyard-style—and analyzed the impact of building layout, orientation, and spacing on urban heating EUI. Likewise, Mangan et al. developed 120 sets of typical urban block models to investigate the influence of urban design and architectural parameters on building performance in Istanbul [13].

Existing studies have demonstrated that conducting EUI research on residential blocks through the simulation school is feasible. However, the number of residential block models in previous research remains relatively limited. Therefore, leveraging the Wallacei multi-objective optimization algorithm to generate a large number of research models is highly necessary.

1.2.2. Microclimate Research

Additionally, in EUI simulations, the impact of microclimate on EUI cannot be ignored. Urban block morphology indirectly influences EUI by affecting microclimate. It alters the internal energy balance of a region [14] and impacts microclimate factors such as solar radiation [15] and humidity, thereby indirectly affecting cooling and heating EUI. Moreover, excessive urban density not only reduces building ventilation rates but also exacerbates the urban heat island effect [16], leading to increased cooling demand. Wu et al., through the construction of 30 ideal residential block models, studied the relationship between the microclimate and the EUI in Beijing. The study revealed that the heat island effect could reduce heating EUI by an average of 15.8%, but increase cooling EUI by up to 30% [17]. Zhang et al., by constructing an ideal residential block model of 300 × 300 m, found that incorporating microclimate factors significantly improves the accuracy of EUI simulations [18]. Studies have demonstrated that urban microclimate significantly affects EUI, and EUI simulations become more accurate when microclimate factors are considered. However, it is important to note that the impact of microclimate on EUI varies across different climatic zones [19]. Therefore, in this study on EUI in Xingtai, incorporating microclimate factors is essential.

1.2.3. Solar Energy Utilization Research

Solar energy, as a renewable resource, has received widespread attention in the field of building energy efficiency [20,21]. Existing studies have primarily focused on enhancing solar radiation potential [22] and improving photovoltaic (PV) conversion efficiency [23].

Throughout this research, modifications in urban morphology have been proven effective in increasing solar radiation potential. Morganti et al. studied urban forms in 14 cities, including Rome and Barcelona, and found a significant correlation between solar radiation potential and indicators such as the sky view factor [24]. Ren et al. investigated the relationship between urban morphology and photovoltaic potential in Hong Kong and found that optimizing spatial layout improved performance by up to 17.7% [25].

Additionally, comprehensive studies on urban block morphology concerning EUI and SEUP have also been demonstrated to be feasible. Xu et al. conducted a study on 58 residential blocks in Wuhan, quantifying the relationships between EUI, EUI-PV, PSR, and urban morphology [26]. Xie et al. analyzed EUI and PV data from 55 university dormitories and used a multiple regression model to explore the impact of urban morphology on these factors [27].

When optimizing both factors simultaneously, sacrificing residential comfort for the sake of energy savings is highly undesirable. Adequate sunlight exposure generally contributes to an improved sense of well-being, making it a viable indicator of comfort [28]. Therefore, this study incorporates Average Sunlight Hours (ASH) as a metric for assessing residential comfort.

1.2.4. Statistical Methods

Overall, research in the field of building performance simulation exhibits distinct methodological differences. However, various schools of thought primarily employ correlation analysis, multiple regression analysis, and structural equation modeling to analyze results. Urquizo et al. used multiple regression analysis to explore the relationship between urban morphology and EUI in the United Kingdom [29]. Haitao Lian et al. conducted a study in Wuhan using Pearson correlation analysis and multiple regression analysis to investigate the relationship between urban morphology factors and Carbon Emissions (CEI) [30]. You et al. applied structural equation modeling (SEM) to reveal how three types of morphological variables influence residential building thermal efficiency in Seoul [31].

These research methods provide valuable insights into the trends of building performance; however, they fail to analyze spatial morphology factors within the optimal solution set, making it difficult to propose targeted optimization strategies. Therefore, this study will employ Pareto analysis to propose optimization strategies for the spatial morphology of residential blocks.

1.3. Research Gap

Existing studies have confirmed that it is feasible to investigate the spatial morphology of urban blocks, building EUI, and photovoltaic potential through simulation. However, in current research, researchers primarily focus on building performance while neglecting the interaction between building performance and residential comfort. Additionally, most studies analyze results based on overall trends, lacking an in-depth examination of the Pareto solution set. It is important to note that this study only considers the differences in building performance caused by spatial morphology, excluding the impact of socio-economic factors on building performance.

1.4. Research Aim

Based on this, this study will utilize the Rhino and Grasshopper platforms, along with the Wallacei multi-objective optimization algorithm, to optimize building EUI, SEUP, and ASH. Additionally, it will analyze the influence of residential block spatial morphology parameters on these targets. Specifically, this work focuses on addressing the following four key issues:

• The extent to which the microclimate influences EUI;
• The impact of spatial morphology factors on optimization objectives;
• How multi-objective optimization can be implemented to reduce EUI while increasing SEUP, and ASH;
• In multi-objective optimization, how to achieve a more targeted optimization of a specific indicator.

2. Materials and Methods

2.1. Research Framework

The working framework is shown in Figure 1. Based on the Rhino and Grasshopper platforms, this paper proposes a multi-objective optimization experiment to explore the relationship between residential block spatial morphology and building performance. The experiment is divided into four phases: data acquisition, building performance simulation, result analysis, and optimization validation.

The first phase involved data acquisition. A combination of field surveys and Google Earth data collection was used to investigate 108 residential blocks. Based on block characteristics, 13 spatial morphology factors were selected. Finally, the surveyed residential blocks were categorized into three types—multi-story residential blocks, high-rise type I residential blocks, and high-rise type II residential blocks—to guide the construction of benchmark models.

The second phase involved a building performance simulation. First, based on the survey data, 3D residential block models were created using Rhino 7.0 and Grasshopper (from Rhino 7.0) by adjusting building length, width, height, and orientation. Next, these models were imported into the Ladybug Tools 1.6.0 plugin for microclimate simulation. The simulated microclimate data were then integrated into the optimization objectives to establish a building performance simulation module. Finally, the three optimization objectives were incorporated into Wallacei for multi-objective optimization, aiming to reduce EUI while improving SEUP and ASH. If the results met the required criteria, an output analysis was conducted; otherwise, the block models were reconfigured.

The third phase focused on a result analysis, incorporating Pareto analysis, k-means clustering, Pearson correlation analysis, and multiple regression analysis to guide the optimization of residential block spatial morphology.

The fourth phase involves optimization validation. A representative model was selected from each of the three types of residential blocks, and optimization strategies were applied. The optimized results were then compared with the initial results to verify the feasibility of the optimization.

2.2. Research Methodology

2.2.1. Simulation Optimization Methods

• Energy Use Intensity

Energy use intensity (EUI) refers to the energy required annually for the operation and maintenance of a building after it has been put into use, measured in kWh/m²/y. Current mainstream EUI simulation software includes EnergyPlus, DOE-2, and DeST [32]. EnergyPlus is advantageous because it better accounts for the impact of the surrounding environment on building EUI. This study will use the EnergyPlus engine (from Ladybug Tools 1.6.0) in Grasshopper for EUI simulation. Building EUI consists of cooling EUI, heating EUI, equipment EUI, and lighting EUI, as shown in the Formula (1) [33].

EUI = E_cool + E_heat + E_equipment + E_light

(1)

(E_cool: cooling EUI; E_heat: heating EUI; E_equipment: equipment EUI; E_light: lighting EUI, all measured in kWh/m²/y)

2.

Solar Energy Utilization Potential

Solar energy utilization potential (SEUP) represents the total photovoltaic power generation produced by installing photovoltaic panels at suitable locations on all external walls and roofs of the building, measured in kWh/m². The simulation of E_Solar through the Radiance engine (from Ladybug Tools 1.6.0) in the Ladybug plugin is considered highly reliable [34]. First, the roofs of all buildings in the residential area are selected, and the roof areas with solar radiation greater than 800 kWh/m²/y are filtered [35]. The SEUP is then obtained by dividing by the average building height, with the optimization goal being the achievement of a larger SEUP.

SEUP = E_Solar/AF

(2)

(E_Solar: The total solar energy received by the building in one year, in kWh/m²/y; AF: the average number of building floors in the block, measured in F.)

3.

Average Sunlight Hours

According to the residential area design standards GB50180-2018 [36], the average sunlight hours (ASH) are simulated from 8 a.m. to 4 p.m. on the winter solstice day, with a test surface above the south facade window till (0.9 m). It should meet at least 2 h of sunshine duration. In this study, the average sunshine duration obtained, ensuring the 2 h daily sunshine requirement, is simulated using the Sunlight Hours Analysis tool in the Ladybug plugin 1.6.0. The simulation precision is 1 m, with the optimization goal of achieving a longer ASH.

4.

Multi-objective optimization

The core of the Wallacei tool V2.7 used in this study is the Pareto optimal sorting genetic algorithm NSGA-II [37]. Wallacei is seamlessly integrated with the Grasshopper platform, and its optimization objectives can target building EUI [38], photovoltaic utilization potential [39], comfort [40], and economic indicators. It provides users with powerful multi-objective optimization capabilities and result analysis tools. During the process, complex design problems can be optimized based on multiple sets of objective functions [41].

2.2.2. Methodology of Data Statistics

This study fully leverages the advantages of multi-objective optimization algorithms by integrating Pareto and k-means analyses into the traditional approach that combines the Pearson correlation analysis and the multiple regression analysis. Different analytical methods focus on distinct aspects, and their combined use allows for a more comprehensive analysis. Pareto analysis helps identify superior solution sets in multi-objective optimization. k-means analysis is then applied to classify these solution sets, enabling an assessment of their optimization performance and spatial morphology characteristics. Pearson correlation analysis is effective in determining the positive or negative impacts of individual factors on optimization objectives. Multiple regression analysis provides insights into the overall simulation trends between the optimization objectives and multiple spatial morphology factors.

2.3. Research Object

2.3.1. Research Area

The research area is located in Xingtai City, Hebei Province, China (Figure 2). Xingtai is situated in the North China Plain. It falls within the cold B climate zone for building thermal zoning. In 2023, the average high temperature was 21 °C, and the average low temperature was 9 °C. Specifically, the average high temperature in January was 6 °C, and the average low temperature was −5 °C. In July, the average high temperature was 35 °C, and the average low temperature was 23 °C. The area experiences a hot summer and cold winter climate. As of early 2024, Xingtai’s population is 6.95 million, and the region has significant demand for building cooling and heating, with a large EUI requirement. Moreover, compared to nearby representative cities like Beijing, Tianjin, and Jinan, there is little research conducted in Xingtai. Therefore, this paper chose Xingtai for the study.

2.3.2. Residence Blocks Category

Through a survey of 108 residential blocks in the city, it was found that 95% of the residential buildings are slab-type, with the building orientation deviation not exceeding 5°. Therefore, in the EUI simulation, the study concluded based on surveys and referred to the residential district design standard GB50180-2018, classifying the blocks by maximum building height. The classifications are as follows in

Table 1. Average number of storeys in different residential blocks.

	Multi-Story	High-Rise Type I	High-Rise Type II
Average number of floors	AF ≤ 9	9 < AF ≤ 18	18 < AF ≤ 26

: multi-story residential blocks under 9 floors, high-rise type I residential blocks between 10 and 18 floors, and high-rise type II residential blocks between 19 and 26 floors.

2.3.3. Selection of Influencing Factors for Residential Block Morphology

There are numerous influencing factors in urban form, and the selection of these factors varies significantly depending on the observation scale. For example, at the macro perspective of urban form, Silva et al. studied the potential correlation between urban density and commuting EUI [42]. Murshed and colleagues studied four cities—Kuwait, Abu Dhabi, Hong Kong, and Singapore—focusing on the impact of the urban form on EUI for vertical mobility (such as elevator use) [43]. However, at the mesoscale of residential blocks, the spatial form indicators of residential areas reflect the space layout, intensity of development, and other factors. Related studies indicate that changes in spatial form can influence building EUI by affecting solar radiation and heat exchange.

This study divides the influencing factors into two main categories: planning layout and volume modeling (

Table 2. Definition of residential block morphological parameters.

Categories	Parameters	Define	Illustrations
Planning layout	Floor Area Ratio (FAR)	The ratio of gross floor area within a block to the size of the block
	Building Density (BD)	The ratio of building floor area to parcel area within the block
	Maximum building Floor (FMax)	Maximum number of floors in the block
	Sky View Factor (SVF)	The ratio of the area of the visible area of the sky at the measurement point to the area of the entire hemispherical sky dome.
Volume modeling	Average number of Floors (AF)	Average number of floors in the block
	Scattered Degree (SD)	The standard deviation of the number of floors of each building in the block from the average number of floors of the building
	Building Orientation (O)	The angle facing the building’s south-facing elevation is 0 degrees due north–south
	Building Floor Undulation (FU)	Difference between the maximum number of building storeys and the minimum number of building storeys in a block
	Open Space Ratio (OSR)	The ratio of open space within a block to the sum of the gross floor area of the individual buildings
	Enclosure Degree (ED)	The ratio of the perimeter of the facade of the building complex within the block to the length of the building control line
	Building Enclosure factor Ratio (BER)	The ratio of the sum of the surface area of all buildings in the block to the site area
	Length–Depth ratio of block (L/D)	The ratio of building width to depth within the block
	Building Shape Factor (BSF)	The ratio of the exterior area of a building within a block to the volume of the building it encloses

). The planning layout includes four indicators: floor area ratio, building density, maximum building floor, and sky view factor. The volume modeling includes nine indicators: average number of floors, scattered degree, building orientation, building floor undulation, open space ratio, enclosure degree, building enclosure factor ratio, length–depth ratio of block, and building shape factor. In total, these two categories comprise thirteen indicators. This study conducts field research and utilizes software such as Google Earth and Rhino to select and calculate the spatial parameters of each block, while exploring the impact of spatial morphology indicators on EUI, SEUP, and ASH.

2.4. Simulation Modeling

2.4.1. Generate Site

Typically, the scale of residential blocks ranges from 80 m to 400 m, with a more comfortable scale being around 250 m. Based on actual survey results, this study simplifies the experimental block as a 220 m × 250 m rectangular vacant land (Figure 3), focusing on the impact of the internal spatial form on the optimization target, and therefore does not consider the influence of the surrounding environment.

2.4.2. Generate Baseline Model

On the generated site, we referred to GB50180-2018 to construct 3D baseline models for three residential blocks, as shown in

Table 3. Residential block baseline model.

Multi-Story	High-Rise Type I	High-Rise Type II

. The multi-story residential block adopts a standard row-column layout with a total of 18 residential buildings, each ranging between 5 and 9 stories. The high-rise type I residential block follows a staggered layout, consisting of 13 residential buildings with heights ranging from 10 to 18 stories. The high-rise type II residential block also adopts a staggered layout, comprising 10 residential buildings with heights between 19 and 26 stories.

2.4.3. Benchmark Model Derivation

Based on this configuration, adjustments were made to the building height range, face width, depth, and orientation (positive values indicating southeast orientation and negative values indicating southwest orientation) for the three residential block types, as shown in

Table 4. Range of adjustments to individual building parameters.

Type of Residential Block	Building Height Range	Face Width	Depth	Orientation
Multi-story	5 F–9 F	52 m–56 m	12 m–16 m	−6°–6°
High-rise Type I	10 F–18 F	42 m–46 m	11 m–15 m	−6°–6°
High-rise Type II	20 F–26 F	40 m–44 m	13 m–17 m	−6°–6°

. These modifications allowed for the derivation of alternative forms to facilitate multi-objective optimization.

2.4.4. Simulation Parameter Settings

In the simulation calculations for the three optimization objectives, the considerations for SEUP and ASH primarily involve solar exposure and radiation. However, during the operational phase of buildings, numerous factors influence EUI differences. This study specifically focuses on the impact of residential block spatial morphology on the EUI. Therefore, in accordance with GB55015-2021 [44], the parameters for heat transfer coefficients (

Table 5. Maintenance structure coefficients.

Heat Transfer Coefficients K(W/m2·K)
External wall	0.6
Roof	0.3
Floor	0.6
Window	2

), window-to-wall ratios (

Table 6. Area ratio of window-to-wall.

	East	South	West	North
Area ratio of window-to-wall	0.45	0.6	0.45	0.4

), and parameter setting for simulation (

Table 7. Parameter setting for simulation.

Parameter	Parameter Data
Lighting power density	5 W/m2
Schedule
Floor space occupied per capita	25 m2/p
Schedule
Power density of electrical equipment	3.8 W/m2
Schedule
Number of air changes	0.5 h−1

). The heat transfer coefficients and window-to-wall ratio affect EUI by influencing heat transfer mechanisms, while the parameter setting for simulation impact EUI by determining the power consumption of indoor equipment.

3. Results and Discussion

3.1. Microclimate and EUI

The Urban Weather Generator (UWG) model (from Ladybug Tools 1.6.0) estimates the building EUI at the urban scale, particularly considering the interaction between buildings and the urban environment. Athar Kamal et al. utilized the UWG model in conjunction with data from local meteorological stations to simulate building EUI, achieving more accurate predictions of EUI [45].

Therefore, this study employs the UWG model to reduce errors in EUI simulations. The meteorological data required for microclimate simulations are sourced from the CSWD meteorological dataset for Xingtai City, available on the Ladybug website. The primary factors influencing the microclimate include transportation power, ratio of green space, and others. The specific details are shown in

Table 8. Factors influencing microclimate.

Microclimate Parameter Setting
Transportation power (W/m2)	4
Ratio of green space	0.35
Plant cover	0.9
Reflection rate	0.6

.

To minimize the impact of urban microclimate variations, this study selects two actual samples for each residential block type, totaling six residential block samples for experimentation. The simulation results, as shown in Figure 4, indicate an approximate 11% increase in average cooling EUI, a 13% decrease in heating EUI, and a 2% overall increase in total EUI. These findings align closely with the results of A. Boccalatte et al., who found that cooling EUI in European cities tends to be approximately 10% higher [46]. Similarly, Michele Zinzi et al. reported that heating EUI in residential buildings in Rome decreased by up to 21%, while office buildings experienced a reduction of up to 18% [47]. Therefore, the results of this study are considered to be reasonably reliable.

3.2. Multi-Objective Optimization Simulation

The multi-objective optimization process was completed on a Windows 11 system computer (intel Core i7-12650H, 16 GB memory), with a total time of nearly 500 h, and the optimization objective values converged to a stable state. The population size for each optimization group was 30, with 50 iterations, and parameters such as crossover and mutation rates were kept at the platform’s default values. A total of 4500 operations were performed during this optimization (Figure 5, Figure 6 and Figure 7).

The EUI fluctuated between 45.46 kWh/m²/y and 54.06 kWh/m²/y, with a fluctuation range of 13.4%, which is within an acceptable range [48]. The solar energy received per square meter of roof was 1264–1278 kWh/m²/y, which is very close to Liu’s results [49]. On the coldest days, if each window receives more than 2 h of sunlight, it meets the standard, and the tests confirmed this standard was met. The following figure shows the optimization process for the three optimization objectives in three residential blocks, including the Standard Deviation and Mean Value Trendline. Each curve in the Standard Deviation graph represents an iteration, with red indicating the first generation and blue indicating the last generation. A steeper curve indicates a smaller standard deviation within the population, as shown in the figure. When the overall Standard Deviation curve shifts leftward, it suggests that the optimization effect is better. The Mean Value Trendline reflects the change in the average value during the optimization process, with the leftmost point representing the first generation and the rightmost point representing the last generation. As shown, the Mean Value Trendline shifts downward, and during the later iterations, it enters a relatively stable phase, indicating a good overall optimization effect and that the results are credible for further analysis.

3.3. Optimization Process

The entire optimization experiment includes the maximum and minimum values for each target across various blocks. Since the same solution might perform equally well in multiple objectives, there are five process solutions in the multi-story residential blocks, four in the high-rise type I residential blocks, and six in the high-rise type II residential blocks, totaling fifteen process cases.

Table 9. Optimization process.

Multi-Story
Gen. 1 Ind.26		Gen.0 Ind.1
EUI (MAX)	52.08 kWh/m2/y	EUI	51.11 kWh/m2/y
SEUP	194.21 kWh/m2/y	SEUP (MIN)	168.46 kWh/m2/y
ASH	7.82 h	ASH (MIN)	6.94 h
Gen.45 Ind.1		Gen.33 Ind.0		Gen.16 Ind.0
EUI (MIN)	46.37 kWh/m2/y	EUI	47.90 kWh/m2/y	EUI	47.11 kWh/m2/y
SEUP	176.39 kWh/m2/y	SEUP (MAX)	244.13 kWh/m2/y	SEUP	224.90 kWh/m2/y
ASH	7.50 h	ASH	8.44 h	ASH (MAX)	8.44 h
High-rise Type I
Gen. 0 Ind.2		Gen.0 Ind.24
EUI (MAX)	53.62 kWh/m2/y	EUI	50.24 kWh/m2/y
SEUP	87.20 kWh/m2/y	SEUP (MIN)	83.51 kWh/m2/y
ASH	5.99 h	ASH (MIN)	5.78 h
Gen.46 Ind.1		Gen.29 Ind.0
EUI (MIN)	47.35 kWh/m2/y	EUI	47.82 kWh/m2/y
SEUP	84.10 kWh/m2/y	SEUP (MAX)	116.75 kWh/m2/y
ASH	6.29 h	ASH (MAX)	7.91 h
High-rise Type II
Gen. 0 Ind.27		Gen.1 Ind.16		Gen.5 Ind.3
EUI (MAX)	50.49 kWh/m2/y	EUI	46.60 kWh/m2/y	EUI	46.00 kWh/m2/y
SEUP	55.47 kWh/m2/y	SEUP (MIN)	53.60 kWh/m2/y	SEUP	57.97 kWh/m2/y
ASH	6.72 h	ASH	6.76 h	ASH (MIN)	6.52 h
Gen.49 Ind.0		Gen.30 Ind.1		Gen.10 Ind.4
EUI (MIN)	45.46 kWh/m2/y	EUI	46.21 kWh/m2/y	EUI	46.55 kWh/m2/y
SEUP	54.99 kWh/m2/y	SEUP (MAX)	62.54 kWh/m2/y	SEUP	58.50 kWh/m2/y
ASH	6.90 h	ASH	7.14 h	ASH (MAX)	7.14 h

presents the evolution trend of block morphology. It is important to note that while EUI performs best when the minimum value is achieved, SEUP and ASH perform better when their maximum values are reached.

From Table 9, it can be seen that the lowest EUI for multi-story residential blocks is 46.37 kWh/m²/y, which is a 10.96% decrease from the maximum EUI of 52.08 kWh/m²/y. The maximum SEUP is 244.13 kWh/m²/y, a 44.32% increase compared to the minimum SEUP of 168.46 kWh/m²/y. The maximum ASH is 8.44 h, which is a 26.61% increase compared to the minimum ASH of 6.94 h. For high-rise type I residential blocks, the lowest EUI is 47.35 kWh/m²/y, an 11.69% decrease compared to the maximum EUI of 53.62 kWh/m²/y. The maximum SEUP is 116.75 kWh/m²/y, a 39.8% increase from the minimum SEUP of 83.51 kWh/m²/y. The maximum ASH is 7.91 h, a 36.85% increase compared to the minimum ASH of 5.78 h. For high-rise type II residential blocks, the lowest EUI is 45.46 kWh/m²/y, a 9.96% decrease compared to the maximum EUI of 50.49 kWh/m²/y. The maximum SEUP is 62.54 kWh/m²/y, a 16.68% increase compared to the minimum SEUP of 53.60 kWh/m²/y. The maximum ASH is 7.14 h, a 9.51% increase compared to the minimum ASH of 6.52 h.

In terms of the overall optimization potential of building performance across different residential block types, the results are as follows: multi-story > high-rise type I > high-rise type II. Ratti et al., through research in London, Toulouse, and Berlin, found that the impact of urban morphology on building EUI can reach up to 10% [50]. This study closely aligns with that trend. Additionally, Liu et al. found that the overall optimization trend for solar radiation potential in Jianhu city could be improved by approximately 30%, which is consistent with this study [51]. Overall, as the optimization progresses, all targets for each residential block have been optimized, reducing the EUI required for housing while increasing residential comfort.

3.4. Comparison of Pareto and Dominated Solutions

After removing duplicate solutions, the multi-story residential blocks yielded a total of 1125 solutions, with 93 Pareto optimal solutions; the high-rise type I residential blocks yielded a total of 1092 solutions, with 134 Pareto optimal solutions; the high-rise type II residential blocks yielded a total of 929 solutions, with 146 Pareto optimal solutions.

In a multi-criteria setup with conflicting objectives, these objectives cannot all reach an optimal state simultaneously. We typically aim to bring these objectives to their best state within a certain range. This is known as multi-objective optimization, and Pareto optimal solutions are generally regarded as the best solutions that minimize conflicts between all objectives [52]. The other solutions, excluding Pareto optimal ones, are referred to as dominated solutions. The relationship between Pareto optimal and dominated solutions is illustrated in the following graph (Figure 8), where the Pareto optimal solutions for multi-story residential blocks are EUI 46.86 kWh/m²/y, SEUP 208.76 kWh/m²/y, and ASH 8.14 h; the dominated solutions are EUI 47.08 kWh/m²/y, SEUP 201.64 kWh/m²/y, and ASH 7.98 h. For high-rise type I residential blocks, the Pareto optimal solutions are EUI 47.54 kWh/m²/y, SEUP 100.23 kWh/m²/y, and ASH 7.16 h; the dominated solutions are EUI 47.89 kWh/m²/y, SEUP 98.30 kWh/m²/y, and ASH 6.89 h. For high-rise type II residential blocks, the Pareto optimal solutions are EUI 45.87 kWh/m²/y, SEUP 58.90 kWh/m²/y, and ASH 7.01 h; the dominated solutions are EUI 46.29 kWh/m²/y, SEUP 58.30 kWh/m²/y, and ASH 6.96 h. Both in terms of solution distribution space and mean values, the Pareto optimal solutions for all three types of residential blocks show better performance than the dominated solutions, with noticeable improvements in all aspects.

Existing research indicates that differences in residential block spatial forms can impact EUI, SEUP, and ASH. By interpreting the residential block forms corresponding to the Pareto optimal solutions, we can conclude that these three energy-efficient, comfortable residential block forms have the following characteristics:

(1)

BD: Compared to dominated solutions, Pareto optimal solutions have higher BD values, with the optimal BD for multi-story, high-rise type I, and high-rise type II residential blocks corresponding to 0.2914, 0.1628, and 0.1304, respectively. Compared to the dominated solutions with BD values of 0.2851, 0.1592, and 0.1271, these represent increases of 2.23%, 2.23%, and 2.63%, respectively.

(2)

AF: Compared to dominated solutions, Pareto optimal solutions have lower AF values, with the optimal AF for multi-story, high-rise type I, and high-rise type II residential blocks corresponding to 6.14, 12.78, and 21.68, respectively. Compared to the dominated solutions with AF values of 6.35, 12.99, and 21.90, these represent reductions of 3.37%, 1.64%, and 1.03%, respectively.

(3)

L/D: Compared to dominated solutions, Pareto optimal solutions have lower L/D values, with the optimal L/D for multi-story, high-rise type I, and high-rise type II residential blocks corresponding to 3.49, 3.06, and 2.49, respectively. Compared to the dominated solutions with L/D values of 3.50, 3.09, and 2.57, these represent reductions of 0.34%, 0.79%, and 3.11%, respectively.

(4)

BSF: Compared to dominated solutions, Pareto optimal solutions have lower BSF values, with the optimal BSF for multi-story, high-rise type I, and high-rise type II residential blocks corresponding to 0.2157, 0.2032, and 0.1807, respectively. Compared to the dominated solutions with BSF values of 0.2160, 0.2054, and 0.1841, these represent reductions of 0.16%, 1.05%, and 1.83%, respectively.

3.5. K-Means Cluster Analysis

K-means clustering analysis, as a machine learning algorithm, automatically divides data objects into multiple categories or clusters by mining the inherent structure and patterns in the data [53]. In this paper, this algorithm is used to classify the Pareto optimal solutions of multi-story residential blocks and high-rise type I residential blocks into two categories, while the Pareto optimal solutions of high-rise type II residential blocks are divided into three categories, providing a clearer view of the performance of each Pareto optimal solution in different objectives (Figure 9).

In

Table 10. K-means clustering distribution.

Type of Residential Block	Cluster	Dataset	Cluster Centers
			EUI (kWh/m2/y)	SEUP (kWh/m2/y)	ASH (h)
Multi-story	Cluster1	36	46.89	210.34	8.16
	Cluster2	57	46.84	207.76	8.12
High-rise Type I	Cluster1	62	47.53	99.50	7.12
	Cluster2	72	47.55	100.86	7.21
High-rise Type II	Cluster1	42	45.84	58.94	6.99
	Cluster2	59	45.86	58.82	7.02
	Cluster3	45	45.91	58.96	7.01

, the clustering results for the three residential blocks are presented. In the two clusters of multi-story residential blocks, Cluster 1 has fewer Pareto optimal solutions, with better performance in SEUP and ASH objectives, while Cluster 2 shows better performance in the EUI objective. In the two clusters of high-rise type I residential blocks, the distribution of Pareto optimal solutions is relatively balanced, with Cluster 1 showing better performance in EUI, and Cluster 2 showing better performance in SEUP and ASH objectives. High-rise type II residential blocks are divided into three clusters, with a relatively balanced distribution of Pareto optimal solutions in each cluster. Cluster 1 demonstrates superior performance in the EUI objective, Cluster 2 excels in ASH, and Cluster 3 shows better performance in the SEUP objective, demonstrating that this clustering classification is reasonable.

Through the K-means clustering analysis, we aim to address two key issues: first, the relationship among the three optimization objectives; second, how to prioritize the optimization of a specific objective in a multi-objective optimization.

(1)

The clustering analysis results indicate that EUI is negatively correlated with SEUP and ASH, while SEUP and ASH are positively correlated. Specifically, an outstanding EUI performance is typically accompanied by moderate SEUP and ASH performance, whereas an excellent SEUP performance is usually associated with a strong ASH performance. The differences between the two clustered spatial morphology groups are primarily reflected in variations in FAR, BD, SVF, SD, and BSF, while other spatial morphology parameters do not exhibit consistent trends across different residential blocks.

(2)

In multi-objective optimization, if the priority is to minimize EUI, this can be achieved by increasing FAR and decreasing BSF. Compared to the clusters with better SEUP and ASH performance, the average FAR in multi-story, high-rise type I, and high-rise type II residential blocks increased by 1.15%, 1.39%, and 1.21%, respectively, while BSF decreased by 0.38, 0.19, and 0.24, respectively. Conversely, if the priority is to optimize SEUP and ASH, this can be accomplished by increasing SVF and decreasing SD. Compared to the clusters with a better EUI performance, the average SVF in multi-story, high-rise type I, and high-rise type II residential blocks increased by 0.4916, 0.9569, and 0.5867, respectively, while SD decreased by 2.26, 0.65, and 4.69, respectively.

Therefore, it can be preliminarily concluded that BSF has a strong correlation with EUI, while SD has a significant impact on SEUP. In the following section, Pearson correlation analysis will be used to assess the relationship between spatial morphology factors and optimization objectives to validate the reliability of this study.

3.6. Correlation Analysis

This section aims to quantitatively explore the impact of residential block spatial morphology on EUI and SEUP. It is important to note that the mechanism through which block morphology influences these two objectives is complex. Therefore, to better understand the relationship between the morphological factors of the block and EUI and SEUP, as well as the correlations between the various influencing factors, Pearson correlation analysis is essential [54]. When the Pearson correlation coefficient exceeds 0.6, it indicates a significant correlation, and when it exceeds 0.8, the correlation is considered strong (Figure 10).

Since this paper primarily focuses on building energy efficiency analysis, and ASH is a supplementary optimization indicator, it is sufficient to meet the residential design requirements. Therefore, Pearson and regression analyses are not conducted for ASH. Through a Pearson correlation analysis, the correlation relationships between the spatial morphology of each residential block and the two relevant objectives are as follows in

Table 11. Pearson correlation coefficient analysis.

Morphological Factors	Pearson Correlation Coefficient	EUI (kWh/m2/y)	SEUP (kWh/m2/y)
FAR	Pearson correlation coefficient	−0.572 **	−0.828 **
	p-value	0.000	0.000
BD	Pearson correlation coefficient	−0.027	0.976 **
	p-value	0.131	0.000
FMax	Pearson correlation coefficient	−0.253 **	−0.964 **
	p-value	0.000	0.000
SVF	Pearson correlation coefficient	−0.042 *	−0.768 **
	p-value	0.018	0.000
AF	Pearson correlation coefficient	−0.300 **	−0.938 **
	p-value	0.000	0.000
SD	Pearson correlation coefficient	0.198 **	−0.606 **
	p-value	0.000	0.000
O	Pearson correlation coefficient	−0.100 **	0.010
	p-value	0.000	0.561
FU	Pearson correlation coefficient	0.271 **	−0.597 **
	p-value	0.000	0.000
OSR	Pearson correlation coefficient	0.805 **	0.517 **
	p-value	0.000	0.000
ED	Pearson correlation coefficient	0.059 **	0.984 **
	p-value	0.001	0.000
BER	Pearson correlation coefficient	−0.478 **	−0.831 **
	p-value	0.000	0.000
L/D	Pearson correlation coefficient	0.534 **	0.857 **
	p-value	0.000	0.000
BSF	Pearson correlation coefficient	0.700 **	0.798 **
	p-value	0.000	0.000

* means the correlation was significant at level of 0.05; ** means the correlation was significant at level of 0.01.

:

(1)

EUI shows a strong correlation with OSR and BSF, both of which are positively correlated with EUI, while FAR is negatively correlated;

(2)

SEUP shows a strong correlation with multiple spatial morphology factors of residential blocks, including FAR, BD, Fmax, SVF, AF, ED, BER, L/D, and BSF. Specifically, BD, ED, L/D, and BSF are positively correlated with SEUP, whereas FAR, Fmax, SVF, AF, SD, and BER exhibit negative correlations;

Xu et al. conducted research on buildings in Wuhan and found that BSF had the greatest impact on EUI, aligning with the research trend on block morphology [5]. This may be because lower BSF reduces heat loss and heat gain, thereby improving energy efficiency. In SEUP research, Fmax, BSF, and SVF are critical influencing factors that cannot be ignored [26]. Additionally, Liu et al., in their study on photovoltaic power generation in Jianhu city, found that FAR and AF are negatively correlated with SEUP, whereas BD is positively correlated, which is consistent with the trend observed in SEUP studies [49].

These findings indicate that the research trends in this experiment are valid. Furthermore, they suggest that while subsequent zoning may introduce some variations in the study, the influence mechanisms of certain factors remain similar.

3.7. Regression Analysis

Through a Pearson correlation analysis, the factors with the highest correlation under the influence of a single variable were identified. In the subsequent multiple regression analysis, the spatial morphological indicators of residential blocks were treated as independent variables X, while the two optimization objectives, EUI and SEUP, were treated as dependent variables, with the aim to quantify the main morphological factors influencing EUI and residential comfort. A Pearson correlation coefficient greater than 0.6 indicates a significant correlation, and a value above 0.8 signifies a strong correlation (

Table 12. Multivariate regression coefficient analysis.

Dependent Variable	Independent Variable	Unstandardized Coefficient		Beta	T	p	VIF	R2
		B	Standard Error
EUI	(Constants)	19.282	0.261	-	73.816	0.000	-	0.843
	SVF	17.731	0.294	0.538	60.369	0.000	1.592
	SD	0.565	0.011	0.377	50.824	0.000	1.105
	BSF	84.782	0.672	1.131	126.228	0.000	1.610
SEUP	(Constants)	−106.761	1.845	-	−57.863	0.000	-	0.970
	BD	677.856	5.823	0.765	116.411	0.000	4.532
	SD	−3.624	0.344	−0.044	−10.542	0.000	1.859
	L/D	34.300	0.817	0.229	42.000	0.000	3.117

).

Three spatial morphological factors of the building block affect EUI, namely SVF, SD, and BSF. Using these as independent variables for regression analysis, we found:

EUI = 19.282 + 17.731X₁ + 0.565X₂ + 84.782X₃

(3)

where X₁ = SVF; X₂ = SD; X₃ = BSF.

The R² value of the model is 0.843, meaning that SVF, SD, and BSF can explain 84.3% of the variation in EUI. All VIF values in the model are less than 5, indicating that there is no collinearity problem, and the model is reliable.

Three spatial morphological factors of the building block affect SEUP, namely BD, SD, and L/D. Using these as independent variables for regression analysis, we found:

SEUP = −106.761 + 677.856X₁ − 3.624X₂ + 34.3X₃

(4)

where X₁ = BD; X₂ = SD; X₃= L/D.

The R² value of the model is 0.970, meaning that BD, SD, and L/D can explain 97.0% of the variation in EUI. All VIF values in the model are less than 5, indicating that there is no collinearity problem, and the model is reliable.

(1)

EUI performs better: SVF, SD, and BSF are positively correlated with EUI. According to the standardized coefficients (Beta), BSF has the greatest impact on EUI, approximately 2.10 times that of SVF and 3 times that of SD. This is likely due to the reduction in heat loss and heat gain, which improves energy efficiency [12]. Therefore, to obtain a low-EUI residential block, one can reduce the building’s BSF and simultaneously reduce the SVF and SD of the residential block.

(2)

SEUP performs better: BD and L/D are positively correlated, while SD is negatively correlated. According to the standardized coefficients (Beta), BD has the greatest impact on EUI, approximately 17.38 times that of SD and 3.34 times that of L/D. This is likely achieved through heat conduction, convection, and radiation between the building and outdoor air [55]. Therefore, to obtain a high-SEUP residential block, one can increase BD while simultaneously reducing the SD of the building and improving L/D.

These results are consistent with the overall trends found in the previous Pareto optimal solutions, K-means clustering analysis, and Pearson correlation analysis, indicating that the experiment has integrity, continuity, and the results are persuasive.

A summary of the above analysis indicates that optimizing all three objectives simultaneously can be achieved by increasing BD while reducing AF, L/D, and BSF. Specifically, increasing BD enhances building density, which helps improve the region’s solar radiation potential, mitigate the urban heat island effect, and increase energy efficiency. Reducing AF can primarily be accomplished by lowering the height of buildings on the southern side, thereby minimizing shading effects and enhancing sunlight exposure and solar radiation potential. Lowering L/D and BSF reduces heat loss, thereby improving energy efficiency and decreasing EUI. Additionally, BSF has a significant impact on EUI, while BD has a greater influence on SEUP.

Additionally, Trepci et al. have confirmed that a higher urban density leads to better energy efficiency [56]. However, it is important to note that while a higher FAR can contribute to EUI reduction, an excessively large BD increases SEUP. If both factors become too high, they may significantly constrain the residents’ activity space within the residential block. Moreover, research by Quan et al. has identified a threshold effect between FAR and EUI, indicating the necessity of setting limitations for these parameters [57]. In this optimization, the FAR range is set between 1.31 and 3.15, while BD is maintained between 0.094 and 0.293, ensuring optimization within these boundaries.

3.8. Experimental Verification

To validate the feasibility of the proposed optimization method, this study selected three actual residential blocks in Xingtai City for simulation-based optimization. In addition to enriching the existing theoretical framework, this also helps verify the accuracy of multi-objective optimization. These three residential blocks correspond to a mixed mid-rise and high-rise type I residential block, a high-rise type I residential block, and a high-rise type II residential block (

Table 13. Residence block optimization before and after comparison.

	Residence Block A	Residence Block B	Residence Block C
pre-optimization
post-optimization

).

By applying the above strategies in the optimization process—namely, increasing BD while reducing AF, L/D, and BSF—the final optimized spatial morphology factors are shown in

Table 14. Comparison of morphology factors before and after residential block optimization.

		BD	AF	L/D	BSF
Residence block A	pre-optimization	0.1944	9.4615	4.2065	0.2379
	post-optimization	0.2207	8.7692	3.5642	0.2178
Residence block B	pre-optimization	0.1345	17	4.3300	0.2177
	post-optimization	0.1579	15.5	3.5083	0.1931
Residence block C	pre-optimization	0.1264	26	4.0658	0.1925
	post-optimization	0.1332	24.5455	3.6585	0.1821

. The optimized models were then imported into the Grasshopper platform for building performance simulation.

A comparison between the simulated building performance before and after optimization is presented in

Table 15. Residential block building performance optimization before and after comparison.

		EUI (kWh/m2/y)	SEUP (kWh/m2/y)	ASH (h)
Residence block A	pre-optimization	52.65	129.73	4.61
	post-optimization	50.00	138.90	4.73
Residence block B	pre-optimization	51.33	75.05	5.47
	post-optimization	48.11	82.94	5.65
Residence block C	pre-optimization	48.59	49.07	4.89
	post-optimization	47.20	51.60	5.11

. It shows that, for the mid-rise residential block, building EUI decreased by 2.65 kWh/m²/y, a reduction of 5.03%; solar energy utilization potential increased by 9.17 kWh/m²/y, an improvement of 7.07%; and average sunlight duration increased by 0.12 h, a rise of 2.61%. For the high-rise type I residential block, building EUI decreased by 3.22 kWh/m²/y, a reduction of 6.27%; solar energy utilization potential increased by 7.89 kWh/m²/y, an improvement of 10.5%; and average sunlight duration increased by 0.18 h, a rise of 3.3%. For the high-rise type II residential block, building EUI decreased by 1.39 kWh/m²/y, a reduction of 2.86%; solar energy utilization potential increased by 2.53 kWh/m²/y, an improvement of 5.16%; and average sunlight duration increased by 0.22 h, a rise of 4.50%.

This validation confirms that the optimization strategies proposed through simulation are feasible. It is hoped that this study can provide insights into the relationship between urban block morphology and building performance.

4. Conclusions

4.1. Main Findings

Taking Xingtai as a case study, this research utilizes the Rhino and Grasshopper platforms along with the Wallacei multi-objective optimization algorithm to simulate and analyze the energy use intensity (EUI), solar energy utilization potential (SEUP), and average sunlight hours (ASH) of residential blocks in Xingtai. Additionally, statistical methods are employed to explore the relationships between spatial morphology parameters and EUI, SEUP, and ASH. The main conclusions are as follows:

• Impact of microclimate on building EUI: Under the influence of microclimate, the cooling EUI increases by approximately 11%, while the heating EUI decreases by about 13%. Therefore, microclimate factors should be considered in EUI calculations to enhance simulation accuracy.
• Studying EUI, SEUP, and ASH through spatial morphology analysis is reliable. The maximum impact on EUI reaches 11.69%, on SEUP 39.8%, and on ASH 36.85%. In terms of overall optimization potential for building performance, mid-rise residential blocks outperform high-rise type I residential blocks, which in turn outperform high-rise type II residential blocks.
• The energy-saving-oriented multi-objective optimization strategy involves increasing BD while reducing L/D, BSF and AF. To achieve a 5% optimization across multiple objectives, BD can be increased by approximately 3%, AF reduced by 5%, L/D reduced by 10%, and BSF reduced by 4%.
• Among spatial morphology factors, BSF has the greatest impact on EUI, being approximately 2.10 times that of SVF and 3 times that of SD.
• Among spatial morphology factors, BD has the greatest impact on SEUP, being approximately 17.38 times that of SD and 3.34 times that of L/D.

This study aims to provide design guidance for residential blocks in Xingtai from the perspective of building energy efficiency, offering practical recommendations for planners and architects.

4.2. Prospective

• To ensure consistency of other parameters, this paper sets the building envelope, window–wall ratio, and schedule parameters to typical values. However, the EUI differences caused by varying household usage patterns and socio-economic factors were not considered during the simulation process.
• In the microclimate simulation, the scope is limited to the block perspective, without considering the impact of the surrounding block’s microclimate on the test site.
• When establishing the residential block optimization model, the combinations of multi-story, high-rise type I, and high-rise type II residential blocks were not considered.