Performance-Oriented Parametric Optimization Design for Energy Efficiency of Rural Residential Buildings: A Case Study from China’s Hot Summer and Cold Winter Zone

Abstract

With the implementation of the rural revitalization strategy, rural residences have become an essential component of China’s building energy conservation efforts. However, most existing research has focused more on urban buildings, with less attention given to rural residences. This study, taking rural residential buildings (RRBs) in the hot summer and cold winter zones in China as an example, proposes a more precise, two-stage optimization design framework using Rhino-Grasshopper for the overall optimization of RRBs. First, field surveys and numerical analysis of collected rural residential design drawings were conducted to clarify spatial characteristics and air conditioning usage. The parametric optimization design of RRBs was then conducted in two steps. The first step involves room function positioning, where spatial geometric models are established. Annual dynamic simulation analyses of AC (air conditioning) and AL (artificial lighting) energy consumption are performed to obtain energy intensity distribution maps. Based on the principle that “space with higher energy consumption is set in the location with lower energy consumption intensity” and the habit of functional space distribution, room function positioning, and adjustments are made. In the second step, the SPEA-2 genetic algorithm was applied for multi-objective optimization of room width, depth, WWR (window-to-wall ratio), SHGC (solar heat gain coefficient), and VLT (visible light transmittance), all based on the logical relationships of the building structure. The final Pareto front solution sets were obtained by multi-objective optimization simulation (MOO). A typical three-bay RRB was selected for application in this study, and the optimized design led to a total energy savings rate of 11% in annual AC and AL energy consumption.

1. Introduction

1.1. Background

As a developing country, China still has approximately 35% of its population in suburban and rural areas [1]. Official statistics indicate that by 2020, the total area of RRBs in China was 23.3 billion m², accounting for 42% of the nation’s total residential building area [2]. In 2018, the Chinese government launched the Rural Revitalization Strategy to improve the well-being of the people [3]. In 2022, the General Office of the CPC Central Committee and the State Council General Office jointly issued the Action Plan on Rural Construction, which proposed the principle of “resource conservation and green construction”. It calls for establishing a green and low-carbon concept, promoting the intensive and efficient recycling of resources, and implementing green planning, green design, and green construction to achieve the organic integration of rural construction with the natural ecological environment [4]. The green, low-carbon, and energy-saving of RRBs is gradually becoming an important part of China’s energy conservation in the future.

Currently, the application of energy-saving technologies in China remains primarily focused on urban buildings. Except for a few exemplary residential buildings, most RRBs have not fully considered building energy-saving issues. Meanwhile, the existing energy-saving standards and technical measures for urban buildings are also unsuitable for the actual needs of RRBs [5]. RRBs are primarily self-built in China. Limited by the level of rural construction, there are common issues such as unreasonable functional layouts, relatively outdated building materials and techniques, and poor thermal performance of buildings. Most RRBs do not implement the national energy-saving standards [6]. Hence, the energy consumption of RRBs is increasing year by year, with a trend that might even surpass the energy consumption level of urban residences [7]. Particularly in hot summer and cold winter areas, RRBs face the dual challenges of severe cold in winter and extreme heat in summer. To meet the goal of energy conservation and reducing emissions, it becomes increasingly important to encourage the advancement of environmentally friendly RRBs characterized by minimal carbon footprints and reduced energy usage [8]. Moreover, as China’s rural revitalization strategy is put into action, an increasing number of RRBs are providing urban residents with leisure, accommodation, dining, and other services [9,10]. Optimizing the living spaces within RRBs has become an important requirement for shaping urban–rural relationships [11].

Parametric design in architecture frees architects from the heavy task of manual computer drafting, greatly improving efficiency while enhancing the rationality and feasibility of architectural design [12]. Parametric design utilizes programming languages to generate logical parameter models, controlling aspects such as the appearance, form, and layout of architecture by altering parameter variables, thereby establishing comprehensive logical connections for generation [13]. This generation of logical connections has positive implications for energy conservation during the architectural design phase. In the design process of RRBs, closely integrating energy-saving design with parametric design will be more conducive to improving the energy-saving effects of RRBs.

1.2. Literature Review

As one of the important types of architecture, the studies of energy conservation of residential buildings have always been a key focus for scholars. Extensive research has been conducted on various topics, including the indoor thermal environment [14,15], human thermal comfort [15], occupant behavior [16,17,18], building envelopes [19,20,21], influencing factors analysis [22,23], carbon emissions [24], energy-saving renovations [25], energy consumption surveys [26,27,28], and the utilization of renewable energy [29,30]. In terms of RRBs, a comparative analysis of indoor thermal conditions and human thermal comfort was carried out by Zhen et al. across cities, towns, and rural areas in the arid regions of China [15]. Li et al. studied the energy consumption patterns and the indoor environment of RRBs in China and discussed energy-saving optimization strategies for improving the thermal environment of RRBs [31]. Tsinghua University carried out a comprehensive survey of RRBs in China. The results proved that the energy-saving space of RRBs was very large, and the building performance needs to be further improved through the optimization of envelope structure and building layout [7,32].

Recently, building performance simulation combined with artificial intelligence has become a hot topic in architectural parametric optimization design for energy efficiency research [33]. Building performance simulation involves using computer-based mathematical models to simulate building performance, which is a more efficient method of predicting building performance than field experiments [34]. Furthermore, as energy efficiency in buildings continues to advance, there is increasing attention to comprehensive improvement of building performance, extending to environmental and economic benefits throughout the building’s lifecycle [35]. Common areas of building performance simulation in existing research include building energy consumption, carbon emissions, indoor thermal environment, lighting conditions, and economic costs [36,37], as well as indoor and outdoor wind environments, acoustic environments, and utilization of renewable energy sources [38]. These aspects of building performance are often simulated by using simulation software or platforms such as EnergyPlus, DOE-2, DeST, ANSYS, Radiance, Daysim, Flunt, Cadna, and DesignBuilder [39].

Numerous factors influence building performance. Passive design factors include the thermal properties of building envelopes, architectural form, layout, building components, and orientation. Active design factors include equipment systems and automated control systems [40,41]. For example, Shen et al. demonstrated that different residential building types present varying energy-saving potentials based on the simulation and survey data from 1995 to 2015 [42]. Moreover, these factors often exhibit contradictions, making it difficult for designers to rely solely on personal experience during the architectural design process. Optimization design provides a more objective evaluation of solutions and is a key approach to achieving comprehensive improvements in building performance. Optimization design can be divided into single-objective optimization (SOO) and multi-objective optimization (MOO), depending on the optimization goals. While SOO considers only one objective and may fall short in addressing the complexities of building design, MOO methods can integrate multiple conflicting objectives and identify optimal trade-off solutions [13]. This approach is widely applied across various domains in architectural design [43]. Key MOO methods include genetic algorithms, particle swarm optimization, ant colony optimization, simulated annealing, and neural networks, with genetic algorithms being among the most frequently used.

With the widespread use of parametric design in architecture, an increasing number of scholars are exploring its applications in architectural design [44]. For example, combined with building information modeling (BIM) technology, Peng et al. investigated the parametric design approach for periodic planar mosaic of building skin [45]. However, current parametric design has evolved from early parametric modeling into an architectural digital technology that integrates computer science with building performance simulation [46]. Numerous studies suggest that this technology is instrumental in decreasing building energy consumption by optimizing architectural parameters during the initial stages of building design [47]. Parametric optimization design, oriented towards building energy efficiency, commonly utilizes platforms such as DesignBuilder for building performance simulation, BIM platforms, or visual parametric design platforms like Rhino-Grasshopper. These platforms optimize aspects such as physical building performance and architectural spatial geometry [39].

The primary elements affecting building energy efficiency include building orientation, window-to-wall ratio (WWR), materials and construction of building envelopes, and air-conditioning systems [48]. These parameters are also the most common optimization parameters in early-stage parametric design for building performance. For instance, Chaturvedi et al. utilized a hybrid method combining Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) to optimize residential building envelopes and air-conditioning zones in India [49]. Similarly, Shao et al. utilized an improved hybrid Particle Swarm-Hooke-Jeeves algorithm (GPSPSOCCHJ), using EnergyPlus as the simulation engine and GenOpt as the execution platform. They optimized building orientation, WWR, and building envelope with a focus on minimizing lifecycle costs and constraints on “low energy consumption” [50]. Wu et al., targeting building energy consumption, daylighting, and indoor thermal comfort, applied BO-XGBoost and NSGA-II optimization algorithms to optimize building orientation, WWR, and air-conditioning systems in multi-story residential buildings [51]. These methods primarily optimize building envelopes or energy systems and do not address the optimization of architectural spatial geometry parameters.

Yang et al. demonstrated that the building form and spatial layout determined in the early stages of architectural design substantially influence both aesthetics and building performance [35]. A reasonable spatial layout can even guide residents to adopt energy-saving behaviors, thereby reducing building energy consumption [52]. Visual parametric optimization design shows its advantages in optimizing building form and spatial layout. For example, Ipek et al. aimed to optimize heating, cooling, lighting energy consumption, and building daylight autonomy (BDA). They used EnergyPlus 8.2 building energy analysis software combined with the NSGA-II genetic algorithm to optimize the WWR of different orientations under various building forms [53]. A new optimization framework was proposed by Xiao et al. for atrium building spaces using the Rhinoceros and Grasshopper platforms targeting building daylighting performance, energy consumption, and thermal comfort [54]. Gan et al. explored a method to optimize the floor layout of high-rise residential buildings using a GA, with building energy consumption and daylighting as optimization objectives [55]. Additionally, parametric optimization design methods have extended to urban planning layouts. For instance, Wang et al. proposed an optimization method for the building form and layout of high-rise residential areas using an Artificial Neural Network (ANN), targeting daylight, visual, and outdoor thermal metrics [56]. Liu et al. developed an optimization method for residential plan layout aimed at energy saving, based on the Grasshopper parametric platform. This method integrates Ladybug Tools for sunlight, microclimate, and energy consumption simulation and employs the single-objective genetic algorithm solver Galapagos [57].

1.3. Original Contributions

This study proposed a more systematic and scientific MOO framework for RRBs in the hot summer and cold winter zones in China. The original contribution of this research lies in the following aspects:

(1)

Table 1. Analysis of representative research on building performance optimization in China.

Reference	Year	Region	Building Type	Parameters	Simulation Objectives	Optimization Algorithms	Simulation Tools	Model
Wu et al. [51]	2024	Urban area/HSCW zone	Residential building	Building envelope	Energy consumption, daylighting, thermal comfort	BO-XGBoost, NSGA-II	Grasshopper, Ladybug, honeybee	Single building/Same plan
Chen et al. [58]	2022	Urban area/SC zone	Office building	Building envelope, Internal gain, System operation	Carbon emissions, thermal comfort, global cost	BPNN, NSGA-III	Python	Single building/Same plan
Gou et al. [59]	2018	Urban area/HSCW zone	Residential building	Building orientation, building envelope	Comfort time ratio, building energy demand	ANN, NSGA-II	EnergyPlus, jEPlus	Single building/Same plan
Xiao et al. [54]	2023	Urban area/HSCW zone	Atrium building(office building)	Geometric parameters	Daylighting, energy, thermal performance	SPEA-2	Grasshopper, Ladybug, honeybee	Single building/Same plan
Zhang et al. [47]	2021	Urban area/Cold zone	Residential building	Geometric parameters	Cooling load, heating load	Genetic algorithm	Grasshopper, Python	Single building/Same plan
Zhang et al. [60]	2022	Rural area/Cold zone	Residential building	Building orientation, Building envelope	Indoor environment, degree discomfort, hours	BP neural network	EnergyPlus	One-story building
Zhu et al. [9]	2020	Rural area/Cold zone	Rural tourism building	Geometric parameters	Energy consumption, daylighting, thermal comfort performance	SPEA-2, HypE	Grasshopper	One-story building
Hu et al. [38]	2023	Urban area/HSCW zone	Residential building	Geometric parameters	Sky view factor, sunshine duration, noise	ANN, NSGA-II	Grasshopper, Pachyderm Acoustics	Buildings
Wang et al. [56]	2021	Urban area/Cold zone	High-rise residential building	Building layout	Daylight, sunlight hours, sky view, outdoor thermal comfort	ANN, NSGA-II	MATLAB	Buildings

lists the representative research on building performance optimization in China in recent years. This indicates that current parametric optimization design in architecture mainly focuses on urban buildings, such as official and residential buildings, with less attention given to RRBs. In this study, we focus on RRBs, which are quite different from urban buildings in terms of building scale, design standards, personnel activity characteristics, and so on.

(2)

Existing studies typically optimize building physical performance or functional space scales based on the existing floor plans. This study, however, first categorizes different functional rooms based on energy consumption intensity at different locations within RRBs before proceeding with optimization. This approach results in more reasonable optimization outcomes that are more conducive to improving energy efficiency.

(3)

Many previous studies chose a typical floor for optimization due to the time required to simulate and optimize the entire building [47]. However, Ekici et al. highlighted the variations in performance between the ground level and the upper floors through optimization research on high-rise residential buildings, which can affect the optimization results [61,62]. In this study, the layout optimization of different building floors is considered according to the functional layout and the structural characteristics.

(4)

Most of the existing studies only considered spatial scale optimization without comprehensively taking the building structure into account. In our study, an optimization framework is introduced based on the logical relationships of building structures, comprehensively considering the load transfer paths between upper and lower floors for holistic building optimization design.

1.4. Aim of This Research

The aim of this research is to optimize the floor plan layout of RRBs and reduce their energy consumption by utilizing the Grasshopper parametric platform and employing the SPEA-2 genetic algorithm for parametric optimization. The optimization objectives are to minimize energy consumption for AC (air conditioning) and AL (artificial lighting). Zhejiang Province, in typical hot summer and cold winter zones, is the birthplace of China’s “Ten Million Project” and “Beautiful Village Construction”, as well as a leader in China’s rural revitalization [63]. Taking Zhejiang Province as an example, the application of this method can provide a reference for the design of RRBs in other similar climate areas and promote it nationwide.

2. Methodology

In this section, the typical characteristics of RRBs in Zhejiang Province, China, will be first presented. Then the complete parametric MOO method based on energy-saving of RRBs will be introduced in detail. Among them, the two main processes of optimization are (1) building layout optimization and (2) MOO of design parameters. The research flowchart is presented in Figure 1. The study is structured into four stages:

Step 1: Investigation into the present situation of RRBs in Zhejiang Province, such as building envelope, building structure, building plan, orientation and energy use, etc.

Step 2: Optimization of planar functional layout. By applying the Ladybug and Honeybee plugins in the Grasshopper parametric design platform, building daylighting and energy consumption simulations are conducted to obtain an energy-saving optimization function location map and carry out room functional layout.

Step 3: MOO of building space. Using the optimized building layout as the initial model, the Octopus plugin is applied to perform MOO, obtaining an optimal set of solutions from which the feasible optimal solution is selected.

Step 4: Case study. A representative RRB is chosen and implemented following the aforementioned steps, and the energy-saving outcomes pre- and post-optimization are juxtaposed.

2.1. Characteristics of RRBs in the Rural Areas of Zhejiang Province, China

2.1.1. Building Spatial Parameters of RRBs

To improve the design level and construction quality of RRBs, the Ministry of Housing and Urban–Rural Development of China, together with other departments, jointly issued the Guiding Opinions on Strengthening the Management of Rural Housing Construction, requiring all localities to compile standard design drawings of RRBs with regional and local characteristics, which can be used by villagers free of charge and provide technical consulting services [64]. The drawings of RRBs have been integrated as a reference for local villagers to build houses. To clarify the spatial parameter characteristics of RRBs, 150 sets of design drawings in Hangzhou, Lanxi, Dongyang, Huzhou, and other regions of Zhejiang Province were collected as data samples. There are eight types of main spatial functional rooms in RRBs, including the living room, entrance hall, bedroom, study room, dining room, kitchen, stairwell, and toilet. Firstly, the rooms were categorized in the drawings by function; then, based on the building floor plans, the width and depth of different rooms were recalculated; according to the building elevations and building sections, the building’s floor height and window height were calculated; based on the direction of the external windows, the orientation of the rooms was determined. Finally, the range of the main design parameters of each functional space, such as the height, width, and depth, was determined, as shown in

Table 2. Design parameters of each functional room.

Space	Width (m)	Depth (m)	Height (m)	WWR
Entrance hall	2.4~5.6	1.5~6.3	3.0~4.0	-
Living room	3.1~8.7	3.0~8.4	3.0~4.0	0.1~0.6
Master bedroom	2.7~6.3	2.4~6.7	2.6~3.8	0.1~0.7
Second bedroom	2.9~6.6	2.7~4.3	3.0~3.3	0.2~0.4
Elders’ bedroom	3.3~4.8	2.7~5.6	3.0~3.8	0.2~0.5
Study room	1.8~4.9	2.1~5.4	2.8~3.3	0.2~0.6
Dining room	2.4~6.0	2.7~7.2	3.0~4.0	0.2~0.6
Kitchen	1.8~5.7	2.0~5.4	2.5~3.8	0.1~0.4
Toilet	1.5~4.1	1.4~4.3	2.4~3.9	0.1~0.4
Stairwell	2.8~4.0	2.4~4.8	2.1~3.6	0.1~0.3

. The WWR is calculated according to the following formula:

$$WWR={\displaystyle \frac{S_{win}}{S_{wal}}}\times 100\mathrm{\%}$$

(1)

where, WWR represents the area rate of window-to-wall, %; $S_{win}$ is the total area of window openings in the same orientation, m²; and $S_{wal}$ is the area surrounded by the height and the positioning line of each functional room, m².

2.1.2. Orientation Distribution of Different Functional Rooms in RRBs

Architectural design is a complex creative process that requires both professional knowledge and respect for local customs and villagers’ living habits [12]. The orientation of rooms in RRBs with different functions is counted according to the collected drawings, and the results are shown in Figure 2a. The practice of placing the entrance hall adjacent to the living room, with a south-facing orientation, accounts for close to 100% and 95.83%, respectively, with 46.9% of lobbies being integrated with the living room. The bedrooms are mostly located in the south and north, accounting for 66.78% and 32.7%, respectively; the proportion of study rooms located in the south and north take up to 49.02% and 32.70%, respectively. In addition, the kitchen and dining room are always adjacent, mainly located in the north and east, followed by the south and west, and the proportion of kitchen serving as ding room is up to 7.45%. The proportion of kitchens located in the north, east, south, and west were about 78.16%, 14.94%, 5.75%, and 1.15%, respectively. Living rooms located in the north, east, south, and west are 51.06%, 23.40%, 14.89%, and 10.64%, respectively. There is a higher proportion of living rooms shared as dining rooms. Stairwells are mainly located in the north, accounting for 52.03%, followed by the west and east, about 38.21% and 9.76%, respectively.

2.1.3. Energy Usage of Different Functional Spaces in RRBs

The categories of end-use energy consumption encompass heating and cooling, lighting, cooking and hot water, and household appliances [7]. Among them, the heating, cooling, and lighting energy consumption are mainly affected by the building plan layout. Zhejiang Province belongs to a region with hot summers and cold winters, which require air conditioning for both heating and cooling purposes. The data from the Zhejiang Statistical Yearbook indicates a yearly rise in the ownership of air conditioning among rural households. And the number of air conditioners reached 184.3 units per 100 rural households in 2022 [65]. To better understand the usage of air conditioners in Zhejiang rural areas, a total of 300 households in Lin’an, Tonglu, Fuyang, etc., were randomly selected to investigate the installation of air conditioners in different rooms by questionnaires; the survey results are listed in Figure 2b. The survey results show that the bedroom and living room were installed with the highest proportion of air conditioning, with an average installation rate of more than 80%. Bedrooms include the master bedroom, second bedroom, and elders’ bedroom, of which the master bedroom and the second bedroom have the highest installation rates, up to 90.3% and 80%, respectively. The air conditioning installation rate for the elders’ bedrooms is slightly lower, about 67%, because elderly people are not accustomed to using air conditioners [15]. In addition, the installation rates of the living room and dining room are close to more than 50%, up to 66.3% and 67.3%, respectively. The results of the questionnaire survey demonstrate that the air conditioning installation rate is relatively high. The reason for this is attributed to the relatively advanced rural economy in Zhejiang, where villagers enjoy a prosperous life and have high demands for comfort. Therefore, the bedrooms, living room, dining room, and study room are defined as air-conditioned rooms whose main energy consumption is heating, cooling, and lighting (air conditioning + artificial lighting[AC + AL]); kitchen, stairwell, toilet, and other functional spaces that do not install air conditioner are defined as non-air-conditioned rooms, and their main energy consumption is lighting energy consumption (artificial lighting[AL]).

2.1.4. Building Envelopes and Structures of RRBs

Before China’s reform and opening up, Zhejiang RRBs were mainly brick-wood structures, and the wall types were gray brick walls, rammed earth walls, stone walls, and wooden board walls. After 2000, RRBs were mainly brick-concrete structures and reinforced concrete structures. According to the statistics of the Zhejiang Bureau of Statistics, by 2022, the proportion of RRBs with brick-concrete structures and reinforced concrete structures was 44.5% and 42.4%, respectively [65]. In addition to the number of stories and building area, the scale of RRBs in China can also be measured by “Jian”. “Jian” refers to the space of RRBs surrounded by load-bearing walls (or columns) and beams, which are the basic structural units of RRBs.

Within RRBs, the thermal performance of building envelopes significantly impacts building energy efficiency, especially the external walls and windows [10]. The most ordinary window types of RRBs in Zhejiang are plastic steel windows and aluminum alloy windows, typically equipped with single-layer glass. As for wall materials, traditional wall materials, ordinary wall materials (sintered solid bricks), and new wall materials are used. Although the government encourages the use of newer wall materials such as sintered porous bricks, concrete bricks, and thermal insulation blocks in RRBs, ordinary sintered solid bricks remain the predominant choice in rural Zhejiang. The thermal performance of wall materials and the heat transfer coefficient of walls are selected and calculated according to the standard [66]. Figure 3 shows the heat transfer coefficient of different types of walls of RRBs in Zhejiang Province. China’s urban residential buildings are mainly multi-stores and high-rise residential buildings. However, RRBs are mostly low-rise residential buildings with three stories or below, of which the architectural form is similar to detached houses in Japan and low-rise houses in the United States. On the other hand, the climate characteristic of Zhejiang Province is also similar to the 3C zone in Japan and 6 zone in the United States. In comparison to the energy-saving standards in urban residential buildings in China and analogous climate zones in Japan and the United States [67,68,69], it can be seen, as shown in Figure 3, that the thermal performance of external walls in RRBs in Zhejiang is generally poor.

2.2. Building Layout Optimization of RRBs

Grasshopper is a parametric design software under the Rhino platform, which can realize visual editing for building parametric modeling [70]. Ladybug and Honeybee are open-source plugins for Grasshopper, a parametric design software that can simulate and analyze building performance in terms of lighting and energy consumption. In this study, the most common RRBs with three “Jian” are taken as an example, and Ladybug 0.0.67 and Honeybee 0.0.64 based on Grasshopper for Rhino 6 are used to optimize the building plan layouts. The detailed procedure is illustrated in Figure 4.

2.2.1. Calculation on Energy Consumption Intensity of Spatial Geometry Model

In this section, the intensity distribution of AC and AL in different locations on the building plan was simulated to obtain the energy consumption intensity (ECI) distribution map (Figure 5b). First, a hypothetical geometric model was created to clear the building energy consumption distribution, setting nine different spatial orientation types. The dimensions of length, width, and height of each model were set to 3.6 m, 3.6 m, and 3.0 m, respectively. The rooms were arranged in the order of ①~⑨, as shown in Figure 5a. Assuming the internal personnel and equipment settings of each model are the same, the energy consumption of each model is associated with the building envelope, WWR, and orientation [71]. The WWR of each room is set at 0.35, and the adjacent walls and roofs are set as insulation surfaces. The equation for calculating ECI is presented below:

$$ECI=E_{AC}+E_{AL}$$

(2)

where $ECI$ is the total energy consumption intensity of AC and AL in every spatial geometry model, kWh/m²; and $E_{AC} \mathrm{a}\mathrm{n}\mathrm{d} E_{AL}$ represent AC energy consumption and AL energy consumption, respectively, kWh.

(1)

AC energy consumption ($E_{AC}$)

The AC of RRBs pertains to the necessary heat quantity to sustain a particular indoor thermal atmosphere and the requisite volume of cool air, which are crucial for determining the air conditioning system. Influencing factors include the number of personnel and their activities, electrical equipment, sunlight exposure, building envelope, and outdoor climate conditions. The AC energy consumption depends on the internal spatial layout, thermal performance of the building envelope, and building orientation. The calculation formula for AC energy consumption is as follows:

$$E_{AC}=E_C+E_H$$

(3)

where $E_{AC}$ represents annual unit area cooling and heating energy consumption, kWh/m²; $E_C$is represents the annual cooling energy consumption per unit area, kWh/m²; and $E_H$ is represents the annual heating energy consumption per unit area, kWh/m².

The calculation formula for cooling energy consumption is as follows:

$$E_C={\displaystyle \frac{{\mathrm{Q}}_C}{A\times {COP}_c}}$$

(4)

where E_C is annual unit area cooling energy consumption, kWh/m²; Q_c is total annual cooling energy consumption, kWh; A is the area of the spatial geometry models, m² (set to 3.6 × 3.6 = 12.96 m²); and COP_c is coefficient of performance of the cooling system, taken as 3.60.

The calculation formula for heating energy consumption is as follows:

$$E_H={\displaystyle \frac{Q_H}{A\times {COP}_H}}$$

(5)

where E_H is annual unit area heating energy consumption, kWh/m²; Q_H is total annual heating energy consumption, kWh; S is the area of the spatial geometry models, m² (set to 3.6 × 3.6 = 12.96 m²); and COP_H is coefficient of performance of the heating system, taken as 2.60.

Honeybee connects the model constructed by the Grasshopper parametric design platform. It adopts the EnergyPlus energy consumption simulation software to perform a dynamic simulation of the cooling and heating energy consumption of 8760 h throughout the whole year. The indoor set temperature is set to 18 °C in winter and 26 °C in summer. The internal personnel, equipment, and other related parameters of all models are the same. The thermal performance of the building envelope is detailed in

Table 3. Interior loads and temperature setting of main zones.

Room	No. People	Metabolic Rate (W/m2)	Set Temperature (°C)		Lighting Power Density (W/m2)	Equipment Power Density (W/m2)
			Summer	Winter
Bedroom	2	40	26	18	3	15
Living room	6	60	26	18	4	15
Dining room	6	60	26	18	6	15
Card room	4	65	26	18	4	15
Study room	1	60	26	18	4	15
Kitchen	1	100	30	8	4	75
Toilet	1	120	30	8	4	15
Stairwell	/	/	30	8	2	/
Others	/	/	30	8	2	/

.

(2)

AL energy consumption ($E_{AL}$)

Adequate lighting establishes a visual ambiance that facilitates the efficient, precise, and secure execution of visual tasks without inducing unnecessary visual strain or discomfort [72]. The illumination may be daylight, electric light, or a combination of both. The calculation of lighting energy consumption includes periods during which artificial lighting is used at night, as well as during the daytime when daylight does not meet the lighting requirements. The duration of lighting fixture usage at night is established based on the usage schedules of various rooms (Figure 6b). Standards specify that the minimum illuminance values for living rooms, bedrooms, dining rooms, kitchens, and bathrooms in RRBs should be no lower than 100 lx, 75 lx, 150 lx, 100 lx, and 100 lx, respectively [6,73]. When the illuminance falls below these standards, artificial lighting is required. Conversely, sunlight may also result in illuminance far exceeding these standards. Research by Nabil et al. demonstrated that when the illuminance on the working face is below 100 lx, the level is too low to meet visual needs, requiring the use of artificial lighting. Illuminance levels between 100 lx and 2000 lx are sufficient for indoor activities and do not require artificial lighting. When the illuminance exceeds 2000 lx, the level is too high on the working face, potentially causing glare [74]. In such cases, sunlight needs to be blocked using curtains, blinds, or other means, and artificial lighting is used instead.

To evaluate whether indoor natural lighting meets the required illuminance, Static assessment metrics, like the daylight factor, are employed in standards to assess the quality of natural lighting. The daylight factor describes the illuminance level on an indoor working face under an overcast sky model, representing the quality of natural lighting under the most unfavorable conditions (no sunlight) throughout the year. However, natural lighting varies continuously throughout the year, making it difficult to represent the quality of indoor illuminance at all times, which presents certain limitations.

Daylight Autonomy (DA) measures the percentage of time during the year when a point on the working face meets the minimum illuminance requirement solely through natural lighting. Continuous Daylight Autonomy (CDA) measures the percentage of time when natural lighting meets the target illuminance and the illuminance at the calculation point is below the target level. Both indicators can be used to assess the quality of natural lighting throughout the year and estimate the reduction in artificial lighting electricity consumption due to natural lighting. Useful Daylight Illuminances (UDI) is defined as the percentage of time during the year that the natural light intensity in a working area falls within a specific range. UDI is typically divided into three categories: UDI_{E<100 lx}, UDI_{100 lx<E<2000 lx}, and UDI_{E>2000 lx}. UDI evaluates not only insufficient illuminance levels that are unusable but also excessively high illuminance levels that cause visual discomfort. RRBs should maximize the use of natural lighting to establish an appropriate indoor lighting environment. Adequate natural lighting benefits the physiological and psychological health of residents and helps reduce artificial lighting energy consumption [6].

Based on the above-related research, this study uses UDI_{100 lx<E<2000 lx} as the evaluation indicator for lighting performance by calculating the proportion of time throughout the year when indoor lighting fails to meet visual needs. This calculation helps determine the additional artificial lighting required. According to the standards, the selected time period for lighting is from 6:00 to 18:00. When calculating the annual unit area lighting energy consumption, the day is divided into daytime and nighttime periods. The calculation formula is as follows:

$$E_{AL}={\displaystyle \frac{W\times t_1+(1-{UDI}_{100\mathrm{l}\mathrm{x}<E<2000\mathrm{l}\mathrm{x}})\times W\times t_2}{t_0\times 1000}}$$

(6)

where E_AL is the annual unit area lighting energy consumption, kWh/m²; W represents lighting power density listed in Table 3, W·h/m²; t₁ represents nighttime lighting usage duration for different rooms, h; ${UDI}_{100\mathrm{l}\mathrm{x}<E<2000\mathrm{l}\mathrm{x}}$ refers to the annual daytime percentage of illuminance distribution across the working plane that is within a range from 100 lx to 2000 lx, %; t₂ is annual daytime operating hours, h; and $t_0$ is yearly hours, which is 8760 h.

After establishing the model on the Grasshopper parametric design platform, the Generate_Zone_Test_Points component is first used to generate test points in the daylighting area, setting the distance from the reference plane to 0.75 m. Then, the Annual_Daylight_Simulation component is used to set the annual daylight simulation analysis, and the Run_Daylight_Simulation component is used for the simulation. Finally, the Read_Annual_Result_II component is used to read the calculation results. The Read_Annual_Result_II component allows for setting the maximum and minimum required illuminance values as well as the working hours.

2.2.2. Energy Consumption Simulation for Different Functional Rooms

Building energy consumption can be classified into broad and narrow definitions. Broadly, it pertains to the total energy consumption throughout a building’s lifespan, including the production of building materials, construction processes, operation, renovation, and demolition stages. In a narrow sense, it refers to the energy consumption during the building’s operational phase, including cooling, heating, lighting, and other daily activities [32]. In residential buildings, over 50% of the energy is used for cooling and heating [75]. The energy consumption levels of different functional rooms in nine different spatial orientations vary due to differences in activities, lighting, and air conditioning usage. The parameters of the building envelope are based on the performance of commonly utilized building envelopes in Zhejiang rural areas (Section 2.1.4). As the performance of building envelope structures and air conditioning systems enhances, the occupancy rate and density within the building’s interior emerge as primary factors influencing building energy consumption. The hourly occupancy rates, lighting equipment usage rates, appliance usage rates, occupant activity schedules, lighting equipment usage schedules, and appliance usage schedules for different rooms are set according to relevant standards [67] and survey results, as shown in Figure 6a. Research indicates that rural inhabitants in China exhibit a greater tolerance for indoor thermal environments compared to their urban counterparts. Therefore, in rooms without heating or air conditioning, such as the kitchen, toilet, and stairwell, the indoor set temperature is 8 °C in winter and 30 °C in summer [6]. In rooms with air conditioning systems, the set temperature is 18 °C in winter and 26 °C in summer.

With the gradual improvement of building envelope performance, the influence factors of external environmental on building energy consumption are decreasing, while internal factors are becoming one of the main reasons influencing building energy consumption [6]. Among these factors, lighting not only impacts the indoor cooling and heating loads but also determines the AL energy consumption. The lighting power density (LPD) of fixtures refers to the installed lighting power per square meter of building area. According to the Energy-Saving Design Standards for Rural Residential Buildings, the LPD for RRBs should not exceed 7 W/m² per household. When the illuminance value of functional spaces is higher or lower than the specified illuminance, the LPD should be proportionally increased or decreased. Therefore, the LPD is set to 4 W/m² for living rooms, studies, kitchens, and bathrooms; 3 W/m² for bedrooms and chess rooms; 6 W/m² for dining rooms; and 2 W/m² for stairwells and other spaces. Figure 6b shows the lighting time usage rates for different functional spaces, and the lighting time is set according to the usage rates. When the UDI is in the range of 100~2000 lx, natural lighting is used. When the UDI is below 100 lx or exceeds 2000 lx, artificial lighting is used.

According to Section 2.2.1, the ECI values of the hypothetical model in different spatial locations can be simulated. However, in actual RRBs, the building area of each functional room varies. Therefore, the actual building area of functional spaces in RRBs is calculated and then ranked by energy consumption according to the following formula:

$$E_n={ECI}_n\times S_n$$

(7)

where E_n is the actual annual AC and AL energy consumption of different functional spaces in RRBs, kWh; ECI_n is the energy consumption intensity of the assumed spatial geometric model, kWh; S_n is the area of different actual functional spaces in RRBs, m²; and n is functional space number, 1, 2, …, 9.

2.2.3. Functional Layout Orientation

Based on the ECI distribution from Section 2.2.1 and the actual energy consumption values of rooms from Section 2.2.2, a preliminary functional layout optimization is achieved by positioning rooms with the principle of “space with higher energy consumption is set in the location with lower energy consumption intensity”. This principle aims to optimize energy efficiency in the initial functional layout. Subsequently, by integrating the statistical data on different room orientations in RRBs from Section 2.1.2, the functional layout is further refined and optimized to obtain the final energy-saving functional layout plan. During the parametric design process, determining control relationships is crucial for achieving energy-efficient architectural solutions. The generation logic and modeling methods of the residential model are based on room functions, design parameters, and positioning adjacency relationships. Constraints on room parameters are set using the Number Slider component in the Grasshopper design platform, followed by the sequential establishment of each functional room.

The construction logic of functional rooms is shown in Figure 7. In the figure, numbers represent space function identifiers, with ‘a’ and ‘b’ denoting the room’s width and depth dimensions, respectively. Subscripts ‘0’, ‘1’, ‘2’, etc., indicate the construction sequence of functional spaces. The starting coordinate (0,0) is based on the bottom-left corner of room 1, with subsequent rooms modeled relative to the preceding room. Considering the architectural characteristics of rural residences with three open spaces, rooms in the same vertical column share identical bay settings, labeled as a0, a1, and a2. Room depths (b0, b1, b2, b3, b4, b5, b6, b7, b8) follow the sequence of functional space construction. Throughout the construction process, models are built according to the principle of constant room area, serving as initial models for MOO.

2.3. MOO Plan Layout of RRBs

With the swift advancement of computer science and artificial intelligence, scholars have attempted to solve engineering design problems using artificial intelligence technologies [76]. These technologies have also been widely applied in various fields of architectural design. Currently, common artificial intelligence methods used in architectural design include optimization algorithms, artificial neural networks, shape grammars, clustering algorithms, swarm intelligence, cellular automata, and more [12]. Among them, optimization algorithms are the most classical type.

2.3.1. MOO Methods and Algorithms

MOO employs optimization methods to obtain the best solutions that balance various objectives and can solve optimization problems involving two or more conflicting objective functions. It has been widely applied in the architectural field [43]. MOO requires setting objective functions, optimization parameters, and constraints, which can be expressed as

$$\min y=F\left(x\right)=(f_1\left(x\right),f_2\left(x\right),\cdots ,f_m(x\left)\right)$$

(8)

$$\begin{array}{c}\mathrm{S}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{o}:g_i\left(x\right)\le 0,i=1,2,\cdots ,p\\ h_j\left(x\right)\le 0,i=1,2,\cdots ,q\end{array}$$

(9)

x ∈ D

(10)

where $f\left(x\right)$ represents the objectives in this study, respectively, indicating AC and AL energy consumption; $g_i\left(x\right) \mathrm{and} h_i\left(x\right)$represent the constraints; and D is the spatial variable, i.e., the threshold range of the optimization parameters.

Common MOO methods include the weighted sum method [37], the ε-constraint method [34], the analytic hierarchy process [77], and the Pareto front [13]. Among these, the Pareto front method is the most popular. The Pareto front approach allows for the concurrent consideration of multiple objectives and facilitates the extraction of the Pareto optimal solution set from all viable solutions [59]. Solutions on the Pareto front are all optimal and of equal importance. For a MOO problem, a Pareto solution may be optimal for one evaluation criterion but poor for another. Therefore, to identify the optimal solutions from the Pareto front set, additional decision-making is necessitated to single out the required optimal solutions [78].

The Pareto front method requires evaluating numerous feasible solutions and can only find the optimal solution after multiple iterations, which makes the algorithm relatively inefficient. Therefore, selecting an appropriate optimization algorithm is a crucial step in the MOO process. An appropriate optimization algorithm can help designers save time during the optimization and iteration process while precisely achieving the preset design goals [79]. Common MOO methods include evolutionary algorithms such as simulated annealing, particle swarm optimization, ant colony optimization, and genetic algorithms. Among these, genetic algorithms are considered a more efficient and accurate approach. Genetic algorithms simulate the mechanism of natural selection and genetics in Darwin’s theory of biological evolution, searching for optimal solutions by mimicking the natural evolution process. Compared to traditional optimization algorithms, genetic algorithms initiate the search process from a collection of solutions instead of commencing with just one solution, and their iterative process uses probabilistic mechanisms, with selection, crossover, and mutation being random operations rather than deterministic precise rules, thus having better global optimization properties. Common genetic algorithms include NSGA-II, NSGA-III, and SPEA-2. Studies have shown that SPEA-2 performs better overall compared to other algorithms.

Rhino + Grasshopper possesses high visualization and extensibility capabilities, making it the most widely used parametric design platform today. SPEA-2 has been integrated into Grasshopper’s optimization tool, Octopus. In this study, the Octopus plugin is used as part of the Grasshopper parametric design platform, employing a multi-objective optimization method based on genetic algorithm theory.

2.3.2. MOO Process

The process of MOO is divided into two stages, as shown in Figure 8. The first stage is to optimize the floor with higher energy consumption. First, based on the collected main design parameters of RRBs in Section 2.1, determine the variable parameters of each functional space; next, construct a parametric residential geometric model according to the functional layout positioning and use the Ladybug + Honeybee plugins to calculate the evaluation indicators; then, use the Octopus plugin to perform iterative calculations to obtain the Pareto front set; finally, utilizing the Pareto front solution set and the developed parametric geometric model, filter the energy-saving design schemes to obtain the optimal rural residential energy-saving design scheme.

The subsequent phase involves optimizing the remaining floor to achieve reduced energy consumption, taking the load transfer logic relationship of the building structure as the constraint condition. Specifically, it analyzes the structural characteristics of the building plan obtained after the first stage of optimization and uses them as the limit of the next stage of building plan space parameter optimization. For instance, if the RRB is a brick-concrete structure building, the load-bearing wall is responsible for the vertical transmission of the load. Then, the load-bearing wall in the first-stage optimized building plan automatically becomes the load-bearing wall in the next-stage building plan, and the spacing between the load-bearing walls will no longer be optimized. Thus, the calculation steps and the amount of calculation can be reduced.

Among the energy consumption of RRBs, AC and AL account for the largest proportion and are intimately associated with the building’s layout. Therefore, AC and AL are selected as the optimization objectives. The calculation principle and method of AC and AL are introduced in detail in Section 2.2. The factors affecting building AC and AL energy consumption of RRBs include the width and depth of functional rooms, solar heat gain coefficient(SHGC), visible light transmittance(VLT), and WWR, which are selected as the optimized variable parameters.

3. Case Study

3.1. Case House Information

An RRB in the Lin’an district of Hangzhou City (Longitude: 120.20° E, Latitude: 30.30° N), situated in the northern region of Zhejiang Province, was selected as a case study, as shown in Figure 9a. The case house is a typical south-facing, three-story RRB, with a floor area of 150 m2 and a total building area of 450 m². The first floor comprises a living room, kitchen, entrance hall, bedroom, dining room (including card room), toilet, and stairwell. The functional layout of the second floor and the third floor is consistent, including the master bedroom, secondary bedroom, study, living room, toilet, and stairwell. The layouts of the RRB are shown in Figure 9b,c. The RRB has a story height of 3.3 m, a north-south WWR of 0.35, and an east-west WWR of 0.25. The other information is listed in

Table 4. Basic information of case house.

Content	Case House
Location	Latitude: 30.30° N; Longitude: 120.20° E
Orientation	North and south
Structure	Brick-concrete structure
WWR	South: 30%; North: 25%;
External walls	240 mm fired perforated brick wall with 20 mm plaster layer; U = 1.83 (W/m2·K)
Windows	Ordinary aluminum alloy windows with single-layer glass; U = 5.8 (W/m2·K); SHGC = 0.75
Roof	Flat roof: U = 3.8 (W/m2·K)
Airtightness	1.0 h−1

.

3.2. Building Layout Optimization of Case Building

3.2.1. Energy Consumption Intensity Calculation of Spatial Geometric Model

In accordance with the approach delineated in Section 2.2.1, a set of spatial geometric models with the length, width, and height of 3.6 m, 3.6 m, and 3.0 m (height), respectively, were constructed on the Grasshopper parametric design platform, and then the energy consumption intensity of AC and AL was simulated. Lighting energy consumption is the cumulative total of daytime and nighttime lighting energy usage. The simulation period of daytime lighting energy consumption is set from 6:00 am –18:00 pm, and the UDI is 100–2000 lx. When the average illumination value is lower than 100 lx, or higher than 2000 lx, artificial lighting is considered. Figure 10a is the AL energy consumption intensity distribution map of different building spatial geometric models without air conditioning. It shows that the AL energy consumption intensity required in the middle location ⑤ is the largest, at 31.33 kWh/m2, because it is surrounded by rooms. Next is ⑥ on the east, for 24.92 kWh/m². The third is ⑦⑧⑨ in the north, for 24.38 kWh/m², due to the same window-to-wall rate and orientation. The following locations are ①②③ in the south, with an AL energy consumption intensity of 23.69 kWh/m². The smallest is the westward position ④, with 22.22 kWh/m².

Figure 10b shows the distribution of AC + AL energy consumption intensity in geometric space when the indoor temperature is set for air conditioning. The energy consumption intensity of AL + AC in the location of ⑦⑨①③ is 310.59 kWh/m², 309.65 kWh/m², 307.25 kWh/m², and 306.87 kWh/m², respectively. The four positions are located at the corners, with the largest surface area and larger energy consumption. Next is the west location ④ and the east location ⑥, which are 287.11 kWh/m² and 286.88 kWh/m², respectively. The following is the north location ⑧ and south location ②, for 286.11 kWh/m² and 284.10 kWh/m², respectively. The position with the lowest energy consumption intensity is in the middle, number ⑤, with an AC + AL energy consumption intensity of 251.31 kWh/m².

3.2.2. Calculation of Energy Consumption in Different Function Rooms

Because the layout of the second and third floors is the same, besides the first floor, one of the two floors was selected for optimization. After the energy consumption intensity of the spatial geometric models in different locations is simulated, the settings of personnel, lighting, electrical appliances, and air conditioning are listed in Figure 6 and Table 3. Subsequently, the ultimate energy consumption was computed in accordance with Formula (7). The results are presented in Figure 11. On the first floor, the AL + AC energy consumption of the dining room (including the card room) is the largest, followed by the living room and elders’ room. The order of energy consumption of non-air-conditioned rooms is the kitchen, toilet, entrance hall, and stairwell, with much smaller energy consumption than that of air-conditioned rooms and little difference between each other. The energy consumption of the rooms on the second and the third-floor room are ranked from large to small as the master bedroom, living room, south bedroom, study room, and north bedroom. The toilet and stairwells have the least energy consumption.

3.2.3. Functional Layout of Building Plans

According to the principle of ‘space with higher energy consumption is set in the location with lower energy consumption intensity’, the arrangement of different rooms in geometric space is set. According to the simulation results of energy consumption from large to small, the functional rooms on the first floor are the dining room (including the card room), living room, elders’ room, kitchen, toilet, entrance hall, and stairwell. The second and third floors are ranked as follows: master bedroom, living room, south bedroom, study room, north bedroom, stairwell, and toilet.

If the functional layout of a building plan relies solely on the simulation outcomes of building energy consumption, there may be some functional room layouts that do not align with the local residents’ lifestyle habits. Therefore, after the initial arrangement, the adjustment is carried out in combination with the statistics of the orientation distribution in Section 2.1.2. Figure 12 shows the building plan layouts of the case house before and after optimization.

3.3. MOO of Case Building

The analysis in Section 3.2 demonstrated that compared with the first floor, the air conditioning area and energy consumption on the second/third floor are larger, and the potential for energy savings is more significant. Therefore, the second/third floor with a larger energy consumption demand is selected for MOO. Then, the MOO of the first floor is carried out according to the logical relationship of the building structure. Leveraging the Grasshopper parametric design platform and employing the SPEA-2 multi-objective genetic algorithm within the Octopus plugin, the Pareto front solution set is determined to extract the most effective energy-saving design strategies. The MOO design program consists of four parts: geometric model construction, daylight performance indicators, energy consumption indicators, and the calculation results. The parameters of the building envelope, personnel, lighting, equipment, and other related parameters are set as listed in Figure 6 and Table 3. The optimization objectives are AC and AL energy consumption. Elitism is set to 0.50; Mut. Probability, Mutation Rate, and Crossover Rate are 0.20, 0.90, and 0.80, respectively; the population size is set to 10.

3.3.1. MOO Simulation Results of the Second/Third Floor

The parameters related to AC and AL energy consumption mainly include width, depth, WWR, SHGC, VLT, etc. The range of every parameter and step is shown in

Table 5. Simulation variable parameters of second/third floor.

Rooms	Width (m)		Depth (m)		WWR		SHGC		VLT
	Range	Step	Range	Step	Range	Step	Range	Step	Range	Step
Study room	1.8~3.3	0.3	2.1~5.4	0.3	0.2~0.6	0.1	0.1~0.9	0.1	0.4~0.9	0.1
Toilet	1.8~3.3	0.3	1.4~4.3	0.3	0.1~0.4	0.1
Stairwell	1.8~3.3	0.3	2.4~4.6	0.3	0.1~0.6	0.1
Master bedroom	3.0~6.3	0.3	2.4~6.7	0.3	0.1~0.7	0.1
Living room	3.0~6.3	0.3	3.0~8.4	0.3	0.1~0.6	0.1
Bedroom(south)	3.0~6.6	0.3	2.7~4.3	0.3	0.2~0.4	0.1
Bedroom(north)	3.0~6.6	0.3	2.7~4.3	0.3	0.2~0.4	0.1

. After 20 generations of iterative simulation, 12 Pareto front solutions are obtained, and the layout of each solution is shown in Figure 13b. By analyzing the plan shape of the 12 solutions, the Pareto front solution of point B is finally selected as the best scheme, which has a more reasonable plan layout, considering comprehensively the AC and AL. The annual AL of scheme B is 24.74 kW·h/m², and the annual AC is 27.79 kW·h/m². The parameters of scheme B are listed in

Table 6. Optimization results of case house.

Floor	Rooms	Width (m)	Depth (m)	WWR	SHGC	VLT	AC (kW·h/m2)	AL (kW·h/m2)
First Floor	Entrance hall	3.0	5.3	/	0.2	0.6	16.47	19.18
	Toilet	3.0	1.7	0.4
	Stairwell	3.0	5.0	0.2
	Living room	4.3	3.7	0.6
	Corridor	4.3	1.4	/
	Ding room	4.3	5.3	0.4
	Elderly room	3.8	2.4	0.5
	Kitchen	3.8	3.2	0.3
Second Floor	Study room	3.0	4.0	0.6	0.2	0.7	24.74	27.79
	Toilet	3.0	1.7	0.4
	Stairwell	3.0	5.0	0.1
	Master bedroom	4.3	5.3	0.6
	Living room	4.3	4.0	0.6
	Bedroom (south)	3.8	2.4	0.2
	Bedroom (north)	3.8	4.2	0.3

.

3.3.2. MOO Simulation Results of the First Floor

RRBs mostly adopt masonry wall load-bearing structures. From the perspective of reasonable structure and economic applicability, the structural arrangement of building plans should be conducive to the vertical transmission of loads. Therefore, the bay and depth of the rooms on the first floor are consistent with that of the corresponding room on the second floor. Only the WWR, SHGC, and VLT are used as variable parameters for the MOO of the first-floor plan. After seven times of iterations, a total of six Pareto optimal solutions are obtained (Figure 14a), and the layout of each scheme is shown in Figure 14b. Through comparative analysis, the D1 solution has a better optimization effect. The annual AL energy consumption of scheme D is 16.47 kW·h/m², and the annual AC is 19.18 kW·h/m². The parameters of scheme D are listed in Table 6.

4. Discussion

4.1. Comparison of Building Plan Layouts before and after Optimization

During the plan optimization, the second/third floor was prioritized, where air conditioning occupies a larger proportion of the building area. The plans before and after optimization are shown in Figure 9c and Figure 15a, respectively; the stairwell was moved to the northwest-facing position with higher energy consumption intensity, which is more conducive to counteracting the adverse effects of the external environment. The master bedroom, secondary bedroom, and study room were all relocated to positions with lower energy consumption intensity than before.

Comparing the first-floor plans before and after optimization in Figure 9c and Figure 15b, to consider both energy consumption and the local residents’ habits, the position of the kitchen remained. In the optimized plan, the dining room (including a card room) was moved to a central north-facing position adjacent to the kitchen. The elders’ bedroom was arranged on the south side, where building energy consumption is lower and more suitable for the comfort and mobility of the elderly. The living room maintains a southern orientation and has been moved to a position with lower energy intensity. The entrance hall is located on the west side facing south, providing better climate buffering.

During the optimization process, considering the impact of the air-conditioned area on building energy consumption, the area of each air-conditioned room remained unchanged. Before optimization, the case building had a three “Jian” structural layout; after optimization, the building plan still maintained a three “Jian” structural layout, and the building structure became more reasonable. However, the shape of the building changed, resulting in an increased building shape coefficient.

4.2. Comparison of Energy Consumption before and after Optimization

Figure 15 shows the final floor plans obtained from multi-objective parametric optimization for the case study building. The main air-conditioned rooms on the first floor are the dining room, living room, and elders’ room. The AC + AL energy consumption before optimization was 3314 kW·h, 2656 kW·h, and 1745 kW·h, respectively; after optimization, the energy consumption was 3130 kW·h, 2500 kW·h, and 1663 W·h, respectively; the energy-saving rates were 5.55%, 5.87%, and 4.70%. The living room has the highest energy-saving rate, followed by the dining room and the elderly room.

The main air-conditioned rooms on the second/third floor are the master bedroom, second bedroom, living room, and study room. The AC + AL energy consumption of the master bedroom, living room, second bedroom 1, study room, and second bedroom 2 before optimization was 3416 kW·h, 2932 kW·h, 2755 kW·h, 2194 kW·h, and 1792 kW·h, respectively; after optimization, the energy consumption was 2932 kW·h, 2497 kW·h, 2276 kW·h, 1971 kW·h, and 1611 kW·h, respectively; the energy-saving rates were 12.62%, 14.84%, 17.39%, 10.16%, and 10.10%. The second bedroom 1 and living rooms have higher energy-saving rates than the others.

As shown in Figure 16, energy consumption for cooling in summer is greater than that for heating in winter and lighting. The figure also indicates that the AC + AL of the air-conditioned rooms on the first floor before optimization was 7715 kW·h. At the same time, after optimization, the AC + AL was 7293 kW·h, reducing the building energy consumption by approximately 5.50%. The AC + AL of the air-conditioned rooms on the second floor before optimization was 13,089 kW·h, while after optimization, the AC + AL energy consumption was 11,340 kW·h, reducing the energy consumption by approximately 13.36%.

The total annual energy consumption after optimization is lower than that of the case building, with energy savings of 661 kW·h and 1739 kW·h, respectively. Using the parametric optimization method described, the overall energy efficiency rate of the optimized RRB is approximately 11%.

4.3. Comparison with Other Studies

Phased optimization is a method often used in optimization simulation that can address the issue of having too many optimization objectives and parameters, which results in excessive computational. There are generally two scenarios; the first one involves phased optimization of the optimization objectives. Wang et al. first choose Cool load and Annual discomfort hours as the optimization objectives, and the NSGA-II genetic algorithm is used for MOO to obtain the Pareto front solutions; then, the TOPSIS decision-making method is employed, with Cool load, Annual discomfort hours, Net site energy, and Global cost as objectives for further optimization [10].

The other type is the phased optimization of optimization parameters, which usually involves optimizing building geometric parameters first, followed by the optimization of building envelopes and equipment systems, etc. For example, in the research of Yang et al., the first step was to perform MOO on four architectural geometric parameters, such as the length and width of the atrium and the WWR, obtaining six optimal solutions; the second step was to further optimize the thermal performance of building envelopes such as external walls, roofs, and windows based on the optimal solutions [35].

In addition, most existing studies on the optimization of geometric parameters are conducted based on the same building layout without considering different functional layouts on different floors [47,54]. Different from other studies, the phased optimization in this paper first optimizes the layout of the building plans; then it optimizes the geometric dimensions and envelopes performance of the building. This simulation optimization method takes into account the unity of architecture and structure, which helps to achieve greater energy-saving effects.

5. Conclusions

This study, taking RRBs in Zhejiang Province as an example, seeks to introduce a novel framework for the parametric optimization of building plans of rural residences in China’s hot summer and cold winter zones aimed at reducing building energy consumption. The framework is based on the Rhino + Grasshopper parametric design platform, focusing on the optimization of AC and AL. It first involves the functional layout of residential building plans, followed by the optimization of spatial geometric parameters of rooms and relevant parameters. The detailed procedure and research findings are presented as follows:

(1)

Field surveys and numerical analysis of standard design drawings for RRBs clarified the spatial geometric characteristics and air conditioning usage of rural residences in Zhejiang. Statistical results show that parameters such as width, depth, and WWR of RRBs fall within certain ranges. The orientation of lobbies, living rooms, master bedrooms, kitchens, and stairwells follows certain patterns. For example, lobbies and living rooms on the first floor are mostly south-facing; kitchens are often south-facing, while stairwells are mostly north-facing. In addition, the proportion of air conditioning installation in major rooms is quite high, reaching over 80%.

(2)

The parametric optimization of rural residential floor plans involves two main steps. The first step is to determine the functional layout of the residential floor plans. Based on the basic structural unit of RRBs, referred to as “Jian”, the building layout is divided into an ideal number of spatial geometric models. An annual dynamic simulation of the building’s AC and AL was performed to obtain an energy consumption intensity distribution map was obtained. Then, the annual energy consumption of actual rooms is simulated. Based on the principle that “space with higher energy consumption is set in the location with lower energy consumption intensity” and the spatial distribution characteristics derived from statistical analysis, the rooms are positioned and adjusted accordingly. The second step involves parametric MOO of the initially positioned building layout. The SPEA-2 genetic algorithm is used for MOO of the parameters such as width, depth, WWR, SHGC, and VLT. During optimization, the floors with larger air-conditioned areas are optimized first. The structural logic relationship between the upper and lower floors is comprehensively considered to constrain the spatial geometric parameters of the corresponding rooms, thereby reducing the computational load and improving efficiency. Finally, the Pareto Front is generated, representing the potential optimal solutions.

(3)

Finally, a typical RRB in Zhejiang was selected, and the proposed parametric optimization design framework was applied. The final energy savings rate reached 11%.

The optimization design framework proposed in this paper can be used for the parametric optimization design of ordinary rural residential layouts, though it also has some limitations. This framework is suitable for the optimization of relatively simple building layouts and structures. However, it has limitations when applied to complex building layouts and structures. As the design level of RRBs improves, the internal space and structural forms of buildings will become more complex, which requires further in-depth research in the future.