An ANN-exhaustive-listing method for optimization of multiple building shapes and envelope properties with maximum thermal performance

Abstract

With increasing awareness of sustainability, demands on optimized design of building shapes with a view to maximize its thermal performance have become stronger. Current research focuses more on building envelopes than shapes, and thermal comfort of building occupants has not been considered in maximizing thermal performance in building shape optimization. This paper attempts to develop an innovative ANN (artificial neural network)-exhaustive-listing method to optimize the building shapes and envelope physical properties in achieving maximum thermal performance as measured by both thermal load and comfort hour. After verified, the developed method is applied to four different building shapes in five different climate zones in China. It is found that the building shape needs to be treated separately to achieve sufficient accuracy of prediction of thermal performance and that the ANN is an accurate technique to develop models of discomfort hour with errors of less than 1.5%. It is also found that the optimal solutions favor the smallest window-to-external surface area with triple-layer low-E windows and insulation thickness of greater than 90 mm. The merit of the developed method is that it can rapidly reach the optimal solutions for most types of building shapes with more than two objective functions and large number of design variables.

Graphical abstract

Keywords

ANN (artificial neural network) / exhaustive-listing / building shape / optimization / thermal load / thermal comfort

1 Introduction

For natural, functional, architectural and other reasons, buildings have evolved in different shapes in history. Representative examples include the pyramids in ancient Egypt, the cylindrical ancient Rome arena, the dome roof of Saint Peter’s Cathedral in Vatican, and the most commonly used rectangular buildings in the modern world. Clearly, different shapes can have different effects on buildings in different manners, such as mechanically, physically and both outside and inside.

It has been recognized that building shapes play an important role in determining the thermal performance of buildings. As such considerable research has been undertaken on this topic, focusing on the impact of different building shapes, e.g., [1–4] and building layout [5,6] on the building thermal performance, various indices have been proposed to measure the thermal performance of a building, such as energy consumption [1,3,7,8], energy demand [2,4], heat gains [6,9–11], and thermal loads [12].

Depecker et al. [1] have studied the impact of buildings with flat tilted roofs on building energy consumption using shape coefficient for severe cold and rare sunny winters. Okeil [5] has proposed a residential solar block (RSB) method to study the building layout to maximize solar radiation on facades and minimize solar radiation on roofs and the ground surrounding buildings in an urban area in winter. Yaşa and Ok [6] have studied the effects of courtyard layout on solar heat gains and energy efficiency under different climatic conditions.

Due to the complication in evaluating the thermal performance for different building shapes, various simplified models have been proposed, e.g., in Refs. [7–12]. For example, Ourghi et al. [8] have developed a simplified analysis method to predict the annual cooling and energy usage for an office building, using typical office space occupancy patterns and schedules for lighting density, equipment power density, occupancy density, uniform window-to-wall ratio, and package variable air volume system for cooling and heating. The coefficients used in the model have been determined based on linear regression with the simulation results from the DOE-2 program, and the R² of which at different locations are 0.65–0.97. Al-Anzi et al. [7] have developed a simplified correlation model to estimate the total building energy usage of office buildings in Kuwait, using typical office space occupancy patterns and schedules suitable for Kuwait, and water cooled chiller with electric resistance heating. The regression results for correlation equations against the simulation results from the DOE-2 program have shown that the R² are 0.9459–0.9464. Jin and Jeong [12] have developed a simple model to predict the annual thermal load that considered only heat gain, and heat loss and solar heat gain through envelope and windows. A discrepancy of –12% to 12% from the results obtained by the thermal simulation using TRNSYS 16 is found.

To improve the thermal performance of a building with different shapes, the optimization of building shape has become necessary. Some sophisticated methods for building shape optimization include coupling thermal performance simulation or simplified models with the genetic algorithm, e.g., Refs. [13–17], employing simplified thermal performance models for shape optimization by specialist computer programs or calculus of variation [9,11,18], coupling simulation software with constrained evolutionary algorithms [10,19], employing simplified models for shape optimization and solved by variational method [20], and employing computer models with the Simplex algorithm [21].

Tuhus-Dubrow and Krarti [15] have coupled DOE-2 simulation with the genetic algorithm to optimize different building shapes, including rectangle, L, T, cross, U, H shapes, and trapezoid, to minimize the life cycle cost (LLC) which includes the capital cost and utility cost. Based on their optimization results, rectangular and trapezoidal shaped buildings outperform others for residential buildings across five different climates in the USA. However, there is less than 0.5% variation in LCC values when building envelope features are considered in the optimization. Caruso et al. [11] have introduced a simplified model to calculate annual solar heat gains and used the theory of calculus of variation to find an optimal theoretical building shape to minimize direct solar irradiation on the building envelop. The daily solar radiation intensity on the building surface has been calculated by tracking the direction of the rays. The results show that the optimal form can help to reduce the solar gains by up to 20%. Caruso and Kämpf [19] have proposed a constrained evolutionary algorithm to optimize three-dimensional buildings for reducing energy consumption due to solar irradiation in Basel and Dubai. The software RADIANCE has been used to calculate the irradiation on buildings, and the solar irradiation that results in extra air-conditioning load has been minimized with optimal building form.

In optimizing building shapes, different objectives have been used, which are summarized in Table 1.

A further review of literature shows that almost all current research is focusing on the effects of building shape on building thermal performance; some with optimised building shapes and some not. Little or no research can be found on the optimisation of building shape for desired thermal comfort of building occupants. Clearly, thermal comfort of occupants in a building is a significant indicator of building thermal performance. For instance, it has been incorporated in optimizing building enveloped design parameters [22] and air conditioning parameters and installation distance by Li et al. [23]. A study has been carried out by Mushtaha and Helmy [24] on the impact of three different building forms (square, rectangular, and octagon) on the energy consumption and thermal comfort conditions in religious buildings in hot climates with several passive measures including improvement in insulation, shading devices, and ventilation. Therefore, it can be misleading to evaluate the building thermal performance without considering the thermal comfort. Neglecting the effect of building shape on desired thermal comfort can hardly achieve optimal solution for building thermal performance. Field surveys and investigations suggest that there is a strong demand from industry and community for studying the relationship between building shape and indoor thermal comfort and for optimising building shapes for both thermal load and thermal comfort. It is in this regard that an attempt is made in the present paper to develop a new method to meet the demand.

ANN (artificial neural network) mimics the biological function of animal brain to handle distributed parallel information. It has advantages to solve complex nonlinear problems. The ANN model has been applied by Magnier and Haghighat [22] to predict the building energy consumption with a maximum error of less than 10% and it helped to reduce the computation time during optimization from over 10 years (estimated) to 3 weeks. Gou et al. [25] have applied ANN to predict indoor comfort time ratio and building energy demand with average relative errors of 0.46% and 1.54%, respectively. The viability of the ANN approach has also been demonstrated by Debnath and Das [26] in predicting the performance coefficients of a three-bucket Savonius rotor with average relative errors of less than 3.66%. There are other prediction approaches that have been used to solve inverse problems. For example, Das and Prasad [27] have used the differential evolution algorithm to predict the porosity and thermal diffusivity in a porous fin. The artificial bee colony algorithm has been applied to model the performance of a solar collector [28] and in maximizing heat transfer in a perforated fin [29]. Compared with other evolutionary meta-heuristics, ANN can offer reliable and direct prediction of objective function while effectively reduce the computation time during the optimization process. Therefore, the ANN approach is used to develop prediction models for building thermal performance.

The intention of this paper is to develop an innovative method to optimize the building shapes and envelope physical properties in achieving maximum thermal performance of the building. A relationship between building shapes and thermal load as well as indoor comfort condition of the building is derived and an algorithm based on the ANN-exhaustive-listing (AEL) technique is developed to achieve an optimal solution for the thermal load and indoor comfort with different building shapes. The training and validation of ANN are also discussed. Besides, four different building shapes are investigated, including pyramid, rectangular, cylindrical, and dome shapes. Building envelope features include wall/roof insulation thickness, window types, and window-to-external envelope surface area ratio (WESR). The developed method is applied to residential houses in selected cities under different climatic conditions in China. The developed method can assist building designers and engineers in their design of building shapes and envelope properties.

2 Formulation of the problem

2.1 Objective functions

The two objectives, thermal load and discomfort hours, as expressed in Eq. (1), are selected to find the optimal building shape.

(1)\mathrm{Min}\hspace{0.17em}{f}_{\mathrm{1}}(\overline{x}),\hspace{0.17em}{f}_{\mathrm{2}}(\overline{x}),\hspace{0.17em}\overline{x}=[x_{\mathrm{1}},x_{\mathrm{2}},\mathrm{...},x_m],

\mathrm{subject\; to}{L}_i\le N_{\mathrm{TCH}}\le U_i,(1\le i\le m).

The total building thermal load can be determined from computer software DesignBuilder (powered by EnergyPlus) [30]. The software has been well validated, and the validations and tests on the thermal comfort, space heating/cooling, etc. can be found in Refs. [31–33]. The thermal load is composed of cooling load and heating load and expressed as

(2)f_{\mathrm{1}}(\overline{x})=Q_{\mathrm{C}}(\overline{x})+Q_{\mathrm{H}}(\overline{x}).

The set-point temperature for heating is 18°C and for cooling is 26°C, according to the energy efficiency design standards for residential buildings in China [34–36]. The load calculation is performed every 0.5 h year round.

The thermal comfort zone is determined in terms of the temperature and humidity ratio as recommended by Chinese standard GB/T 50785-2012 [37] based on the calculated predicted mean vote (PMV) and predicted percentage of dissatisfied (PPD) [38]. When PPD≤10% and –0.5≤PMV≤+0.5, it is considered as the comfort zone. The total number of discomfort hours can be calculated as

(3)f_{\mathrm{2}}(\overline{x})={\displaystyle {\sum }_{i=\mathrm{1}}^{\mathrm{8760}}{\delta }_i(\overline{x}),}({\delta }_i(\overline{x})=\mathrm{0}\mathrm{if\; inside\; the\; comfort\; zone},\mathrm{otherwise}{\delta }_i(\overline{x})=\mathrm{1}).

For general use of the developed method, Eqs. (4) and (5) are used to normalize the outcomes of the two objectives functions f₁ and f₂.

(4){\bar{f}}_{\mathrm{1}}={\displaystyle \frac{F_{\mathrm{1}}-\mathrm{Min}(f_{\mathrm{1}})}{\mathrm{Max}(f_{\mathrm{1}})}},

(5){\bar{f}}_{\mathrm{2}}={\displaystyle \frac{F_{\mathrm{2}}-\mathrm{Min}(f_{\mathrm{2}})}{\mathrm{Max}(f_{\mathrm{2}})}}.

The resultant objective of the optimization can then be expressed as

(6)f_n={({\overline{f}}_{\mathrm{1}}^{\mathrm{2}}+{\overline{f}}_{\mathrm{2}}^{\mathrm{2}})}^{\mathrm{1}/\mathrm{2}}.

Equation (6) is then used for ranking all solutions in terms of optimization criteria.

2.2 Basic models and design variables

The basic building models used are shown in Fig. 1. Each building has the same floor area, internal volume, heating and cooling temperature setpoint, etc.

The initial values for building parameters are set as follows for selected building and summarized in Table 2. The floor area for pyramids and rectangular buildings are calculated as

(7)S_1=a\times b=1\mathrm{0}m\times 1\mathrm{0}\mathrm{m}=1\mathrm{00}{m}^2,

and for cylindrical and dome shape buildings

(8)S_2=\mathrm{\pi }{r}^2=3.\mathrm{142}\times 5.{\mathrm{64}}^2=1\mathrm{00}{m}^2,

where S₁ and S₂ are the floor areas, in m²; a and b are the width and length of the floor, equal to 10 m; and r is the radius of the base for cylindrical and dome shape buildings, equal to 5.64 m.

The volumes for four different types of buildings are calculated as

(9)V_{\mathrm{1}}={\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}{S}_{\mathrm{1}}{h}_{\mathrm{1}}={\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}\times \mathrm{100}\times \mathrm{10.8}=\mathrm{360}\hspace{0.17em}{\mathrm{m}}^{\mathrm{3}},

(10)V_2=S_1{h}_2=1\mathrm{00}\times 3.6=\mathrm{36}\mathrm{0}{m}^3,

(11)V_3=S_2{h}_3=1\mathrm{00}\times 3.6=\mathrm{36}\mathrm{0}{m}^3,

(12)V_{\mathrm{4}}={\displaystyle \frac{\mathrm{\pi }}{\mathrm{3}}}(\mathrm{3}r-h_{\mathrm{4}})h_{\mathrm{4}}^{\mathrm{2}}={\displaystyle \frac{\mathrm{\pi }}{\mathrm{3}}}\times (\mathrm{3}\times \mathrm{5.64}-\mathrm{5.48})\times {\mathrm{5.48}}^{\mathrm{2}}=\mathrm{360}\hspace{0.17em}{\mathrm{m}}^{\mathrm{3}},

where V₁, V₂, V₃, and V₄ are the building volumes, in m³; and h₁, h₂, h₃, and h₄ are the heights of the buildings, in m.

Building shape variables are defined as Types 1, 2, 3, and 4 for pyramid, rectangular, cylindrical, and dome shapes, respectively as shown in Fig. 1.

Three envelope design variables are selected, which are external wall/roof insulation thickness, window-to-envelop surface area ratio, and window type. Table 3 lists the design variable types and value ranges.

Since there is no recognizable difference in the surface between external wall and roof for pyramids and domes, a window-to-external envelope surface area ratio (WESR), instead of a window-to-wall ratio, is used to define the impact of window size on building thermal load, expressed as

(13)\mathrm{WESR}={\displaystyle \frac{S_{\mathrm{W}}}{S_{\mathrm{EW}}+S_{\mathrm{R}}}},

where S_W is the window area, in m²; S_EW is the external wall surface area, in m²; and S_R is the external roof surface area, in m². The selected values for WESR are 10%, 15%, 20%, 25%, 30%, 35%, and 40%.

Residential building models are developed with typical residential occupancy patterns and schedules in China. In particular, the lighting power density, equipment power density, and occupancy density are assigned to be 4 W/m², 4 W/m², and 20 m²/person, respectively [39,40].

Five typical cities, covering all the five climatic regions in China, are selected whose climatic information is listed in Table 4, and whose base thermal loads are presented in Table 5.

2.3 Optimization framework

The optimization framework for the objective function of Eq. (1) is summarized in Fig. 2 with four main steps. In the first step, building simulation software is employed to obtain the thermal load and number of discomfort hours for a selected number of samples of design variables described in Section 2.2 to form a database for different building shapes. In the second step, the samples from the database are used to train and validate the ANN to establish models of thermal load and discomfort hours with different building shapes. In the third step, the exhaustive listing technique is employed to evaluate all potential solutions using the ANN models for thermal load and number of discomfort hours established in Step 2, and to rank all the solutions in an order of descending optimization. In the last step, the building simulation software is used to validate the optimal solutions and a final ranking for the optimized solutions given. The outcomes on the glazing ratio and envelop properties are compared with the requirements from the energy efficiency standards for residential buildings in China [34–36] to make sure that the requirements are met.

2.4 Constraints and inputs

The input variables in this optimization problem include building shapes (x₁), external wall/roof insulation thickness (x₂), window-to-envelop surface area ratio (x₃), and window type (x₄).

The constraints of the variables are presented as

(14)\mathrm{Type\; 1}\le x_1\le \mathrm{Type\; 4},(\mathrm{Type\; 1\; is\; pyramid},\mathrm{Type\; 2\; isrectangular},\mathrm{Type\; 3\; is\; cylindrical},\mathrm{Type\; 4\; is\; dome\; shape}),

(15)1\mathrm{0}\le x_2\le \mathrm{12}\mathrm{0},

(16)1\mathrm{0}\%\le x_3\le 4\mathrm{0}\%,

(17)\mathrm{Type\; 1}\le x_4\le \mathrm{Type}6,(\mathrm{Type1\; to\; 6\; are\; different\; window\; types\; as\; shown\; in\; Table\; 3}).

3 ANN training and validation

3.1 Generation of database

Simulation of thermal performance, i.e., thermal load and discomfort hours, can be very time-consuming due to a large number of design variables and their ranges of values as tabulated in Tables 2–4. For example, it takes at least 0.5 h for one simulation or realization of thermal performance with given values of design variables in Tables 2–4 for one given building in one given city. The maximum number of simulations for the given variables in Tables 2–4 for 4 building shapes in five cities is 4 × 12 × 7 × 6 × 5= 10080. It takes 210 days to simulate on an Intel i-5desktop computer.

To reduce the number of simulations, i.e., sample size, the well-established Latin hypercube sampling method (LHSM) [41] is used to generate samples of building parameters and design variables as shown in Tables 2–4. With these generated samples, the thermal performance can be simulated and a database of design variables and thermal loads and discomfort hours can be constructed. The sample size used in LHSM also varies. McKay [41] has suggested a sample size of 2 × N, where N is the number of variables. Zhou and Haghighat [42] have applied the principle to predict ventilation performance. However, Conraud [43] and Magnier and Haghighat [22] have tested the ANN performance by playing with the number of inputs and outputs, and it is found that a sample size of 22.5 × N is more appropriate to accurately sample the search space. But their cases are for certain type of buildings. In this study, although the building shape is considered as a design variable, the following three methods are proposed for data sampling:

Method one: the optimization problem is composed of four variables, i.e., building shape, window type, external envelope insulation thickness, and WESR. With N = 4, the total number of samples is 22.5 × N = 90 and all types of building shapes are included in one simulation;

Method two: the building shape is not considered as a design variable, which means that each type of building will be simulated separately. The number of samples is 70 (i.e., 22.5 × N rounded to 70) for each type of building and a total of 280 samples are generated for all four building shapes;

Method three: the building shape is first not considered as a design variable for which the number of samples of 70 for each type of building is generated. Then, the building shape is added as the fourth variable to give a total of 280 samples. One simulation model is developed for all types of buildings.

DesignBuilder is used for all simulations of thermal performance for generated samples of design variables with a time step of 30 min. It takes about 2 days for the simulation of 90 sample data, and, it takes about 7 days for 280 sample data using a desktop computer configured with Intel i-5 CUP @1.60 GHz and 4 G memory.

3.2 Training and validation

Clementine 12.0 is used to train and validate the ANN models of the thermal comfort and thermal load as a function of design variables. Each model is composed of one input layer, one hidden layer, and one output layer, the learning rates of which are presented in Table 6 using the default values from the system. The models are configured to stop on 100% of accuracy but are manually stopped when the highest accuracies of the model are achieved. 10% of the sample data are used for validation.

The city of Wuhan is taken as the first example to apply the ANN models, and the applications to other cities are conducted afterwards. The actual accuracies for the thermal load and thermal comfort models for the city of Wuhan are 99.419% and 98.588%, respectively.

The relative error (RE) is calculated as

(18)\mathrm{RE}={\displaystyle \frac{R_{\mathrm{P}}-R_{\mathrm{S}}}{R_{\mathrm{S}}}},

where R_P is the outcome from the ANN prediction model and R_S is the outcome from the DesignBuilder simulation software. The ranges of relative errors for the prediction of thermal load and discomfort hours (N_dis) using different methods for the city of Wuhan are listed in Table 7. Here, “Simulation” means the results from the DesignBuilder simulation software, and “Prediction,” the outcomes from the ANN prediction model. The maximum relative errors for the three thermal comfort models are less than 0.72%, which vindicates the accuracy of the proposed method. This result is better than the findings from Magnier and Haghighat [22], where the average error of thermal comfort prediction is 3.9% based on PMV. The maximum relative errors for the three thermal load models are 7.96%, 4.73%, and 4.34%, respectively, which is less than the result of 10% from Jin and Jeong [12]. The regressions between the target simulated outputs and ANN predictions are presented in Fig. 3. Good agreements are found between the simulation and prediction results, as the regression coefficients are very close to 1.0 for the three methods.

4 Results and discussion

4.1 Application to the city of Wuhan

The developed AEL method is first applied to the city of Wuhan. A program is written in FORTRAN Power Station 4.0 to generate the input files. As there are 12 levels of insulation, 7 values for the WESR, 6 types of windows, and 4 types of building shapes, a total of 2016 combinations of input variables are generated. The input files are then imported to SPSS and used by Clementine 12.0, where the prediction models are stored for prediction and generation of the output files of thermal load and discomfort hours for analysis. Figure 4 depicts the distribution of thermal loads and discomfort hours (N_dis) for all possible combinations. It can be observed that the predicted lowest thermal load and discomfort hours from Method one are higher than those of Methods two and three, indicating less satisfactory prediction results from Method one under optimal solutions.

Ranking is then performed based on the f_n values calculated according to Eq. (6). The final ranking is adjusted by performing simulations on the selected optimal solutions to calibrate the f_n values. Table 8 lists the optimal solutions using different methods. It can be seen that there is a good agreement between the predicted and simulated discomfort hours (N_dis), with maximum errors of less than 1.17%. The prediction on the thermal load is less satisfactory than N_dis, with –22.23% maximum errors using Method one, 10.45% using Method two, and –4.24% using Method three. Therefore, Method three can be considered as the best method for thermal load prediction.

4.2 Comparison with multi-objective optimization method

The developed AEL method is compared with the widely used multi-objective optimization schemes. For this purpose, the ANN model developed using Method three is used as the fitness function for a multi-objective genetic algorithm (ANNGA) developed in MATLAB to find the Pareto front solutions. A total of four optimal solutions are found. Figure 5 presents the comparisons of the solutions (calibrated with the simulation results from DesignBuilder) between the optimal solutions using the AEL and ANNGA methods. It is observed that the AEL method picked up more solutions, which are better than the ones generated by the ANNGA method.

4.3 Application to other cities

After being verified, the AEL method using Method three for sampling is then applied to other four cities, i.e., Harbin, Beijing, Guangzhou and Kunming, to find the optimal building shape and envelop features under different climatic conditions. Table 9 lists the top 10 optimal solutions for each city. It can be seen that in the severe cold and cold climate regions (Harbin and Beijing), an insulation level of at least 110 mm is preferred; in the hot summer/cold winter region and mild region (Wuhan and Kunming), the smallest insulation level of at least 90 mm is preferred; in the hot summer and warm winter region (Guangzhou), the smallest insulation level of at least 80 mm is preferred. With the increase in the ambient air temperature, there is less heat loss through the building envelope, therefore the required thickness of insulation deceases. The WESR in all climate regions are between 10% and 15%. Interestingly, 15% of WESR is allowed in the severe cold, cold climate regions, and cold winter and hot summer regions. Compared to 10% WESR, it results in the slight decrease in the discomfort degree hour and increase in the thermal load in Harbin and Wuhan, implying less fluctuation in indoor air temperature and more heat loss through the building envelop. Both of the discomfort degree hour and thermal load are increased in Beijing, indicating more indoor air temperature fluctuation and heat loss due to the increase of glazing ratio. In all climatic regions except the mild weather (Kunming), the triple-layer low-E window is preferred. In the severe cold or cold climate region, the triple-layer low-E window can minimize the heat loss through the glazing. In the warm winter/hot summer region, the heat gain through the glazing in summer is effectively reduced. In the cold winter and hot summer climate region, it both reduces the heat loss in winter and heat gain in winter. In the mild weather region, the double-layer low-E window is favorable, which means that the heat flow through the glazing is moderate. It can also be seen that rectangular buildings typically have the highest thermal comfort level in all climatic regions, meaning less indoor air temperature fluctuation year-round due to relatively high thermal mass compared to other building shapes. The thermal loads of the dome shaped buildings are the lowest for all climate regions except in the mild weather region. The dome shape accounts for 40% of all the optimal solutions, suggesting that it is a good practice to design buildings by learning from the optimal form existing in nature. In the mild weather region, the cylindrical buildings has the lowest thermal load, however the thermal load in this region is only 179.93–357.68 kWh, which is less than 6.5% of that in other regions. It can also be observed that cylindrical and rectangular shapes account for 28% and 30% of all the optimal solutions, which are equally favorable while the pyramid shape accounts for only 2% which is least favorable due to its high discomfort degree hour and thermal load.

5 Conclusions

In this paper, an ANN-exhaustive-listing (AEL) method has been developed for optimizing building shapes and envelope features with minimal building energy consumption and improved thermal comfort. After being verified with multi-objective optimization method, the developed AEL method has been applied to four different building shapes in five different climate zones in China. From this study, the following conclusions can be drawn:

Building shapes need to be treated separately to achieve sufficient accuracy of prediction of thermal performance. When treated separately, the overall error of prediction can be reduced from 19.22% (when treated in the same way as other variables) to less than 5%.

ANN is an accurate technique to develop models for thermal comfort with errors of less than 1.5%. The prediction of thermal loads with ANN is less accurate but can be improved with more representative data set.

Typically the thermal load of the dome building is the smallest, followed by the cylindrical building, the rectangular building, and the pyramid building. However, in the mild weather region, the thermal load of the cylindrical building is the smallest. The rectangular building features a good balance of thermal load and indoor thermal comfort.

The optimal solutions favor the smallest window-to-external surface area (10%), with the triple-layer low-E window and an insulation thickness greater than 90 mm.

The merit of the developed method is that it can rapidly reach optimal solutions for most types of building shapes with more than two objective functions and a large number of design variables.

References

[1] Depecker P, Menezo C, Virgone J, Lepers S. Design of buildings shape and energetic consumption. Building and Environment, 2001, 36(5): 627–635

[2] Aksoy U T, Inalli M. Impacts of some building passive design parameters on heating demand for a cold region. Building and Environment, 2006, 41(12): 1742–1754

[3] Choi I Y, Cho S H, Kim J T. Energy consumption characteristics of high-rise apartment buildings according to building shape and mixed-use development. Energy and Building, 2012, 46: 123–131

[4] Premrov M, Žegarac Leskovar V, Mihalič K. Influence of the building shape on the energy performance of timber-glass buildings in different climatic conditions. Energy, 2016, 108: 201–211

[5] Okeil A. A holistic approach to energy efficient building forms. Energy and Building, 2010, 42(9): 1437–1444

[6] Yaşa E, Ok V.. Evaluation of the effects of courtyard building shapes on solar heat gains and energy efficiency according to different climatic regions. Energy and Building, 2014, 73: 192–199 doi:10.1016/j.enbuild.2013.12.042

[7] AlAnzi A, Seo D, Krarti M. Impact of building shape on thermal performance of office buildings in Kuwait. Energy Conversion and Management, 2009, 50(3): 822–828

[8] Ourghi R, Al-Anzi A, Krarti M. A simplified analysis method to predict the impact of shape on annual energy use for office buildings. Energy Conversion and Management, 2007, 48(1): 300–305

[9] Marks W. Multicriteria optimisation of shape of energy-saving buildings. Building and Environment, 1997, 32(4): 331–339

[10] Kämpf J H, Robinson D. Optimisation of building form for solar energy utilisation using constrained evolutionary algorithms. Energy and Building, 2010, 42(6): 807–814

[11] Caruso G, Fantozzi F, Leccese F. Optimal theoretical building form to minimize direct solar irradiation. Solar Energy, 2013, 97: 128–137

[12] Jin J, Jeong J. Thermal characteristic prediction models for a free-form building in various climate zones. Energy, 2013, 50: 468–476

[13] Wang W, Rivard H, Zmeureanu R. Floor shape optimization for green building design. Advanced Engineering Informatics, 2006, 20(4): 363–378

[14] Yi Y K, Malkawi A M. Optimizing building form for energy performance based on hierarchical geometry relation. Automation in Construction, 2009, 18(6): 825–833

[15] Tuhus-Dubrow D, Krarti M. Genetic-algorithm based approach to optimize building envelope design for residential buildings. Building and Environment, 2010, 45(7): 1574–1581

[16] Jin J, Jeong J. Optimization of a free-form building shape to minimize external thermal load using genetic algorithm. Energy and Building, 2014, 85: 473–482

[17] Zhang L, Zhang L, Wang Y. Shape optimization of free-form buildings based on solar radiation gain and space efficiency using a multi-objective genetic algorithm in the severe cold zones of China. Solar Energy, 2016, 132: 38–50

[18] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilisation example. Building and Environment, 2002, 37(12): 1249–1253

[19] Caruso G, Kämpf J H. Building shape optimisation to reduce air-conditioning needs using constrained evolutionary algorithms. Solar Energy, 2015, 118: 186–196

[20] Adamski M. Optimization of the form of a building on an oval base. Building and Environment, 2007, 42(4): 1632–1643

[21] Fokaides P A, Panayidou A, Hadjichristos C, Phocas M C. Application of non-linear programming to optimize buildings’ solar exposure. Journal of Building Engineering, 2017, 11: 127–133

[22] Magnier L, Haghighat F. Multiobjective optimization of building design using TRNSYS simulations, genetic algorithm, and Artificial Neural Network. Building and Environment, 2010, 45(3): 739–746

[23] Li J, Yin S W, Shi G S, Wang L. Optimization of indoor thermal comfort parameters with the adaptive network-based fuzzy inference system and particle swarm optimization algorithm. Mathematical Problems in Engineering, 2017: 3075432

[24] Mushtaha E, Helmy O. Impact of building forms on thermal performance and thermal comfort conditions in religious buildings in hot climates: a case study in Sharjah city. International Journal of Sustainable Energy, 2017, 36(10): 926–944

[25] Gou S, Nik V M, Scartezzini J L, Zhao Q, Li Z. Passive design optimization of newly-built residential buildings in Shanghai for improving indoor thermal comfort while reducing building energy demand. Energy and Building, 2018, 169: 484–506

[26] Debnath B K, Das R. Prediction of performance coefficients of a three-bucket Savonius rotor using artificial neural network. Journal of Renewable and Sustainable Energy, 2010, 2(4): 043107

[27] Das R, Prasad D K. Prediction of porosity and thermal diffusivity in a porous fin using differential evolution algorithm. Swarm and Evolutionary Computation, 2015, 23: 27–39

[28] Das R, Akay B, Singla R K, Singh K. Application of artificial bee colony algorithm for inverse modelling of a solar collector. Inverse Problems in Science and Engineering, 2017, 25(6): 887–908

[29] Das R, Singh K, Akay B, Gogoi T K. Application of artificial bee colony algorithm for maximizing heat transfer in a perforated fin. Proceedings of the Institution of Mechanical Engineers. Part E, Journal of Process Mechanical Engineering, 2018, 232(1): 38–48

[30] DesignBuilder. Simulation made easy. 2017–07–05,

[31] EnergyPlus. Testing and Validation. 2018–05,

[32] Coakley D, Corry E J, Keane D M. Validation of simulated thermal comfort in the context of building performance evaluation & optimisation. In: Proceedings of the 13th International Conference for Enhanced Building Operations, Montreal, Quebec, Canada, 2013

[33] DesignBuilder. Tests for the calculation of energy use for space heating and cooling. 2017–08–05,

[34] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Design Standard for Energy Efficiency of Residential Buildings in Hot Summer and Cold Winter Zone. Beijing: China Architectural Engineering Industrial Publishing Press, 2010 (in Chinese)

[35] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Design Standard for Energy Efficiency of Residential Buildings in Hot Summer and Warm Winter Zone. Beijing: China Architectural Engineering Industrial Publishing Press, 2012 (in Chinese)

[36] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Design Standard for Energy Efficiency of Residential Buildings in Severe Cold and Cold Zones. Beijing: China Architectural Engineering Industrial Publishing Press, 2010 (in Chinese)

[37] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Evaluation Standard for Indoor Thermal Environment in Civil Building. Beijing: China Architectural Engineering Industrial Publishing Press, 2012 (in Chinese)

[38] Fanger P O. Thermal Comfort. Copenhagen: Danish Technical Press, 1970

[39] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Standard for Lighting Design of Buildings. Beijing: China Architectural Engineering Industrial Publishing Press, 2013 (in Chinese)

[40] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (MOHURD). Design Code for Design of Hating Ventilation and Air Conditioning of Civil Buildings. Beijing: China Architectural Engineering Industrial Publishing Press, 2012 (in Chinese)

[41] McKay M D. In: Ronen Y, ed. Sensitivity Arid Uncertainty Analysis Using a Statistical Sample of Input Values, Uncertainty Analysis. CRC Press, 1998, 145–186

[42] Zhou L, Haghighat F. Optimization of ventilation system design and operation in office environment, part I: methodology. Building and Environment, 2009, 44(4): 651–656

[43] Conraud J. A methodology for the optimization of building energy, thermal, and visual performance. Dissertation for Master’s Degree. Montreal: Concordia University, 2008

RIGHTS & PERMISSIONS

Higher Education Press