0 Introduction

Building energy consumption accounts for 40% of the world's energy consumption and carbon dioxide emissions account for 30% of the global emissions^[1]. At the same time, the green building design has great potential for decreasing energy consumption and the emission of carbon dioxide^[2]. Therefore, more and more architects and environmentalists appeal to the green building design^[3-4]. Although there are many building technologies that could enhance building performance^[5], some scholars have proved that the multiple objective optimization (MOO) method could be more efficient^[6]. In the green buildings design process, there are many building indexes that should be considered, such as the building economic quality, outdoor ecological environment, and the energy utilization, where it is difficult to weigh the multiple building performance indicators comprehensively based on the existing building performance simulation (BPS) method, while the MOO method could do it. To sum up, the MOO method has the following advantages:

1) MOO could provide many building design selections among the Pareto Frontier Solution (PFS) for designers to select;

2) MOO demonstrates greater potential than traditional optimization to aid designers to balance the building formation and the multiple high-performance^[7].

All the advantages listed above could make the MOO method an ideal method for designing green buildings. For example, Lobaccaro et al.^[8] used the MOO method based on the Galapagos and Octopus plugin in Grasshopper to control buildings features and obtained the least environmental impact. Sommer and Pont^[9] utilized the MOO method to design a free-form building to decrease the thermal load characteristics in the early design stage, which shows an ideal result. Brown and Mueller^[10] utilized the MOO method to generate and select a solution from a diverse range of high-performance building forms, which has proved to be an effective sustainable design strategy. Facundo Bre's team proposed an efficient method to solve MOO problems using a novel metamodel-based approach coupled with artificial neural network metamodels and NSGA-II Algorithm in 2016. During the experiment, the method was applied to optimize the energy efficiency and thermal comfort to obtain the Pareto front of the building between heating and cooling performance, and the result shows that the presented method could keep a good accuracy of the results^[11]. Sun and Han^[12] utilized the MOO method to realize the improvement of the timber-glass building performance in the conceptual design phase. All of the examples mentioned above show that the MOO method could aid the green building design process and obtained a high-performance of the building. More recently in 2019, Binghui Si's team developed a surrogate model to couple ANN to reduce computing time. They utilized four MOO algorithms to evaluate the proposed performance to select the best parameters value as well as the number of generations. The results show that the NSGA-II with generations of 40 and 50 performed best in the case study^[13].

When considering the advantages of the MOO methods for designing the green buildings, increasing number of scholars have carried out studies on the development of the tools to optimize MOO process. Als et al.^[14] proposed a tool for the building performance optimization, named BPOpt, which combines the BIM, parametric modeling, cloud-based simulation, and optimization algorithms together to operate the BPS process, and it showed a better result than a previous study. Asadi et al.^[15]proposed a building performance optimization tool based on the Genopt building simulation software, Latin hypercube sampling (LHS), ANN, and multi-objective GA to aid in the decision-making in the context of the retrofit project, which shows great potential.

As for the solution of the MOO retrofit problem^[16], Kerdan et al.^[17] proposed an automated energy economic tool, named "ExRET-Opt", for the building retrofit-oriented energy economic based optimization that could provide users with thermodynamic efficient and cost-effective design process. The tools mentioned above could obviously improve the MOO methods and enhance the efficiency as well as the final calculation accuracy of the MOO process. As for the MOO disadvantages, there are mainly three aspects, which have been listed as follows.

First, it is lacking in the sensitivity analysis (SA) function of the design parameters for the uncertainties in the selected parameters that lead to the loss of performance in the MOO process. Aiming at the SA problem, there are various SA methods that have been studied to find the high-sensitive parameters from the technical and economic points of view, which show that they could obtain the final high-performance of the simulated results^[16-18]. However, there are no studies that could combine SA with MOO on a platform.

Second, the results of the calculation of building performance fitness function have the convergent tendency features that are not suitable for the building design parameters SA. The Gradient Boosting Regression Tree algorithm (GBRT) based design parameters SA needs the random building simulated database. The LHS could help to sample the building performance simulated data and obtain the random building performance simulated database for the GBRT in the next step.

Third, the MOO process contains parametric modeling, BPS, and the self-adjustment of building model steps. The different step might rely on different software that would lead to the complex operation process between different software and the instability of each software, which have a great influence on the whole MOO process. Aiming at this problem, the integrated platform would be the main effective method which combines all these steps together.

In the light of the problems existing in the MOO process as well as for the better BPS simulated results, the GBRT algorithm and the SA were added in the building performance optimization process. The GBRT algorithm could help to calculate the parameters' importance for the building performance, and the SA could help to select the sensitive parameters for the MOO process which could help to improve the MOO efficiency and the optimized performance. As a result, the limitations of the previous studies have been overcome by this study and a building performance optimization tool is introduced, named GPPre, which allows designers to build the parametric model, operate the design variable sensitive analysis, and complete the building performance optimization. The innovation of the paper is that the GPPre tool is built based on Python programming that integrates different computational architectural design technologies into one performance optimization tool in Grasshopper. In Section 1, the overview of the GPPre tool as well as the construction of building SA module based on the GBRT algorithm and the MOO plugin is presented. Section 2 applies the GPPre tool to the performance optimization of an office building in the severe cold region to decrease the building's annual energy consumption (AEC), total cost (TC), and increase the useful daylighting illuminance (UDI). It is worth noting that the GPPre tool is not limited to the performance optimization of UDI, AEC, and TC, but it could be extended to the optimization of other building performance categories in Grasshopper^[19-20].

1 Materials and Methods

The GPPre is developed as an integrated tool for enhancing the performance of building through the MOO method in Grasshopper and it integrates the parametric building modeling module, the BPS module, the SA module, and the Genetic Search module based on the Honeybee & Ladybug, GH_Cpython, and Octopus plugin in Grasshopper. Correspondingly, the modules in GPPre could realize the parametric modeling, BPS, building performance sampling, and the SA of design parameters. The following sections mainly discuss the development and function of the GPPre tool.

1.1 The Parametric Building Modeling Module

The parametric building modeling module developed in Grasshopper relied on the basic batteries in Grasshopper that allow architects and engineers to develop an algorithm to select the parametric building model and operate the BPS and MOO process.

This module is developed based on visual programming tool Grasshopper, which mainly includes two types of objects: parameters and components. The parameter objects could store the inherit data or transmit data. The components of objects could input data, perform operations, and output parameters. Based on the two types of objects, the parametric building modeling module composed of four categories is constructed:

1) Objective modeling: this module includes the building form design parameters, the building materials design parameters, the building generation of the building formation components, and the building material components;

2) Associative modeling: this module includes the dynamic relationship between the design parameters and building formation, as well as the design parameters and thermal properties of enclosure structures;

3) Dataflow modeling: this module includes the data link between building formation, building material, and primitive data;

4) Procedural modeling: this module includes building formation and material generation principles, which include the generation of building a plane, the enclosure structure generation of the building, opening windows of the building envelope, and defining the material of building geometry.

In general, the main procedure could be listed as the following steps. Firstly, designers should investigate the constraint of each design parameter in the designated climatic zones. Subsequently, based on the investigated data, the typical models would be established. Afterwards, the investigated data would be associated with typical models to construct associative modeling. Finally, the associative modeling could be divided into multiple thermal zones and the relevant details would be discussed in the following sections.

Additionally, the parametric building modeling module could export the simulated data of the BPS and the MOO process. The database could also be integrated into the building design parameters and the building performance in one database, which could reflect the mapping relationship between two types of data.

1.2 The BPS Module

The BPS module is established to operate the BPS based on the parametric building modeling recording the simulated data results. This simulated database could include the building design parameters, building performance simulated results to operate the SA and ANN in the next steps. This module is developed based on three parts, including the parametric building modeling module, which could be used to identify and evaluate the design parameters to improve the understanding of the building performance. Additionally, Ref.[21] mentioned that the Ladybug & Honeybee proposed that BPS plugin in Grasshopper could enable the BPS engine, like Days, Open studio, Radiance, and EnergyPlus engines, to carry out the daylighting, energy consumption, and TC simulation.

The main procedure of the BPS module includes the following steps. Firstly, designers should ensure if the BPS design parameters and the decision variables are proper. Secondly, the simulated groups based on the controlled variable experiment (CVE) method or the orthogonal test method should be listed. Thirdly, the BPS according to the simulated groups could also be carried out based on the parametric building modeling. Finally, the simulated building performance data could be recorded into the building performance database via the data recording plugin in Grasshopper. After adjusting the building design parameters, the BPS module could output a building performance database that reflects the relationship between building performance and design parameters, such as climate, building envelope design parameters, building equipment setting parameters, indoor environmental conditions, and so on.

1.3 The LHS Module

When the building performance database obtained based on the CVE is regular, it is not suitable to operate the SA. The LHS module is established based on the Python programming in Grasshopper to obtain the random building performance database.

The function of the LHS module could be achieved by installing the LHS algorithm into the GH_Cpython plugin based on Python programming. To obtain the final LHS results, firstly, designers should define the number of the sample data in the database. Secondly, the corresponding domain [m, n] of the sample database should be divided into n intervals and the LHS could sample one building simulated data from each interval. Thirdly, the algorithm would turn the data order into t random numbers, so that the t random data could be generated by the inverse function of the probability distribution function. Finally, the LHS module could output the random distribution values into Excel.

After inputting the regular building performance database into this module, the LHS algorithm would help to randomly extract the data and store them into the building performance sampling database. Based on the LHS module, the number of the building performance sampling database could be used to operate the building design parameters SA in the next step.

1.4 The SA Module

The SA module could operate the SA of design parameters that play an important role in developing a better understanding of how a building performance could be affected by the design variables^[22], so that designers could define the optimized design parameters in the MOO process.

The establishment of the SA module is similar to the LHS module, which is selected based on the GBRT written in Python programming. In terms of the GBRT algorithm, the task of parameters SA could be categorized as a supervised regression problem from the machine learning point of view and all of the data input into the algorithm would correspond to the target data. Boosting is a powerful learning strategy that is designed for classification and regression. The function of boosting is to add the "weak learners" into a powerful "committee"^[22].

In addition, there is much existing literature about the SA of building performance. The common features about these studies are that the learners focus on building design parameters' sensitivity on different building performance like daylighting, ventilation, and heating. Recently, Navid Delgarm's team explores the sensitive design parameters of the night ventilation performance to reduce the overheating and energy-extensive consumption problem. In this study, a holistic approach integrating SA and parametric simulation analysis is developed to explore the key design parameters, and the simulated result show that the window-wall ratio, internal thermal mass level, internal convective heat transfer coefficient as well as night mechanical air change rate are the most sensitive design parameters^[23]. Richard Gagnon's team in 2018 used three methods, the standard regression coefficients, partial rank correlation coefficients, and Sobol indices, to obtain the sensitive design parameters of 30 design variables based on the TRNSYS model. The results show that the sensitive variables obtained from the three methods are similar and the sensitive design variables can really reduce the building energy consumption^[24]. Besides, the main procedure of the SA module includes the listed steps. Firstly, the building performance database and the setting parameters of the SA module like iteration, learning rate, and Excel path (the database handled by LHS module) should be defined. Afterwards, the Python Figure of the sensitivity ranking of the design parameters could be shown in front of the Grasshopper and the designers could gain sensitive design parameters for the latter MOO process.

1.5 The Genetic Search Module

The genetic search module could be used to operate the MOO to find the building design scheme with high performance. Based on the sensitive design parameters that were obtained from the SA module, the building performance of the MOO process would be more effective.

The genetic search module is elected in Grasshopper achieved by the Octopus plugin^[25] and the data recording plugin is similar to the one in the BPS module. During the MOO process, different building performance would rely on different objective functions and different evolutional algorithm, such as NSGA-II, SPEA-2, HypE Reduction algorithm, and so on. The main procedure of the genetic search module covers five steps. Firstly, the category of the building design parameters as well as the range of parameters should be defined. Secondly, the office building optimized performance category and the optimized value or domain should be defined. Besides, the Octopus includes the Elitism and the Mut. Probability, mutation rate, cross rate, and population size should be converted to the suitable value. Thirdly, designers should define the searching algorithm, like NSGA-II or SPEA-2, and then click the button to start the calculation. Fourthly, the optimized solutions would be shown on the 3D visualization interface that covers the basic architectural design information. Finally, the information of the sampling results could be recorded in the Excel database.

After inputting the sensitive parameters, a 3D model is obtained which shows the final optimization results, in which the axes in different directions represent three different optimized objective options. Moreover, the cubes are represented by different solutions. The red transparent ones represent the elite solution of the latest generation, the yellow transparent ones represent the historical solution, and the solid cube represents the PFS. Clicking on the solid body in the PFS, designers could select the final HPB design results.

The genetic search module could aid designers to search for the ideal building design scheme by balancing different building performance.The optimization design scheme result of the design variables, as well as the corresponding BPS values, would be recorded, which could provide designers with the high-performance building design decision supporting.

2 Case Study 2.1 The Study Workflow

Based on the constructed tool modules mentioned above, the high-performance building design workflow with the GPPre tool could be described in the following five steps, which are demonstrated in Fig. 1 along with the plugins that are used in each step. The different modules in Grasshopper have different functions, which include the parametric building modeling function, BPS function, building performance sampling function, building design parameters SA function, and the building performance MOO function. The following content describes the GPPre function in the high-performance building design process.

In the first step, the parametric building modeling module in the GPPre tool is established based on the objective modeling, associative modeling, data flow modeling, and the four parts of the modeling that could combine the building formation, building design parameters, and the investigated constraints together. The relationship between parametric building formation and design parameters could be established in this module so that the simulated model could realize the self-adaption during the MOO process. Additionally, the input parameters of this module are design parameters that are obtained by investigating the current research, and the output parameters of this module are the parametric building model for the next building simulation phase.

In the second step, the BPS module in the GPPre tool would be used to operate the BPS based on the parametric building module with different BPS engines, such as Radiance for the building lighting simulation and the EnergyPlus for the building energy simulation. Additionally, the operating steps of this module include the parameters adjustment, BPS running, and BPS collection. During the operation process of this module, the simulated process is usually based on the CVE method. After inputting and operating the adjustment of the design variables, the BPS simulated results could be recorded into building performance database that is used as the input of the LHS module in the next phase.

In the third step, the LHS module could be used to sample the designated number of the BPS data in the building performance database to disturb the data arrangement rule, which is established based on the Python Programming and the GH_Cpython plugin in Grasshopper. The LHS module could realize the data sampling after pressing the button of the module, which would be more convenient than the previous one based on the MATLAB. The input parameters of this module include the number of the database, the sampling number of the database, and the building performance database. The output parameters of this module were contained in the sampling database used to operate the SA process in the next section.

In the fourth step, the SA module could realize the SA of the design variables and this module establishment method is similar to the LSH modules, which are based on the GBRT algorithm. After inputting the building performance sampling database and the GBRT operation parameters, the module could output the Python Figure of the design variables sensitivity ranking and designers could select 3-6 kinds of sensitive design parameters. The SA process that is based on this module provides great convenience for designers to analyze the correlation between design parameters and building performance.

In the fifth step, the genetic search module could realize the MOO and the data recording of the optimized process based on the sensitive design parameters that are established based on the Octopus plugin and the data recording part of the TT toolbox. After the parameters setting of the Octopus plugin, the design parameters and relevant building performance simulated data of the MOO process would be recorded into the building performance optimization database, and the building modeling module would output the final high-performance building design scheme. This module could aid designers to realize the searching of the high-performance building design scheme automatically and record the building performance data of the MOO process.

The workflow with the GPPre tool could lead architects to operate the high-performance building design process that could be operated in a few steps to output the final MOO results to develop the high-performance design scheme.

2.2 Preparation of the Experiment with GPPre

An office building performance optimization study based on the GPPre tool could be operated to obtain the high-performance building design scheme in order to evaluate the performance of the GPPre tool proposed in this study. To test the function of the GPPre tool, a case study was carried out. The case is located on the south side of the campus of the Heilongjiang Business College, which is adjacent to the reservoir with no building around the site (Fig. 2). In addition, the site is wide enough to accommodate multiple office buildings, which creates conditions for optimizing the office buildings around the building.

As mentioned above, the application of the GPPre tool to the office building performance optimization is mainly composed of five steps. In the following sections, the building performance optimization workflow could be listed in the following steps:

1) The office building parametric building modeling: this step mainly develops the basic parametric office building model in Grasshopper for the BPS and MOO process.

2) BPS: this step mainly operates the BPS based on the CVE to obtain the relationship between building design parameters and building performance.

3) Building performance sampling: to obtain the random BPS database in Excel, building performance sampling is operated based on the LHS module for the latter SA prediction.

4) Parameters SA: based on the LHS sampling database, the sensitive design parameters could be analyzed based on the SA module.

5) MOO: based on the sensitive design parameters, the MOO could be operated based on the genetic search module to obtain the high-performance office building design scheme.

The following study is focused on the GPPre operation based on the steps mentioned above to carry out the high-performance building design scheme. The final building design scheme would be demonstrated at the end of the MOO process. After all, to verify the performance of the final design scheme, this experiment would compare the optimized building performance result with the previous building performance-optimized result to verify the utility and efficiency of the GP.

2.2.1 Preparation of the office building parametric model

An office building model is elected based on a case study^[26] that is implemented on an office building in severe cold regions in China. This model is built based on the typical values according to the survey. The basic length of the building plane is 48 m, the basic width of the building is 18 m, and the total building area is 4500 m². Besides, the details of the building construction material could be listed as follows: the wall structure of the building is assumed as the reinforced concrete. The window design of the office building is aluminum alloy window frames with single glazing. The information of the weather and the climate data is included in the CDWN weather file. During the simulation process, what designers needed to do is selecting the simulated time and weather-related information which would be processed during the simulation process.

As for the design parameters' categories, domain, and simulated step length, they were investigated from the previous studies^[27-28] and according to the building design architectural design standard^[29]. Besides, the equipment, occupancy, and HAVC system were defined by designers in EnergyPlus and the design parameters domain was obtained based on the investigation of a large number of existing research literature. As has been mentioned above, the parametric building contains four types of design parameters, which include the office building form design parameters like building story height, the air conditioning setting parameters like unit area light density, the construction equipment load setting parameters like refrigeration, the surrounding building design parameters like north building height, and the air conditioning cooling temperature parameters of building envelope like thickness of the wall. The 30 design parameters that are mentioned above have been investigated from the previous studies, which are shown in Table 1.

There are many building design parameters in the table. Here a brief explanation of the uncommon building design parameters is given:

1) Energy consumption per unit area refers to the building energy consumption like heating and cooling for a whole year per building area;

2) Air permeability per unit area refers to whether the building is well sealed and how easy it is to allow gas to pass through;

3) Ventilation per unit area refers to the ventilation volume per unit time of the building;

4) Unit area light density refers to a physical quantity of indoor light intensity;

5) SHGC refers to the ratio of the solar radiation that becomes the indoor heat gain through the door and window or curtain wall components to the solar radiation projected on the door and window or curtain wall components.

After the establishment of the parametric office building model, it could be exported into the Ladybug & Honeybee BPS plugin to help transfer the building model into the thermal zones. Each building story was divided into four thermal zones near the external walls and represents the open office areas. The windows were set around the building to support sufficient daylighting for the daytime work, and the center space of each building was an outdoor atrium space. Afterwards, the model could be used for operating the BPS.

2.2.2 Preparation of the BPS model

The GPPre workflow is developed in Grasshopper that enables designers to make parametric changes of the design variables and obtains the simulated building performance accordingly in order to gain the relationship between building design parameters and building performance in a severe cold region. Based on the 30 design parameters and three objective options, the parametric building modeling module and the BPS module in Grasshopper were established based on the Honeybee & Ladybug plugin to operate the BPS and MOO (which would be discussed in the following section). Both of the two modules established together contained seven parts, including the parametric building modeling module, the energy simulation part, the daylighting simulation part, the total cost simulation part, the simulated data recording data part, and the genetic search part. The building design parameters contain five types, which include the building form design parameters, the HVAC design parameters, the surrounding building design parameters, the wall property design parameters, and the building equipment design parameters. Besides, Fig. 3 shows the building performance simulation result of the office building to show the material property, which is one of the simulated conditions of the office building.

As for the detailed types of simulation results of the BPS, the building daylighting performance was measured by the UDI^[30]index. The energy consumption collected the building cooling consumption in winter, building heating energy consumption in summer, the lighting energy consumption, and the building equipment consumption. Additionally, the total cost includes the cost of the building material and electricity, which is shown in Eq. (7):

$ \mathit{C}{\rm{ = }}{\mathit{C}_{{\rm{wall}}}} + {\mathit{C}_{{\rm{glass}}}} + {\mathit{C}_{{\rm{ele}}}} $

(7)

where C is the total cost of the office building in the severe cold region (Yuan); C_wall is the cost of the reinforced concrete wall, which is 25 Yuan/m²; C_glass is the cost of aluminum alloy window frames with single glazing glass, which is 30 Yuan/m² and C_ele is the cost of total electricity for the whole year, which is 0.5 Yuan/(kW·h).

Based on the parametric building model and BPS module, the building energy consumption performance simulation, and building daylighting simulation, building total cost simulation for 800 times were operated, and the building performance database was gained, which would be used in the next section.

2.2.3 Preparation of the building performance sampling module

After obtaining the database of 800 groups of building performance, it is necessary to disturb the regularity of the simulated data for the next SA function. The database of 800 groups of building performance was divided into three Excel files and each reflects the relationship between building design parameters and building performance, like energy consumption, building daylighting, and building total cost. Then, based on the LHS module that was constructed in Grasshopper, the building performance database would be put into the LHS module separately. Then, building performance sampling could be operated, respectively. The LHS module setting parameters are listed as follows:

1) The learning rate is 0.1;

2) The trained data ratio is 0.8;

3) The total data number is 800;

4) The data extraction number is 500;

5) The path of the extracted database;

6) The path of the stored database.

Subsequently, 500 random groups of building performance data could be extracted into each Excel automatically and the distribution of the extracted data would be shown on the Python Figure. As shown in Fig. 4, 500 groups of sampling data are evenly distributed throughout the original 800 groups database and the building performance sampling database could be used in the next parameters SA section.

2.2.4 Preparation of the parameters SA module

The LHS module provides three databases composed of 500 groups of building performance data that could be used to separately operate the design parameters SA. It has been mentioned that the design SA module is established based on the GBRT algorithm that was written by Python programming and the module setting parameters in this case study are listed as follows:

1) The trained data ratio is 0.8;

2) The number of the iteration is 3000;

3) The learning rate is 0.1;

4) The path of the input database.

After pressing the button of the SA module, the sensitivity ranking results could be calculated automatically based on the GBRT algorithm and the sensitive ranking is listed on the python figure. Designers need to select the first five sensitive parameters obtained which are windowsill height (the relevant variable importance is 100%), north WWR (the relevant variable importance is 56.88%), north building height (the relevant variable importance is 41.55%), and eastward building height (the relevant variable importance is 29.92%). These selected sensitive parameters could be used for the MOO in the next MOO process (Fig. 5).

2.2.5 Preparation of the MOO process

After completing the development of the building performance model, the BPS, the simulation database sampling process, and the parameters SA process, the MOO process based on the sensitive design parameters could be operated. Same as the BPS process, the decision variables are UDI, AEC, and TC in the MOO process. Additionally, each design parameter was evaluated according to three objective options. The parameters settings of the Octopus plugin are listed as follows:

1) The elitism is 0.5, which shows the number of next-generation' chromosome copying;

2) The most probability is 0.1, which would affect the speed of convergence and the depth of solution space exploration;

3) The mutation rate is 0.5, which shows the degree of gene mutation;

4) The crossover rate is 0.8, which refers to the possibility of exchanging parameters between two successive generations;

5) The population size is 100, which would reflect each generation of operations with the value of the solution and the size of the specific settings to determine the complex problem-solving. The algorithm of this case study is SPEA-2 reduction, which is a good choice for MOO problems with powerful searching ability.

As could be seen from the MOO process (Fig. 6), three-dimension PFS and three dimensions are represented by different design results of optimized objection (UDI, AEC, and TC of the building material and energy consumption). With the one optimized objective decrease, the others would increase. In other word, it would be difficult to minimize all of the objective functions.

2.3 Results and Discussion

After 336 h of MOO process, the calculation was stopped and 15 generation feasible solutions were generated. There were 11 PFS in the final generation feasible solutions, and the corresponding simulated result and building formation are recorded in Fig. 6. As is demonstrated in Table 2, the Pareto frontier solution of the last generation feasible solution is closer to each coordinate axis and it has better building performance than the other generation feasible solution. The reason of choosing scheme 11 is that comparing the UDI, AEC, and TC values of each building design result, the energy performance of scheme 11 is more excellent than others. Then, a controlled trial based on the case in the study^[24] was carried out, of which the sensitive parameters are "a number of persons per unit area", "ventilation per unit area", "heating opening temperature", "cooling opening temperature", and "SHGC", which is different from the sensitive design parameters obtained from the GPPre. As a result, the two-building performance simulated experiment would be carried out to test which group's sensitive design parameters are more important to the building performance, so that the final optimized building performance would be better.

Table 3 and Table 4 list the experimental sensitive variables in the experiment operated with the SA module and the control groups. When comparing the experimental results that have been generated from the GPPre, it could be concluded that the performance of the optimized scheme is better than the original result optimized by experiment. More specifically, the analytical sensitive parameters are totally different from the previous ones. The energy-optimized result was 891048.33 (kW·h)/year, the UDI optimized result was 198.643 and the cost-optimized result was 502574.60 Yuan. It could save 4.1% of the building energy and 11.3% of the building's TC. What is more, scheme 11 could also slightly improve the indoor lighting quality of the office buildings.

3 Conclusions

The building performance MOO-based GPPre tool shows great potential in improving the time-consuming defect and increases the building performance optimization quality. Combining the GBRT algorithm and the MOO process could help lead to a more efficient exploration of the solution space and provide more accurate decision supporting for designers. The computational aided design methods have made great advancement because the high-performance building design methods are increasingly needed. There is a clear growth in the popularity of the high-performance building design tool. Additionally, the development of the GPPre is a response to the lack of tools in Grasshopper in the high-performance building design area.

There are two challenges in the GPPre tool development. One is the process of placing the LHS and GBRT module into The Grasshopper, which has been solved by utilizing the Python programming and GH_Cpython plugin to integrate the SA and MOO process. The other is the building performance MOO process based on the Octopus to operate the daylighting, energy consumption, and TC performance of the building for the optimization process, which could be complex and time-consuming. Designers should adjust the suitable Octopus parameters to gain good performance.

The GPPre tool aims to help designers use Grasshopper model logic to operate the SA-based performance optimization by utilizing the building parameters in the design process. By early adoption of the GBRT algorithm, the GPPre tool could select sensitive parameters, so as to save the performance calculating time. The ANN module could predict the building performance based on the sensitive parameters accurately, and the parametric energy and daylighting performance optimization tool could be used to prove the effectiveness of the GPPre tool.

The use of the GPPre tool in the experiment in this paper demonstrates that designers could efficiently obtain the optimized high-performance building scheme. The whole process cost about 1.5 days and the most time was cost at performance simulation and MOO process. When compared with the previous high-performance building design studies, the GPPre tool could save 4.1% of the total building energy. The GPPre tool has reduced the designing complexity and the expense of the time. What is more, the simulation database could be saved for the future design parameters SA and performance optimization of the same type of building.

The case study shows how the GPPre tool could help to design the high-performance office building design, which leads to the largest amount of natural lighting, while the AEC and the building TC could be reduced to the minimum. Besides, the GPPre tool is not limited to the daylighting and energy consumption performance optimization, but other building performance optimization, such as building structure, wind pressure, and so on. With the assistance of the GPPre tool, designers could obtain the influence of the design objective options on the decision variables at the design phase to select the final building design scheme with better performance.

In the future, the authors expect to improve the MOO speed by improving the calculating algorithm, such as the GA-PSO algorithm, so that the GPPre tool could be more efficient and accurate. Moreover, the authors also considers a high-performance building "design calculator" interface to replace the existing Grasshopper tool logic, which would make it easier for designers to operate the high-performance design process, even for those with no previous building experience.