Optimizing Window Design on Residential Building Facades by Considering Heat Transfer and Natural Lighting in Non-tropical Regions of Australia

Windows account for a significant proportion of the total energy lost in buildings. The interaction of window type, Window-to-Wall Ratio (WWR) scheduled and window placement height would influence the natural lighting and heat transfer through windows. This is a pressing issue for non-tropical regions considering their high emissions and distinct climatic characteristics. A limitation exists in the adoption of common simulation-based optimisation approaches in the literature, which are hardly accessible to practitioners. This article develops a numerical-based window design optimisation model using a common Building Information Modelling (BIM) platform adopted throughout the industry, focusing on non-tropical regions of Australia. Three objective functions are proposed; the first objective is to maximize the available daylight, and the other two emphasize on the undesirable heat transfer through windows in summer and winter respectively. The developed model is tested on a case study located in Sydney, Australia, and a set of Pareto-optimum solutions is obtained. Through the use of the proposed model, energy savings of up to 16.43% are achieved. Key findings on the case example indicate that leveraging winter heat gain to reduce annual energy consumption should not be the top priority when designing windows for Sydney.


Introduction
The built environment accounts for up to 40 percent of the global energy consumption. Greenhouse gas emission is anticipated to double by 2030 if no actions are taken [84]. Among all sectors in the built environment, residential buildings on average contribute to around three quarters of the total energy consumption [85]. Building performance varies notably across countries and regions. With this in mind, there needs to be alternative measures adopted to enhance the sustainability of buildings based on the local climate of the region in which they are built. Building design offers a great opportunity to address energy consumption involved. This includes numerous passive measures which are incorporated into design strategies to reduce energy consumption [19]. Passive design features can achieve more than 50% reduction in energy expenditure [28]. In particular, the glazing system, regarded as an important design consideration, is responsible for approximately 47% of total energy loss from the residential building envelope; this is attributed to the comparatively high thermal conductivity values of windows [23], which can lead to more extensive use of mechanical heating and cooling. A study found that US residential windows contribute to 32 percent of the total building heating ventilation and air conditioning (HVAC) load [7]. By nature, windows have weak thermal effects, causing undesirable heat loss in cold climates and heat gain in warmer regions [38]. Studying the impact that windows have on energy loss requires an understanding of associated intrinsic optical properties [75], including Visual Light Transmittance (VLT), Solar Heat Gain Coefficient (SHGC), and Conduction Coefficient (U value). One square meter of double-glazing window can lose more than ten times as much heat as the same area of a properly insulated wall [44]. Gong et al. [33] investigated passive design strategies by altering window sizes in different climate zones in China and found that thermal load doubled after increasing Windowto-Wall Ratio (WWR) from 0.15 to 0.6 in cooling-dominated climate. That said, smaller window areas could limit the natural daylight penetration to the interior, leading to the use of artificial lights in order to fulfil lighting requirements [61]. This can be partially compensated by positioning windows at suitable height to allow for a deeper solar penetration [17,60].
Glazing type is reported as one of the most influential passive window design factors [52]. Arasteh [6] reviewed the advancement of glazing technology, focusing on modifications done in terms of glass properties for thermal and lighting purposes. Cheung et al. [22] studied glazing types' influence on a passive envelope design in hot and humid climates and reported a 4.6% reduction in annual cooling load by applying reflective coating on glazing. In terms of window positioning, Bokel [17] investigated impacts of window placement height on the heating and cooling energy. Further to this, Kim et al. [41] reported a 1% reduction on total thermal load by placing windows at middle height.
Choosing an appropriate window design is a challenging task. On the one hand, increasing the size of windows will lead to an increase in the amount of daylight [30,50]. At the same time, this will inevitably increase the amount of energy lost through the window [33]. As such, window properties, size and position are three highly interrelated parameters that would affect available natural daylight and heat transfer through windows [54]. The window design dilemma is extremely challenging for non-tropical regions given that these areas account for more emissions and carbon footprint, in comparison to tropical nations [89], and their distinct seasonal meteorology characteristics [78] call for more diverse thermal and lighting design requirements.
To deal with window design problems, the state-of-the-art method discussed in the literature is based on a simulation-based approach [59]. However, several limitations of this approach have been identified, including the need for sophisticated training and expertise to conduct the simulations, time-consuming nature of the method, and its ill-adapted nature [11]. Given the time and resource constraints, along with the limited training of design and construction practitioners in these fields [10], there is a need for developing an easy-to-handle tool that caters for common building modelling software that is utilized in the field. This paper proposes a novel approach which automatically optimizes window designs, including the window type, which extends the notion of glazing type to include the framing materials, and the WWR, and window placement height, as a response to the current limitation in the literature. The aim of this research is to investigate the feasibility of conducting a numerical-based optimisation in a user-friendly modelling environment, focusing on the three design criteria mentioned above to enhance energy and daylighting aspects in non-tropical regions of Australia. The objective is to deliver an optimisation tool using a common BIM platform utilized in industry (Revit) [15] and to test the proposed approach on a case study.
This paper is structured as follows. A literature review is presented in the next section to help identify methodological limitations in the current knowledgebase and to give an overview of the thermal and lighting mechanism of windows. Following that the research methodology and process are discussed in which an optimisation framework is proposed in Revit and Dynamo [14], a Revit extension, to maximize the available daylight and minimize undesirable heat transfer, while considering the type of window, and its size and placement height. The next section presents a case study with the optimum design solutions visualized. Finally, concluding remarks on passive window design strategies are offered.

Optimisation Technique
In the literature, sustainable design optimisation can be classified as either simulation-based optimisation or numerical-based optimisation [59]. Simulation-based optimisation searches for the optimum design criteria based on the outcomes of a simulation [10]. Although there are several commercial optimisation software available, it is reported that they are time-consuming, and not user-friendly [11]; such approaches do not seem to fit well in real-life design procedures. To fill in this gap, modelling software, such as Rhino [72] and Revit are both incorporated with optimisation packages. Popular packages include Octopus [62], Galapagos [29] and Optimo [69]. Both Octopus and Galapagos are available for Grasshopper [71], a visual programming platform exclusively designed for Rhino [39]. Optimo is a plugin for Dynamo, a visual programming tool used in Revit, and is interoperable with other BIM-based services [40,76].
These software can deliver a simulation-based optimisation workflow that updates the target model with the desirable design parameters seamlessly [21,83]. A few attempts have been made to formulate different window design problems using optimisation packages in modelling environment. Table 2 summarizes some key features presented in the studies and the optimisation software employed. It can be concluded that the majority of previous works was carried out in Rhino/Grasshopper environment with Honeybee and Ladybug packages as the energy simulation engines, which are powered by Radiance [46], EnergyPlus programs [64] and DOE-2 [36]. As a result, previous research studies have demonstrated the possibility of building optimisation workflows using either Rhino/Grasshopper or Revit/Dynamo. Note that the energy and daylight simulation packages in Dynamo are customized [70] and are not available to the public. The challenge is further exacerbated due to the fact that Dynamo is reported to have occasional compatibility issues with other energy simulation plugins due to the dependency of such plugins on Dynamo build; this is inevitable given that the plugins are mostly contributed and maintained by third party developers [82]. Despite these limitations, if Dynamo is adopted for a numerical-based optimisation problem, there would be minimum dependencies on external packages. This can help alleviate the problem and hence can lead to a more efficient workflow given Revit/Dynamo are integrated with other BIM services [39,70].

Window Lighting and Thermal Effects
In an early work that examined the influence of glazing on buildings' lighting requirements and energy usage, the term Effective Aperture was defined as the product of WWR and VLT [37]. The same study also found that there was a negative relationship between the Effective Aperture and the lighting energy consumption. However, as Effective Aperture increases, the lighting energy saving starts to level off because of constraints such as latitude and solar radiation to the site [47]. In a subsequent study, the term Solar Aperture, obtained by multiplying the SHGC by WWR [48], was introduced to capture the effect of solar heat gain and was coupled with Effective Aperture to predict the cooling and lighting energy consumption in warm regions [79]. Sullivan et al. [79] found that once the 'saturation level' is reached, cooling load continues to increase due to solar heat gain, and further electricity savings can only be realized via leveraging Solar Aperture. Although the authors acknowledged Effective Aperture and Solar Aperture alone are not adequate to predict the energy consumption without modelling the effects of heat loss [79], the term Effective Aperture nowadays is often used as an indicator of daylight availability in the interior of building spaces [25,73].
Heat gain through windows occurs when solar radiation enters the interior, or as the result of the conduction of heat absorbed through the window [74]. However, for non-tropical regions solar radiation is the most prominent source of heat gain [19,54], while conduction contributes more to heat loss in winter times [54].
As evidenced by the literature above, there is a lack of method that is readily available and can be easily integrated into BIM procedures. The next section will present a novel framework for automatically designing the WWR, window type and window placement height and the formulation of these design criteria. As a result, minimizing undesirable Summer Heat Gain and Winter Heat Loss, while maximizing Effective Aperture are the objectives of the window design optimisation problem examined herein. It is critical to clarify that the detailed geometry of windows on each façade is not the focus of the study. In fact, Acosta et al. [1] had demonstrated that window shape has no effect on the energy consumption of a building. Optimo is a Multi-objective Optimisation (MOO) plugin that is readily downloadable as a package in Dynamo. It employs Non-Dominated Sorting Genetic Algorithm (NSGA-II), which is a Multiobjective Evolutionary Algorithm that uses nondominated sorting [24]. NSGA-II is one of the most commonly used algorithms in dealing with multi-objective building design problems [26]. The accuracy of Optimo has been validated by Rahmani Asl et al. [69] and it was proven to be a robust NSGA-II optimisation tool. The building needs not be designed in a particular BIM software so long as it is in the Industry Foundation Classes (IFC) file format. Stage 1 of the framework involves defining three classes of optimisation input, namely:(i) optimisation variables and parameters; (ii) population size and iteration number; and (iii) fitness functions. To define the optimisation variables and parameters, Visual Programming Language (VPL) is used to interact with Revit and extract user defined geometries from the building model. Available design options can be listed down and then retrieved from a separate Comma-Separated Values (CSV) files. Optimo requires user inputs to specify acceptable ranges for the variables optimised.

Figure 1 -Proposed Optimisation Framework
The population size, that is defined as the total number of random values needs to be specified as it will be used as the input for the next generation in NSGA-II. The user will also specify a targeted iteration that would terminate the optimisation process. Fitness Functions in Optimo context refer to customised functions that evaluate the design objectives [70]. In this study three design objectives as discussed earlier are constructed, namely maximising Effective Aperture, minimising Summer Heat Gain and minimising Winter Heat Loss; all the objectives are formulated as part of the Fitness Functions in a Dynamo interpretable format using VPL, DesignScript [2] and Python.
Penalty functions are also included in Fitness Functions to penalize values that do not satisfy three classes of constraints identified from the optimisation model. The first type of constraint is related to the architectural model. It defines the model boundaries for window placement. The second type specifies a Window-to-Floor Ratio (WFR) range to prevent overglazing. The third constraint draws upon the nationwide construction regulation in Australia, the National Construction Code (NCC) [56], which states a maximum value allowed for the heat transfer through windows.
At Stage 2 ( Fig. 1), a list of random values for the variables to be optimized is created as the initial generation for the Optimisation. This will be used as the input for the customized Fitness Functions, from which the results are to be evaluated using the NSGA-II algorithm. This process is iterative and only stops when it reaches the pre-determined number of iterations. NSGA-II generates a spread of equally optimal solutions such that any variable cannot be further improved without compromising at least one other variable, which is commonly known as Pareto Front. Note that during this process, Fitness Function results at each generation and points on the Pareto Front are both to be exported and saved in a CSV file for further visual analysis in Stage 3.
At the final stage, Stage 3, the exported datapoints will be visualized for subsequent analysis. Design criteria and corresponding objective values at each generation are to be displayed in a 3dimensional scatter plot to show improvements as the iteration proceeds. A sample of points selected Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 6 October 2020 doi:10.20944/preprints202010.0111.v1 from the final Pareto Front is plotted using parallel coordinates to visualize the highly interrelated design parameters.
A number of assumptions are made for the framework presented above, based on existing design practices in industry:  On each story level, windows facing the same direction should be placed at the same height.
 The overall window system is installed with the same type of window.
 Shading devices attached on the same wall face have the same width, measured as the perpendicular distance from the edge of the shading device to the wall [54].
From here on, window elements discussed in this paper refer to windows located on the building envelope and their framing system.

Computing Effective Aperture
Effective Aperture in this study is used as a measure to assess the daylight availability, with a larger value indicating less reliance on artificial lights [49], contributing to potential savings in energy consumption. Since no skylights are discussed in this paper, the equation of 'effective aperture for vertical fenestration' offered by Green Building Initiative (GBI) in ANSI/GBI 01-2019 [5] is adopted, where the Effective Aperture for windows on vertical façades is calculated as the product of the VLT value and the proportion of the window area (including framing) to the 'gross wall area' [4,5], which is measured from the top of the floor to the bottom of the roof [9]. The Effective Aperture measured on each floor can be expressed in Eq. (1): where is the total number of glazed walls on a particular level. and correspond to design variables window type and the WWR scheduled for wall respectively.

Computing summer heat gain and winter heat loss
Heat gain and heat loss via solar radiation and conduction are functions of window properties and the window size, and the equations are generally formulated as given in Eq. (2) [42] and Eq. (3) [80] respectively: In these two equations, is the total window area on each story, is the solar irradiance, and ∆ is the indoor and outdoor temperature difference. Solar irradiance and temperature difference are two factors that are highly dependent on real operating conditions. Solar irradiance can vary significantly according to the seasonal solar angle [66] and window orientations [18], and can also be manipulated by changing window positions and adding shading devices. In other studies, this parameter relies on simulation results or direct measurement to form the basis of calculation, for example, see [34,45]. The value of ∆ in previous studies is often assumed as a constant based on local construction compliances [8].
In this study, in order to calculate Summer Heat Gain and Winter Heat Loss, a term Exposure Factor introduced in NCC [54] is adopted. Exposure Factors are a range of coefficients representing windows' exposure to the sun for different building orientations in heating and cooling seasons respectively across all climate zones in Australia [54]. For a given climate zone and orientation, Exposure Factors for summer and winter design considerations are associated with a term , where when the width of the shading device and the wall geometries are constants, Exposure Factors on each wall are only dependent on window placement height, calculated as the total wall height minus ℎ , which is measured from the base of the window to the bottom of the shading device. Therefore, we can deal with discrete Exposure Factors instead of the continuous window height variables in the optimisation.
where is the gross area of a glazed wall, and by multiplying it and , the glazing area on a wall is calculated. and denote the Summer Exposure Factor and Winter Exposure Factor adopted. and are design variables obtained from two reference tables for Summer Exposure Factors and Winter Exposure Factors respectively, which are originally obtained from the NCC and stored in CSV files following the table format shown in Fig. 2 Note that for values that are not present in the table, the next lowest value will be adopted for identifying an , while the next highest will be adopted for Winter Exposure Factors for more stringent results [54]. This will provide us with discrete height ranges at the end of the optimisation process. In these equations, and are associated to the same window type as . Eq. (4) aims to minimize the heat gain in summer, while Eq. (5) conveys the strategy of leveraging beneficial winter heat gain to offset heat loss.

Model constraints
As discussed earlier, three classes of constraints are defined in the proposed optimisation framework. The first constraint class defines the model boundaries for window placement. The second constraint class prevents overglazing. The third constraint class imposes a maximum value allowed for Summer Heat Gain and Winter Heat Loss, respectively. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 6 October 2020 doi:10.20944/preprints202010.0111.v1

Window placement constraint
This constraint class refers to the underlying design requirement that there exists a height range on each wall that is feasible for installing a window. Considering the functionality of windows and the design feasibility, two considerations are accounted for: (i) windows should be placed above a certain working plane; and (ii) a minimum distance that is proportional to a scheduled WWR should be maintained at the top of the wall to prevent design clashes. These two constraints are defined in Eq. (6) and Eq. (7) respectively: where and represent the lowest and highest placement points for positioning a window on a wall, is the height of the hosting wall given as a predefined parameter. The height of the working plane, is to be determined by the designer.

Window-to-Floor Ratio (WFR) constraint
Eq. (8) specifies a restriction on the total glazed areas on each floor by setting a lower and upper bound for the WFR, to ensure feasible design.
is the fully enclosed covered area of the corresponding floor, and hence the WFR indicates the proportion of floor to be heated via the glazing system. Designers have the liberty to determine the inputs of the maximum and minimum WFR, represented by and .
As the tolerance to WFR varies depending on the daylight factor and exterior illuminance level in the local context [90], as a general guideline, the WFR adopted can be as low as 10% [54,58], and can also go up to 50% [90] in some studies.

Maximum thermal values constraint
NCC Volume Two outlines design requirements for the maximum aggregate heat gain and aggregate conductance, allowed for residential houses [54], which are the basis for the formulation of Summer Heat Gain and Winter Heat Loss in this study. Considering the similarities in energy use and thermal performance in all residential dwellings [57], this paper applies the same set of compliance to other residential buildings under the research scope to achieve more realistic optimisation results.
The maximum values allowed for Summer Heat Gain and Winter Heat Loss are given in Eq. (9) and Eq. (10)

Penalty function
Two different approaches are adopted to handle the constraints identified above. Eq. (7) -(10) are imposed using penalty functions. This can be achieved because they are either restricting the objective function values or are dependent on optimisation variable selection. The lower bound of the Window Placement Constraint as in Eq. (6) is specified via design inputs.
Given that any violation on optimisation constraint would yield equally unfeasible design, in this study penalties are applied without distinguishing the level of violations or the number of violations. To achieve this, a structure that is suitable to implement in Optimo is proposed to evaluate and penalize unfit results, see Fig. 3. Note that although the evaluation of the Summer Heat Gain and Winter Heat Loss objective functions is expressed using one logical path, their evaluation process is independent.

Figure 3 -Penalty Function Structures
Once the Summer Heat Gain and Winter Heat Loss objective function results are obtained, they are first compared with the Maximum Thermal Objective Values defined in Eq. (9) and Eq. (10), respectively; if any violation occurs, a constant penalty, denoted as , will be applied to the offending objective function value, leading to a termination of its evaluation process at this generation. The performance of the Summer Heat Gain and Winter Heat Loss objective values are represented using binary variable and ,respectively, which will equal 1 if there is any violation. Further examination on design variables against the upper bound of the Window Placement Constraint and WFR Constraint would be executed if the preceding Maximum Thermal Objective Value is respected, meaning that the corresponding or is equal to 0. The Boolean expressions for the Window Placement Constraint and the WFR Constraint are represented using two binary variables and respectively; for either Summer Heat Gain or Winter Heat Loss, any violation on these two conditions would impose the same constant penalty . The Effective Aperture value is examined in a similar but more straightforward fashion with only the WFR Constraint assessed. At each generation, only the evaluated objective function results could continue with the NSGA-II nondominated sorting and reproduction process [90]. Therefore, the proposed penalty function structure can be expressed using Eq. (11) - (13): Let (HG) and (HL) be the penalty function for Summer Heat Gain and Winter Heat Loss described above, and (EA) aims to evaluate Effective Aperture. is the constant penalty 1000. , , and are binary variables representing four possible situations the algorithm might encounter, i.e. whether and exceed the maximum values allowed and the violation on the Window-to-Floor Ratio Constraint and the upper bound of Window Placement Constraint.

Dynamo Workflow
To execute the proposed framework, a Dynamo workflow illustrated in Fig. 4-6 has been developed. The structure corresponds to the framework shown in Fig. 1. Main components at each stage are grouped under their respective labels.
In Fig. 4, under Optimisation Variables, users are asked to choose the file path where design variables are stored. It is expected that available design variables are prepared a priori and saved in CSV file format. Similarly, users are also required to select window hosting walls as highlighted in Optimisation Parameters. Fig. 4 illustrates an example of selecting four glazed walls. Fig. 4. will be input to Fitness Functions, see Fitness Function Lists in Fig. 5. Each Fitness Function comprises one of the design objectives discussed earlier together with penalty functions to restrict variables involved. However, Fitness Functions will not be able to retrieve variables without the commands labelled under Generating and Sorting to obtain the variable ranges specified in Optimo Configuration. In addition, Generating and Sorting contains the main body of the NSGA-II algorithm for sorting and evaluating Fitness Function results.   6 illustrates the workflow of preparing the data for plotting the parallel coordinates. This graph enables us to visualize three design objectives in a 2-dimensional space by plotting all design attributes as parallel lines [16]. As this optimisation problem involves multiple design criteria for consideration, this presentation offers a more compact way to view and compare different designs. An iterative data exportation for 3-dimensional scatter plot is achieved by including relevant codes under each Fitness Functions. Since some design variables, such as window type and WWR, including the window height variable, could be presented as discrete values in the Optimisation, each variable is handled an index by Optimo, and Retrieve Associated Variable is where 'real' variable values are retrieved from the original CSV file.

Case Study
In order to demonstrate the applicability of the framework proposed herein, a case study of a realistic single-story house is examined in Dynamo using the proposed optimisation framework. Minor modifications were made to the BIM model for confidentiality reasons. As seen in Fig. 7, the house is facing west and has a verandah and eaves for shading purposes. Fig. 8 indicates the plan view. The total area of the building is 59.4 . A WWR of 55% and 45% are scheduled for its west and north façade, respectively, and its southern and eastern facing walls have a WWR of 50%. All windows are clear single glazing with aluminum framing and designed with a sill height of 500mm. Australian regions are categorised under eight climate zones: (i) Zone 1 -high humidity summer, warm winter; (ii) Zone 2 -warm humid summer, mild winter; (iii) Zone 3 -hot dry summer, warm winter; (iv) Zone 4 -hot dry summer, cool winter; (v) Zone 5 -warm temperature; (vi) Zone 6 -mild temperature; (vii) Zone 7 -cool temperature; and (viii) Zone 8 -Alpine. The project is located in a South-Western suburb of Sydney and is within climate zone 5 (warm temperate) [12].

Varaible selection
In many building design optimisation models, continuous variables are commonly used as they are often computationally easier to deal with compared to discrete variables [59]. However, continuous variables sometimes cannot well represent real design practices [87]. In the proposed window design problem, all design criteria were input as discrete variables to represent realistic solutions possible in industry practice. At Stage 1 as shown in Fig. 1, variable acceptable ranges were therefore defined according to their associated indices.
Window types used for this case study were obtained from the list of 88 Default Windows [13], which is developed by Australian Fenestration Rating Council to represent performances of glazing products in the market. Four commonly used clear glass windows, namely aluminum windows or timber/uPVC windows with either single or double glass panels [31], and their four tinted alternatives were selected and the associated properties for the glazing and framing system are shown in Table 3. As the window operating type may have an influence on the vision area, the values adopted are based on double hung, sliding, fixed and louvre windows [13].
Four WWR values tested range from 20% to 50%, and this variable was incremented at a 10% interval. This was adopted with reference to a previous study that investigated the WWR of 20%, 30%, 40% and 80% on a hypothetical residential building in Sydney [81]. The study found significant influence on cooling energy consumption by increasing WWR. In this paper, considering it is recommended to reduce the WWR to a maximum of 50% for Sydney residential buildings [67], the highest input glazing ratio was set as 50%.
An initial height range for window placement was also defined. A horizontal reference work plane, which is usually taken as 750mm in Australia [42], is assumed for this case study. The maximum window placement height was determined based on the minimum possible WWR of 20% and the hosting wall height. Corresponding Exposure Factors for each initial height range can therefore be extracted. In addition, a WFR range of 10% to 40% is adopted to restrict glazing areas. A general design rule of thumb for WFR is 20% to 25%, whereas this does not factor in the impacts of the geographical locations of different projects [35]. In this study, the lower bound 10% is a threshold for natural lighting requirement clearly stated in the NCC Volume Two [54]. Although there is no empirical data that specifies an allowance for WFR in Sydney region, a 10% average daylight factor, which is considered as the maximum allowed for the interior [86], was obtained by Ibrahim & Hayman [35] when the WFR is between 30% to 40% in Sydney. In the interest of brevity, this case study took 40% as the upper bound. However, it is acknowledged that setting 40% as the allowance is prone to yield larger than usual WFR. This highlights the importance for designers to determine such data as per project requirements.
Each design option shown in Table 3 has been associated with an index and Table 4 gives the variable range input in Optimo based on the indices.

Results and discussion
The calculation process was conducted on a personal computer with a 2.5 GHz processor and 8 GB of RAM in Windows 10 environment. The mutation and crossover probability were set as 0.01 and 0.9, respectively. The distribution indices for crossover and mutation are 20 [70]. In this study, the Pareto Front was obtained after 150 iterations with a population size of 200. The whole process, including exporting approximately 100,000 data points, was completed within 30 mins. Fig. 11 indicates the evolution of objective function values through generations. Generally , as the process approaches the end of the optimisation, the color of the points displayed exhibits a red color scheme. The Pareto Front generated is presented in Fig. 12, where the red points represent optimum design solutions. In this graph, the Effective Aperture, Summer Heat Gain and Winter Heat Loss correspon to the X, Y and Z axis, respectively. One sample point is highlighted below, which has an Effective Aperture value of 0.441, a Summer Heat Gain Value of approximately 4.03 and a Winter Heat Loss value of 2.13 after rounding up.   Fig.13a indicates the efficacy of using winter heat gain to compensate heat loss in a warm temperate climate. Fig.13b and Fig.13c depict the relationship between Effective Aperture and windows' thermal performance in summer and winter, respectively. It is observed in Fig.13b that a positive relationship exists between the Effective Aperture and Summer Heat Gain, which is in line with previous findings on Effective Aperture's effect on increasing cooling load [37,79]. Fig.13c shows a more dynamic relationship between the Effective Aperture and Winter Heat Loss, where the effect of solar gain illustrated in Fig.13a also comes into play. Further to this, when controlling Effective Aperture, both Fig.13b and Fig.13c have shown that solar gain and heat loss can be modified by changing the window height. One way to understand Fig.13b and Fig.13c is by investigating some sample datapoints labelled as group A in Fig.13a. It can be deduced that group A represents the optimum designs when only considering the objective of minimizing Summer Heat Gain and Winter Heat Loss as no smaller value of either of these two objectives can be found while maintaining the performance of the other objective. Seventeen datapoints are captured in group A. The same series of data have also been highlighted in Fig.13b and Fig.13c as group B and C, respectively. Among the 17 designs, it is found that they are all scheduled with tinted double glazing with aluminum framing and adopt the same WWR strategies, namely, 20% to eastern, southern and western façade, and a 40% to the northern wall. Review Eq. (1) for calculating the Effective Aperture, and it can be concluded that different values on Y-axis shown in group B and C are only attributed to different window placement heights. The remaining points that have the same Effective Aperture values might be a result of the interaction of these three variables. After removing six penalized values, there were 194 individuals that remained in the final generation. Fig. 14 and Fig. 15 take a closer look at the optimum height range and WWR for different wall faces. It is noted that two different strategies to optimize windows' thermal performance can be observed from the Pareto Front. One is the common approach of minimizing glazed area on northern façade in Southern Hemisphere and placing windows at the top part of the wall to avoid heat gain. Another strategy, which has been proven to be effective according to Fig. 13a, is to encourage sufficient solar penetration from north-facing wall to reduce winter heat loss. Installing windows at lower heights would exaggerate this effect. As such, the intense solar radiation from the north is fully used as an alternative to mechanical heating in winter, savings from which in theory may potentially offset the additional summer cooling expenditure induced. Among all 194 solutions, around 87% of the total favour this strategy by positioning northern windows at a lower height (750mm -1525mm), and more than half of the designs also offer generous glazing areas to the north. In addition, noting that optimum design solutions tend to allocate relatively small windows (<30%) to east, south and west-facing walls; this is reported in all cases for eastern façade and around 90% for southern and western façade. This is in line with the strategy of taking advantage of sunlight from the north while designing small windows to these three orientations only for cross-orientation purpose [65]. It is also observed that no WWR of 50% was recorded in the Pareto Front. One possible explanation is WFR shown in Eq. (8) plays a prominent role in restricting the total window area.  Four solutions that obtained a single optimum value were identified as a sample of the Pareto Front. The detailed window design options offered by these four designs are presented in Table 4. Optimum window design attributes have been plotted using parallel coordinates to display a clear design trade-off, see Fig. 16, where solution A, B, C, and D are represented using different colours. All solutions have a WWR of 20% scheduled for the east and west-facing wall. Design A aims to minimize Winter Heat Loss by placing better thermally insulated timber framed windows at lower parts of the wall to allow for more solar penetration in winter. In addition, generous window area is scheduled for north-facing wall to capture winter solar radiation. On the contrary, design B tends to limit the window size and window placement points are higher in order to avoid direct exposure to the sun. Double glazing with low SHGC value is selected to eliminate unwanted heat gain. Design C and D are focusing on optimizing the Effective Aperture requirement by employing glazing with high VLT value and average thermal performance and assigning large window areas to the south.     Approximately 8.57% reduction on annual energy consumption is observed for design A, C and D, while this figure has nearly doubled for design B, which emphasizes the passive window design strategy that minimizes Summer Heat Gain. This seems to be conflicting with the finding reported earlier on that leveraging winter heat gain to compensate heat loss in Sydney region.
This can be partially explained by the fact that Sydney has a temperate climate and is heating and cooling balanced [88]. When it comes to the total energy consumption, which is the function of summer heat gain, and winter heat loss and effective aperture in this case, extra cooling load induced from generous solar gain might not be fully recovered from reduced use of heating equipment in winter for Sydney. As these sample designs are obtained from the Pareto Front, they all represent equally good practices when controlling other design parameters. Therefore, by contrasting Design A with B, it is informed that over emphasis on the effect of leveraging northern sunlight to offset winter heating could in fact jeopardize the efficacy of the design.
Design A took an opposite design approach compared to Design C and D; small windows are scheduled to the south and tinted glass are installed, while the other attributes are similar. These designs achieved the same energy performance. Again, this corresponds to the findings from Fig.  13b, and coincides with the established theory on Effective Aperture's effect on increasing cooling load, which has been discussed earlier on.

Conclusions
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 6 October 2020 doi:10.20944/preprints202010.0111.v1 A window design optimisation problem was proposed in this study for the window type, WWR and window height for residential buildings in non-tropical regions in Australia using a BIM platform, Revit and its extension Dynamo. Three objective functions concerning the natural light, undesirable heat gain in summer and heat loss in winter together with four penalty functions that impose realistic design constraints were formulated and solved using an NSGA-II Optimisation package of Dynamo, Optimo. A range of coefficients offered by the Australian construction regulatory framework, NCC, were adopted to translate the continuous window height variable into discrete values. Architectural model geometries, such as hosting wall areas and heights were extracted from the building model as optimisation parameters.
The results were presented in the form of Pareto Front with the improvements of design objectives throughout the optimisation process visualized using 3-dimensional scatter plot. To further showcase the interplay of different design attributes, a sample of four designs identified from the result set, representing the most ideal solution for each objective, was displayed using parallel coordinates. A Revit energy analysis plugin, Insight, was employed to simulate these four designs to get the annual energy consumption in order to contrast with the base case. The simulation results suggest a maximum of 16.43% energy reduction could be realized when applying the design that focuses on minimizing heat gain in summer.
This novel optimisation framework offers a BIM-integrated approach to deal with a practical window design problem. The findings shed some light on the window design strategy in temperate regions that even though winter sunlight is beneficial, winter sun penetration is not the top design priority as these regions most likely have a balanced heating and cooling requirement. The proposed workflow has demonstrated the feasibility of conducting a numerical-based design optimisation on a common modelling platform, providing an opportunity for integrating optimisation into industry design practice.
That said, one weakness of this work is that the developed framework still requires to be tailored on a project basis for similar window design problems. Furthermore, new Fitness Functions need to be formulated from scratch if users are interested in other optimisation scenarios. This is primarily rooted in the identified industry knowledge gap that basic DesignScript and Python are still not common languages. This will hinder the adoption of the propsoed optimisation workflow. Another limitation is that no sensitivity analysis was conducted to understand the role each design parameter played in the window design problem.
Future work built upon this study could involve generalizing the proposed Optimo optimisation framework so that designers only need to choose the file paths for variable input, while the remaining process will be competed automatically. Further to this, the proposed framework could be integrated with the modelling software as an addon and the interaction could be achieved via the use of Application Programming Interface (API), delivering a fully automated optimisation workflow. Similar interaction was realized by Rahmani Asl, Zarrinmehr, et al. [70] by linking an Optimo framework with Green Building Studio for real-time simulation. However, the connection was discontinued [3] due to lack of maintenance, which also sheds light on the importance of continuing collaboration between key industry players and the academia.