The Road to Developing Economically Feasible Plans for Green, Comfortable and Energy Efﬁcient Buildings

: Owing to the current challenges in energy and environmental crises, improving buildings, as one of the biggest concerns and contributors to these issues, is increasingly receiving attention from the world. Due to a variety of choices and situations for improving buildings, it is important to review the building performance optimization studies to ﬁnd the proper solution. In this paper, these studies are reviewed by analyzing all the different key parameters involved in the optimization process, including the considered decision variables, objective functions, constraints, and case studies, along with the software programs and optimization algorithms employed. As the core literature, 44 investigations recently published are considered and compared. The current investigation provides sufﬁcient information for all the experts in the building sector, such as architects and mechanical engi-neers. It is noticed that EnergyPlus and MATLAB have been employed more than other software for building simulation and optimization, respectively. In addition, among the nine different aspects that have been optimized in the literature, energy consumption, thermal comfort, and economic beneﬁts are the ﬁrst, second, and third most optimized, having shares of 38.6%, 22.7%, and 17%, respectively.


Introduction
During recent years, the standard of living has raised increasingly [1][2][3][4]. Moreover, the issues such as energy and environmental crises have led to growing concerns about the future of human-beings on the planet [5][6][7][8]. Since there are a lot of buildings in different applications all around the world, any improvement in the building sector, in which all the previously mentioned parameters are involved, is greatly appreciated by the entire world [9][10][11]. Different experts, including architects, energy engineers, mechanical engineers, etc., with different points of view, corporate in the design process [12]. This means that acquiring a desirable condition is a really challenging matter [13][14][15][16]. As a solution, optimization approaches, which are systematic ways to deal with such problems, have been increasingly applied [17].
Depending on the project goal and expected requirements, single-objective optimization (SOO) or multi-objective optimization (MOO) can be employed. In SOO, only one objective is minimized or maximized, whereas in MOO two or more than two objective functions are enhanced, simultaneously.
Optimization problems can be categorized in different ways, for example, based on the optimized objective functions, considered decision variables or constraints, and so on.
In order to perform further studies, being well informed about the investigations done in the past is of great importance. The more comprehensive information provided from the literature, the higher quality the future studies will be.
Investigating the review studies in the field of building performance optimization (BPO) clarified that, despite providing valuable information, these studies also have some drawbacks. The main drawbacks of the review articles done recently are collected in Table 1. Table 1. List of the recent review studies in the field of building performance optimization (BPO).

Study Year The Main Drawbacks
Wong and Zhou [18] 2015 • The research aimed to provide an overview of the ways to improve buildings environmental sustainability in their life cycle. The studies that optimized other objectives were not investigated.
• Visual comfort definitions, and its constraints and indicators were well defined; however, details about other building aspects, decision variables, employed algorithms, and software were not reported.
Shi et al. [20] 2016 • This paper discussed the literature from the architectural perspective. Other perspectives were not taken into account.

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The investigation did not classify different optimization approaches.

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The constraints imposed to the optimization problems were not mentioned. • Studies which employed both MOO and SOO were not compared to the ones which conducted either MOO or SOO.
Bonyadi and Michalewicz [21] 2017 • Only a brief description about the previous review studies was presented. It means that the research papers were not taken into account.

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The review was limited to the particle swarm algorithm; other algorithms were not taken into account. • MOO problems were not studied.

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The information about decision variables, constraints, and other key parameters in an optimization problem were not presented.
Kumar et al. [22] 2017 • Methods and software programs were the only investigated parameters.
Tian et al. [23] 2018 • The review merely covered passive design buildings. • There is the lack of reviewing decision variables, objective functions, constraints, software, and so on.

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The review was written from the architectural point of view and there is no sufficient information for the other experts.
Ekici et al. [24] 2019 • Among all the key parameters, only the building aspects which were considered as the objectives were discussed. • Among evolutionary, juts swarm algorithms were investigated.

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The consideration of decision variables was restricted to form-finding ones.

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The investigated MOO publications were in the range of 2012-2016, which is not up to date. • Explanations about some important parameters of an optimization problem, such as the considered decision variables and employed software programs were not given.
• The optimization problems are classified to SOO and MOO, and they are compared to each other. In addition, the studies that evaluated both SOO and MOO are also taken into account. • All the key parameters in an optimization problem are considered and the investigations are analyzed based on each of them, separately. The key parameters include objective functions, decision variables, and constraints. There have been nine different aspects from which objective functions have been selected so far. The review investigates all the nine aspects completely and in detail.

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The studies are also categorized and investigated based on other criteria, such as optimization algorithms and software programs. Moreover, software programs are divided into building simulation-based and optimization tools.

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The review is written in a way that it provides information for not only architects but also other experts in the building sector.
Therefore, this study serves as a reference to acquire brief but detailed information for researchers in the future to achieve better results in their further studies. Having the information about the previously done investigations reported in this review will help the researchers who are going to conduct BPO studies to select the key parameters in a more efficient and comprehensive way. Moreover, they will not forget some points which make the optimization results unfavorable from some aspects. This paper has the following structure. After this part, i.e., the introduction, the core literature is introduced. Then, it is analyzed from different aspects, including the considered objective functions, decision variables, constraints, and the case study. Next, the algorithms employed for optimization and the software used are reviewed, and after that, conclusions are presented.

Paper Searching Methodology
This review concentrates on investigations within the building performance optimization (BPO) framework found from Scopus and Science Direct databases. Since the optimization algorithms and computer infrastructure have been significantly enhanced during these years, the studies done in the years before 2015 were usually simple, and for that reason, only recent studies that were published in the period of 2015 to 2019 were taken into account. Moreover, some keywords, such as "multi-objective optimization", "single-objective optimization", "simulation-based optimization", "zero-energy buildings", "energy consumption", "thermal comfort", "daylighting", "visual comfort", and "life cycle cost" were used to select the relevant studies. This search method resulted in collecting 44 studies that were considered as the core literature.

Overview of the Studies Selected
Here, a general classification of the core literature is presented based on the year and the optimization approach. As is seen in Table 2, two different approaches have been followed in the optimization processes of these studies, including single-objective optimization (SOO) and multi-objective optimization (MOO). Moreover, in some of the reviewed studies, the results of these two approaches have been compared with each other. Such investigations are presented in the category of "single-objective versus multi-objective approach" in Section 3.3.  As is shown in Figure 1, about 30% of the selected studies were done in 2019. This demonstrates that there is a growing interest in the BPO topics among researchers worldwide.

Single-Objective Optimization (SOO)
In the optimization process, based on the SOO approach, only one aspect is optimized. In order to achieve better results, the researcher may consider other aspects than the constraints which are very likely to have the readers confused with the objective functions (e.g., [27,30,33,35]). It should be noted that Mangkuto et al. [28] claimed the MOO approach was proposed in their paper. In fact, in that paper, in the optimization process minimizing lighting energy demand was subjected to the limitation of five daylight indicators. This Sharif and Hammad [63] 2019 √ Fang and Cho [64] 2019 √ Sohani et al. [65] 2019 √ Lu et al. [66] 2015 √ √ Delgarm et al. [67] 2016 √ √ Delgarm et al. [68] 2016 √ √ Delgarm et al. [69] 2016 √ √ Xiong et al. [70] 2019 √ √ Figure 1. Comparing the number of applicable studies done in each year.

Single-Objective Optimization (SOO)
In the optimization process, based on the SOO approach, only one aspect is optimized. In order to achieve better results, the researcher may consider other aspects than the constraints which are very likely to have the readers confused with the objective functions (e.g., [27,30,33,35]). It should be noted that Mangkuto et al. [28] claimed the MOO approach was proposed in their paper. In fact, in that paper, in the optimization process minimizing lighting energy demand was subjected to the limitation of five daylight indicators. This means that lighting energy demand was the only objective function, and the five daylight indicators were the constraints of the SOO.

Multi-Objective Optimization (MOO)
MOO is used to optimize different objectives at the same time. Reviewing the studies belong to this group shows that, in such investigations, two, three, or four objectives were optimized simultaneously. In order to choose the objective functions, three different types of approaches have been employed: • Type 1: optimizing two or more than two indicators of one aspect (e.g., [36,40]); • Type 2: optimizing one indicator of two or more than two aspects (e.g., [37,39,41]); • Type 3: a mixture of both (e.g., [38,55,57]).

Multi-Objective Optimization (MOO)
MOO is used to optimize different objectives at the same time. Reviewing the studies belong to this group shows that, in such investigations, two, three, or four objectives were optimized simultaneously. In order to choose the objective functions, three different types of approaches have been employed: • Type 1: optimizing two or more than two indicators of one aspect (e.g., [36,40]); • Type 2: optimizing one indicator of two or more than two aspects (e.g., [37,39,41]); • Type 3: a mixture of both (e.g., [38,55,57]).

Single-Objective Versus Multi-Objective Optimization
In these studies, different objectives have been optimized independently by SOO. Since different objectives usually behave contrary to each other, the impact of other objectives might be considered as the constraints of SOO (e.g., [70]). On the other hand, MOO has been also conducted, and the results of SOO considering different objective functions are compared to the MOO outcome.

Single-Objective Versus Multi-Objective Optimization
In these studies, different objectives have been optimized independently by SOO. Since different objectives usually behave contrary to each other, the impact of other objectives might be considered as the constraints of SOO (e.g., [70]). On the other hand, MOO has

Overview of the Selected Studies
In this part, the core literature is analyzed based on three key parameters in an optimization process, namely, objective functions, decision variables, and constraints. As is shown in Figure 3, in the BPO procedure, there is a strong connection among these three parameters.

Single-Objective Versus Multi-Objective Optimization
In these studies, different objectives have been optimized independently by SOO. Since different objectives usually behave contrary to each other, the impact of other objectives might be considered as the constraints of SOO (e.g., [70]). On the other hand, MOO has been also conducted, and the results of SOO considering different objective functions are compared to the MOO outcome.

Overview of the Selected Studies
In this part, the core literature is analyzed based on three key parameters in an optimization process, namely, objective functions, decision variables, and constraints. As is shown in Figure 3, in the BPO procedure, there is a strong connection among these three parameters.

Objective Functions
Reviewing the studies shows that nine different aspects have been considered in the optimization process. Each of these aspects has been assessed with some indicators, and the objective functions have been chosen among them. In the MOO approach, two or more than two indicators were chosen and defined. As it was mentioned in Section 3.2, these indicators might belong to the same aspects or not.
These aspects have been taken into account in the reviewed studies:

Objective Functions
Reviewing the studies shows that nine different aspects have been considered in the optimization process. Each of these aspects has been assessed with some indicators, and the objective functions have been chosen among them. In the MOO approach, two or more than two indicators were chosen and defined. As it was mentioned in Section 3.2, these indicators might belong to the same aspects or not.
These aspects have been taken into account in the reviewed studies: As it is shown in Figure 4, energy consumption indicators were the dominant objectives in the reviewed studies, accounting for 38.6%. Thermal comfort and economic benefit indicators, with 22.7% and 17.0%, were the second and third most-optimized objectives, respectively. The aspects and objective functions considered in each study are presented in Table 3.

Energy Consumption
To the best of our knowledge, researchers have used 13 indicators to minimize energy consumption in buildings. These indicators are shown in Figure 5. In some studies (e.g., [42,61,62]), the three most used indicators, heating, cooling, and lighting energy consumption, have been optimized as one objective function, named the total energy demand. That is usually done to simplify the computational difficulties of the optimization process caused by the increase in the number of objective functions. In addition, for more simplification, the combination of two of these three indicators might be taken into account, depending on the parameters such as location and function of the case study. As an example to clarify the impact of climate on choosing the energy related objective functions, Zhang et al. [45], studied the performances of school buildings in the cold climate of China by investigating heating and lighting energy demands as one objective to describe the energy performance for thermal and visual comfort indicators. In that work, due to the climatic conditions, the energy demand for cooling was not considered.    To the best of our knowledge, researchers have used 13 indicators to minimize energy consumption in buildings. These indicators are shown in Figure 5. In some studies (e.g., [42,61,62]), the three most used indicators, heating, cooling, and lighting energy consumption, have been optimized as one objective function, named the total energy demand. That is usually done to simplify the computational difficulties of the optimization process caused by the increase in the number of objective functions. In addition, for more simplification, the combination of two of these three indicators might be taken into account, depending on the parameters such as location and function of the case study. As an example to clarify the impact of climate on choosing the energy related objective functions, Zhang et al. [45], studied the performances of school buildings in the cold climate of China by investigating heating and lighting energy demands as one objective to describe the energy performance for thermal and visual comfort indicators. In that work, due to the climatic conditions, the energy demand for cooling was not considered.
Moreover, the function of the case study can also help to simplify the optimization process in temporarily occupied buildings, such as office buildings. This means that if the building is only occupied during the day, the main concerns are about cooling and lighting energy consumption. It should be pointed out that reviewing some other studies (e.g., [36,67,69]) has made it clear that the best condition is achieved while the energy demands for heating, cooling, and lighting are optimized together and independently. However, Mangkuto et al. [28], Zhou et al. [32], and Xue et al. [35], have optimized lighting, heating, and cooling energy demands using the SOO approach, respectively. Figure 6 shows the eight different indicators that have been taken into account in the reviewed studies to investigate thermal comfort. These indicators can also be assessed for different seasons, independently. In the work published by Carlucci et al. [38], the percentages of dissatisfied people in summer and winter were optimized as two independent objectives, using the MOO approach. In another study [30], the operative air temperature was considered as the thermal comfort-describing objective function. Based on the definition, the operative air temperature is dependent on the season. It means that in the cooling and heating periods, it should be minimized and maximized, respectively.

Economic Benefit
In the reviewed studies, the optimum solution for this aspect has been achieved by optimizing nine different indicators imposed on both SOO and MOO. Among all these indicators mentioned in Figure 7, life cycle cost has been the most optimized. In the process of evaluating the life cycle cost, the significance of minor costs such as water cost might be disregarded. To avoid that, Sohani et al. [55] considered operating costs and water costs separately.

Visual Comfort
Despite the importance of visual comfort to both occupants' behavior and energy use, only five indicators describing this aspect have been considered in the reviewed studies. These indicators are introduced in Figure 8. In the research done by Mangkuto et al. [28], other metrics such as daylight factor, uniformity, and daylight glare probability have been taken into account as the constraints imposed on the SOO.

Environmental Impact
The growing concern for the environmental impacts of buildings has built a strong urge in researchers to consider this aspect in the optimization studies. Figure 9 shows the four indicators used in the studies we reviewed. It should be noted that there is a huge difference between carbon dioxide emissions and the equivalent carbon dioxide emissions, as two of the four indicators that describe the environmental impact. In the equivalent carbon dioxide emissions, unlike carbon dioxide emissions, other types of emissions besides carbon dioxide have been also taken into account. Moreover, the function of the case study can also help to simplify the optimization process in temporarily occupied buildings, such as office buildings. This means that if the building is only occupied during the day, the main concerns are about cooling and lighting energy consumption. It should be pointed out that reviewing some other studies (e.g., [36,67,69]) has made it clear that the best condition is achieved while the energy demands for heating, cooling, and lighting are optimized together and independently. However, Mangkuto et al. [28], Zhou et al. [32], and Xue et al. [35], have optimized lighting, heating, and cooling energy demands using the SOO approach, respectively. Figure 6 shows the eight different indicators that have been taken into account in the reviewed studies to investigate thermal comfort. These indicators can also be assessed for different seasons, independently. In the work published by Carlucci et al. [38], the percentages of dissatisfied people in summer and winter were optimized as two independent objectives, using the MOO approach. In another study [30], the operative air temperature was considered as the thermal comfort-describing objective function. Based on the definition, the operative air temperature is dependent on the season. It means that in the cooling and heating periods, it should be minimized and maximized, respectively.

Economic Benefit
In the reviewed studies, the optimum solution for this aspect has been achieved by optimizing nine different indicators imposed on both SOO and MOO. Among all these indicators mentioned in Figure 7, life cycle cost has been the most optimized. In the process of evaluating the life cycle cost, the significance of minor costs such as water cost might be disregarded. To avoid that, Sohani et al. [55] considered operating costs and water costs separately.  In the reviewed studies, the optimum solution for this aspect has been achieved by optimizing nine different indicators imposed on both SOO and MOO. Among all these indicators mentioned in Figure 7, life cycle cost has been the most optimized. In the process of evaluating the life cycle cost, the significance of minor costs such as water cost might be disregarded. To avoid that, Sohani et al. [55] considered operating costs and water costs separately.

Visual Comfort
Despite the importance of visual comfort to both occupants' behavior and energy use, only five indicators describing this aspect have been considered in the reviewed studies. These indicators are introduced in Figure 8. In the research done by Mangkuto et al. [28], other metrics such as daylight factor, uniformity, and daylight glare probability have been taken into account as the constraints imposed on the SOO.

Environmental Impact
The growing concern for the environmental impacts of buildings has built a strong urge in researchers to consider this aspect in the optimization studies. Figure 9 shows the four indicators used in the studies we reviewed. It should be noted that there is a huge difference between carbon dioxide emissions and the equivalent carbon dioxide emissions, as two of the four indicators that describe the environmental impact. In the equivalent carbon dioxide emissions, unlike carbon dioxide emissions, other types of emissions besides carbon dioxide have been also taken into account.

Environmental Impact
The growing concern for the environmental impacts of buildings has built a strong urge in researchers to consider this aspect in the optimization studies. Figure 9 shows the four indicators used in the studies we reviewed. It should be noted that there is a huge difference between carbon dioxide emissions and the equivalent carbon dioxide emissions, as two of the four indicators that describe the environmental impact. In the equivalent carbon dioxide emissions, unlike carbon dioxide emissions, other types of emissions besides carbon dioxide have been also taken into account.

Others
Here are the four other aspects that have been rarely studied in the reviewed investigations:

Others
Here are the four other aspects that have been rarely studied in the reviewed investigations: Artwork preservation risk; The indicators that have been used to optimize these aspects are introduced in Figure 10. Shape, artwork preservation risk, and aesthetic perception are well defined aspects in architecture; however, water consumption is popularly used in energy engineering. Zhang et al. [40] presented a three-objective optimization method to enhance the shape of a free-form building by maximizing solar radiation gain and shape efficiency and simultaneously minimizing the shape coefficient. Moreover, artwork perseveration risk is an important aspect that should be considered where the damage to sensitive objects is needed to be decreased [71]. Light, for example, can cause damage to artifacts, but it is critical for displaying them in museums; thus, an optimal solution should be presented [71]. In the study done by Schito et al. [52], artwork preservation risk was promoted by evaluating a lifetime multiplier to avoid artwork degradation; and an Italian museum was simulated as the case study where assessing artwork preservation risk is more effective.
Furthermore, reviewing a very recent study [57] that considered aesthetic perception as a qualitative aspect and changed it into a measurable goal has opened up a new perspective for future investigations. Additionally, Sohani et al. [72] optimized the water consumed during a year in a residential building.

Summary Report
Based on the review conducted, these different ranges of improvements have been achieved for each building aspect: • E.C has been reduced in the range of 1.6% [67] to 60.1% [65] with an average of 26.13%. • T.C has been improved in the rage of 1.5% [37] to 60.0% [52] with an average of 25.61%. • E.B has been enhanced in the range of 4.6-39.56% [54] with an average of 24.0%. • V.C has been increased in the range of 15.0-63.0% [45] with an average of 35.0%.
It should be underlined that these wide ranges were attributed to case study factors (function and location), optimization approaches, and key parameters considered (decision variables, objective function, and constraints), which are all investigated in different parts of this review. Moreover, since A.P is a qualitative aspect, it was not possible to report its enhancement in a numerical format.  Moreover, artwork perseveration risk is an important aspect that should be considered where the damage to sensitive objects is needed to be decreased [71]. Light, for example, can cause damage to artifacts, but it is critical for displaying them in museums; thus, an optimal solution should be presented [71]. In the study done by Schito et al. [52], artwork preservation risk was promoted by evaluating a lifetime multiplier to avoid artwork degradation; and an Italian museum was simulated as the case study where assessing artwork preservation risk is more effective.
Furthermore, reviewing a very recent study [57] that considered aesthetic perception as a qualitative aspect and changed it into a measurable goal has opened up a new perspective for future investigations. Additionally, Sohani et al. [72] optimized the water consumed during a year in a residential building.

Summary Report
Based on the review conducted, these different ranges of improvements have been achieved for each building aspect: • E.C has been reduced in the range of 1.6% [67] to 60.1% [65] with an average of 26.13%. • T.C has been improved in the rage of 1.5% [37] to 60.0% [52] with an average of 25.61%. • E.B has been enhanced in the range of 4.6-39.56% [54] with an average of 24.0%. • V.C has been increased in the range of 15.0-63.0% [45] with an average of 35.0%.
It should be underlined that these wide ranges were attributed to case study factors (function and location), optimization approaches, and key parameters considered (decision variables, objective function, and constraints), which are all investigated in different parts of this review. Moreover, since A.P is a qualitative aspect, it was not possible to report its enhancement in a numerical format.

Decision Variables
In the simulation-based optimization, achieving the best solution is done by adjusting decision variables [73][74][75]. The decision variables are chosen among a group of parameters that affect the value of each objective function; they are called effective parameters [76]. In general, the decision variables reported in Table 4 are classified into two groups: architectural and mechanical. It should be noted that, in order to find the highest possible performance enhancement in the optimization, the decision variables from both groups should be taken into account.

Constraints
According to the limitations that come from technical or economic issues, some constraints are usually imposed on the optimization problem [77][78][79]. Constraints have been considered in 50% of the core literature. Technically, constraints are sorted out into two groups, equality and inequality [80][81][82]. Equality constraints are those that bind the optimization to satisfy the equations. In contrast, inequality constraints are not enforced to be at their limits [83][84][85]. Due to the computational difficulties caused by employing equality constraints, the constraints are usually considered in the form of inequality.
In some studies, several aspects that are mentioned in Section 4.1 have been taken into account as the constraints. As it was described before, this usually happens to reduce the number of objective functions and subsequently simplify the optimization process. For instance, Ascione et al. [60], Gadelhak and Lang [41], and Li et al. [33], have imposed thermal comfort, visual comfort, and energy consumption constraints, respectively. It should be underlined that the range of the decision variables (called as bound) has not been considered among the constraints, which are reported in Table 5.

The Considered Case Studies
In order to show the application of the proposed multi-objective optimization procedure, a case study has been usually considered in each investigation. The case study is a parameter which has substantial impacts on the values of objective functions and decision variables in the optimal condition, and it also might lead to adding or removing a number of objective functions, decision variables, and constraints. Table 4. Decision variables which have been considered in the core literature.

Study Decision Variables
Abdallah and El-Rayes [27] • Baglivo et al. [30] • Thermal characteristics affect the building load • Glazing optical properties • Windows orientation and extension • Shading devices operation and typology • Thermo-physical properties of external walls, roof, and floor Ascione et al. [39] • Solar absorptance and infrared emittance of the external plastering • The thermal insulant thickness • Brick thickness and density • Windows thermal transmittance Zhang et al. [40] • The curve and the surface control-point coordinates. Each of them is made up of X, Y and Z coordinates.

Study Decision Variables
Grygierek and Ferdyn-Grygierek [51] •  In each optimization project, two factors about the case study have to be defined, including its function and location. As it is shown in Table 6, 13 different functions and a variety of locations have been taken into account in the core literature. These different functions and the number of papers in which each one has been studied are presented in Figure 11.
Delgarm et al. [67] [70] Office West Lafayette in Indiana Figure 11. Different functions which have been considered as the case studies in the core literature in addition to the number of papers in which each one has been studied.
As two examples of the mentioned point about the impacts of the function and location of the case study on the selection of the objective functions, the investigations done by Schito et al. [52] and Zhang et al. [45] are considered, respectively. Schito et al. [52]  As two examples of the mentioned point about the impacts of the function and location of the case study on the selection of the objective functions, the investigations done by Schito et al. [52] and Zhang et al. [45] are considered, respectively. Schito et al. [52] chose a museum as the case study, which resulted in adding artwork preservation risk as one of the objective functions. In addition, considering the case study in Tianjin in China, Zhang et al. [45] eliminated the energy consumption for cooling because of its small portion of the total energy demand in the cold climate of China compared to the heating and lighting energy demands.
In order to provide more extensive insights, the graphical representation of the frequency of objective functions is given in the tree map format in Figure 12. The branches in this figure demonstrate a hierarchy view of the considered building functions in different colors. Moreover, the frequency of the building aspects in each of these functions is illustrated in the form of sub-branches. chose a museum as the case study, which resulted in adding artwork preservation risk as one of the objective functions. In addition, considering the case study in Tianjin in China, Zhang et al. [45] eliminated the energy consumption for cooling because of its small portion of the total energy demand in the cold climate of China compared to the heating and lighting energy demands.
In order to provide more extensive insights, the graphical representation of the frequency of objective functions is given in the tree map format in Figure 12. The branches in this figure demonstrate a hierarchy view of the considered building functions in different colors. Moreover, the frequency of the building aspects in each of these functions is illustrated in the form of sub-branches.

Optimization Algorithm and Simulation Software
Based on the type of optimization approach, i.e., either SOO or MOO, different algorithms have been used to acquire the optimum solution. The optimization algorithm and the software which have been used in each study are shown in Table 7. For SOO, the genetic algorithm is the most dominant method, whereas the non-dominated sorting genetic algorithm II (NSGA-II) has been the mostly-used in the MOO. Both SOO and MOO have

Optimization Algorithm and Simulation Software
Based on the type of optimization approach, i.e., either SOO or MOO, different algorithms have been used to acquire the optimum solution. The optimization algorithm and the software which have been used in each study are shown in Table 7. For SOO, the genetic algorithm is the most dominant method, whereas the non-dominated sorting genetic algorithm II (NSGA-II) has been the mostly-used in the MOO. Both SOO and MOO have been usually done using MATLAB. Table 7. The optimization algorithms and the software which have been used in the core literature.

Study
Optimization Algorithm Software

Ferdyn-Grygierek and
Grygierek [29] Genetic   For the simulation of the building, EnergyPlus has been the favorite software in the reviewed investigations. EnergyPlus and OpenStudio, which is used as its graphical user interface, are both open-source software programs, and that is a big advantage of them. Moreover, EnergyPlus has the potential of being easily coupled with MATLAB. In addition to EnergyPlus, Rhino has been increasingly used in recent studies. In fact, its user-friendly environment accounted for its popularity among researchers, although it is not open-source. Furthermore, among all the software programs that have been used in the literature, eQuest, Radiance, and some of Rhino's plugins, including Ladybug and Honeybee, are free to use.
Software programs in the future could be promoted by taking the following items into account to become more helpful:

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Using artificial intelligence tools to provide predictions from changes in occupants' behavior and climate change in the future years of building life. • Adding more powerful economic databases for better evaluation of the building from this point of view. • Providing "tagging" possibility for each project done by an individual in a way that if wanted, could enable the tags to be shared on an online database with other people. In this way, researchers will have better interactions together.

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Applying the virtual reality to get the chance of understanding the graphical issues related to works in a much more perfect way.

Conclusions
In order to provide a new perspective into the literature, the studies that have been conducted to optimize the building performance were reviewed from different viewpoints. The core literature consists of 44 recent studies that were investigated in detail and all the key parameters involved in the optimization procedure were described individually. The review showed that there is a strong connection among these parameters. Moreover, selection of such parameters in the optimization should be done based on the function and location of the case study, and the requirements of the experts who are involved in the project practically. In addition, it is found that EnergyPlus and MATLAB have been the most-used software programs for building simulation and optimization, respectively. Among the nine various aspects that have been considered in the reviewed studies, energy consumption has been taken into account as the objective function more than others, accounting for 38.6%. Thermal comfort and economic benefits with shares of 22.7% and 17% are the second and third mostly optimized aspects, respectively. Figure 13 demonstrates a graphical view of the conclusion.
Among the nine various aspects that have been considered in the reviewed studies, energy consumption has been taken into account as the objective function more than others, accounting for 38.6%. Thermal comfort and economic benefits with shares of 22.7% and 17% are the second and third mostly optimized aspects, respectively. Figure 13 demonstrates a graphical view of the conclusion. In addition, based on the conducted review, a number of open questions could be identified, which are:

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How could the policy makers help to put the results of BPO into practice for a town, a city, or a country? • How could changing the occupants' behavior could affect the optimum values of decision variables and objective functions? • Could some dimensionless numbers be defined as the decision variables and objective functions to reach a general BPO method and provide the possibility of better comparisons for various buildings? • Would it be possible to find an updated procedure for BPO in which different buildings are optimized altogether? How much further improvement will be achieved under that condition? • Could the current BPO procedure be modified to provide plans for adding renewable energy resources? • How many changes will be made to the results of BPO by the future changes in the climate, buildings design techniques, and the employed masonry materials?
Moreover, as observed, in a large number of the studies, objective functions, decision variables, and constraints have not been selected comprehensively. For instance, the researchers who have a background in architecture have not considered the objective functions, decision variables, or constraints from energy or mechanical sides and vice versa. The reported information of this review will help the future researchers to avoid such issues.
Furthermore, the following items can be suggested based on the conducted literature review for future investigations: In addition, based on the conducted review, a number of open questions could be identified, which are:

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How could the policy makers help to put the results of BPO into practice for a town, a city, or a country? • How could changing the occupants' behavior could affect the optimum values of decision variables and objective functions? • Could some dimensionless numbers be defined as the decision variables and objective functions to reach a general BPO method and provide the possibility of better comparisons for various buildings? • Would it be possible to find an updated procedure for BPO in which different buildings are optimized altogether? How much further improvement will be achieved under that condition? • Could the current BPO procedure be modified to provide plans for adding renewable energy resources? • How many changes will be made to the results of BPO by the future changes in the climate, buildings design techniques, and the employed masonry materials?
Moreover, as observed, in a large number of the studies, objective functions, decision variables, and constraints have not been selected comprehensively. For instance, the researchers who have a background in architecture have not considered the objective functions, decision variables, or constraints from energy or mechanical sides and vice versa. The reported information of this review will help the future researchers to avoid such issues.
Furthermore, the following items can be suggested based on the conducted literature review for future investigations:

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Conducting multi-objective optimization in which more aspects from different sides are taken into account; • Performing multi-objective optimization by considering the objective functions based on the application and the climatic zone; • Combining the efficient software programs and algorithms to have more effective and faster calculations; • Selecting the case studies in which the multi-objective optimization has been done less often, and taking the advantage of BPO for them; • Identifying the aspects which have not been usually optimized in each application and considering them; • Studying the impacts of different strategies for giving incentives to implement the results of BPO; • Taking advantage of new optimization techniques like dynamic multi-objective optimization to provide a better outcome.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.