Multi-Objective Optimization of Building Design Parameters for Cost Reduction and CO₂ Emission Control Using Four Different Algorithms

Abstract

Thermal insulation applications on the exterior facades of buildings have been the subject of numerous studies from the past to the present. Some of these studies focus on the cost reduction effect of insulation, while others emphasize its ecological benefits. In this study, multi-objective optimization, the objectives of which are minimum cost and minimum CO₂ emission, has been carried out with the NSGA-II method. In emission calculations, in addition to fuel-related emissions, the carbon footprint of all materials comprising the wall has also been included. The multi-objective optimization study examined four design variables: wall thickness, wall material (light concrete, reinforced concrete, and brick), insulation material (expanded polystyrene, extruded polystyrene, mineral wool, and polyurethane foam), and heating source (natural gas, electricity, fuel oil). Analyses have been carried out for four cities (Osmaniye, Bursa, Isparta, and Erzurum), which are located in different climatic regions, and considering solar radiation effects. An existing building has been taken as the base case scenario, and the study has determined the improvements in the total cost and the amount of CO₂ released into the environment when the appropriate insulation material, insulation thickness, wall material, and heating source identified in the multi-objective optimization study have been used. At the cost-oriented optimum point in the study, the most suitable insulation material was found to be expanded polystyrene, the most suitable wall material was brick, and the most suitable heating source was natural gas. In the CO₂-oriented optimum, in contrast to the cost-oriented approach, optimal results have been obtained when light concrete was selected as the wall material.

1. Introduction

The imperative of energy conservation and carbon footprint reduction in buildings has escalated in tandem with global population growth, rapid technological progress, and elevated living standards. Buildings are significant consumers of energy, accounting for 30–45% of global energy use and one-third of total greenhouse gas emissions [1]. With energy consumption in buildings projected to double by 2050, there will be a substantial increase in greenhouse gas emissions [2]. As can be seen here, insulation applications in residential and service buildings play a significant role in reducing global energy consumption and, consequently, carbon emissions since the majority of heat transfer occurs through the building envelope. Thermal insulation helps conserve energy and reduces the carbon footprint by decreasing the energy requirements in summer and winter conditions.

In the field of building insulation applications, numerous studies have investigated the intricate balance between energy efficiency, cost considerations, and ecological impacts. Early research primarily focused on optimizing insulation thickness with total cost as the primary consideration. However, as sustainability and carbon footprint concerns have gained significance in recent years, studies have increasingly started to incorporate the environmental impacts of insulation applications. Asdrubali et al. [3] provided a comprehensive review of unconventional sustainable building insulation materials, shedding light on natural or recycled options that are not widely commercialized. Their study underscores the importance of exploring alternative materials to enhance the sustainability of building insulation practices. However, they concluded their study by noting numerous challenges must be solved before unconventional sustainable building insulation materials can replace traditional ones. Braulio-Gonzalo and Bovea [4] emphasized the significance of optimizing insulation thickness to achieve energy demand reductions in building envelopes. By integrating life-cycle assessment and life-cycle costing methodologies, they highlighted the need to consider both environmental and economic aspects when selecting insulation materials for building applications. The findings demonstrate that sheep wool and recycled cotton, in addition to the conventionally utilized mineral and glass wool, can be used in the construction sector for their high eco-efficiency compared to the other insulation materials examined. Dylewski [5] conducted a study focused on determining the optimal thermal insulation thicknesses for external walls based on economic and ecological considerations, emphasizing the importance of life-cycle assessment in evaluating insulation materials. Based on their study, it may be preferable to use thicker thermal insulation than the optimum insulation thickness for economic reasons. This yields greater ecological benefits from the investment while maintaining economic advantages. Ali et al. [6] highlighted the critical contribution of the building sector to CO₂ emissions and its environmental ramifications. They discussed the difficulties in reducing CO₂ emissions due to the heavy reliance on non-renewable energy sources and suboptimal building designs. The authors suggested some strategies, such as implementing low-carbon technologies and enforcing stringent policies, to minimize CO₂ emissions during the construction and operation of buildings. López-Ochoa et al. [7] focus on enhancing the energy efficiency of residential buildings in cold Mediterranean regions through the optimization of thermal envelope insulation thicknesses. The research emphasizes the significance of increasing the thermal insulation of the opaque elements of the thermal envelope as a highly effective method for energy refurbishment. Zhu et al. [8] examined the embodied carbon dioxide emissions within China’s building industry. Utilizing a process-based approach alongside a disaggregated input-output model, they estimated the annual embodied carbon dioxide emissions and determined that they constitute a significant share of the total emissions in the sector. Their research underscored the need to address embodied and operational carbon to meet China’s carbon emission targets by 2030. Bharadwaj and Jankovic [9] proposed a self-organized approach to designing building thermal insulation, aiming to achieve energy efficiency standards through innovative insulation practices. Their research visualizes the heat loss field within buildings in three dimensions and suggests creating thermal insulation patterns that adjust in thickness according to the heat loss intensity. They aim to enhance the thermal performance of buildings by customizing the insulation thickness based on the heat loss characteristics of different areas within the structure. In a different context, Li et al. [10] explored low-carbon optimization design for low-temperature granary roof insulation in different ecological grain storage zones in China, highlighting the inclusion of carbon emission costs in economic analysis models. The researchers found the optimum insulation thicknesses of expanded polystyrene (EPS) for different cities, ranging from 2.5 cm to 14.8 cm. Min et al. [11] explored the influence of CO₂ emissions on the energy efficiency of buildings. They analyzed how the construction industry, through its energy consumption and material production, is a major contributor to CO₂ emissions, exacerbating global warming. The study investigated various methods for reducing these emissions, including the use of sustainable materials, energy-efficient building designs, and green technologies. The research highlighted the necessity of lowering both operational and embodied CO₂ emissions to enhance building energy efficiency and support sustainable development initiatives. Er-Rradi et al. [12] conducted an experimental study to enhance the thermal performance of composite materials used in building exteriors by incorporating ecological and locally available wastes. Their results indicated that incorporating wood chips, sawdust, and granular cork into the plaster improves thermal conductivity by approximately 57%, 38%, and 68%, respectively. Wang et al. [13] conducted a study by taking into account the effect of moisture on external wall insulation since the walls of harbor buildings are exposed to moisture throughout the year. According to their study, accounting for moisture effects, using XPS instead of EPS as insulation material increased thermal performance. Stamoulis et al. [14] examined the effect of roof insulation on indoor comfort using a genetic algorithm called Domus 2.0 software. The optimization results indicated that 1-cm thick polyurethane insulation was the optimal choice for the roof, considering the building’s operational characteristics, occupant metabolic rate, clothing thermal resistance, and prevailing weather conditions. When examining the studies conducted so far, it is seen that there are many researchers working on insulation materials [3,4,7,12,13,14]. These studies have investigated not only the appropriate insulation materials but also the thickness of the insulation. Earlier, it has been mentioned that studies on insulation thickness were primarily focused on cost and energy savings [15,16,17]. However, the studies discussed here target not only cost and energy but also ecological improvements. Ali et al. [6] and Zhu et al. [8] have focused solely on ecological impacts and have emphasized strategies for reducing CO₂ in the building sector. On the other hand, various researchers [3,4,7,10,11,18] have considered both cost and CO₂ emissions as objective functions.

Optimization methods are frequently used by researchers to achieve the highest performance of the design created in the field of engineering [19,20,21,22,23]. Recently, the use of multi-objective optimization methods has increased in many different fields of engineering to reveal the most ideal states of design. Albak [24] conducted a multi-objective optimization study to improve the crashworthiness performance of impact-absorbing structures, taking the maximum crash force and specific energy absorption of impact-absorbing structures as objective functions. Wu et al. [25] established a multi-objective optimization model with four design variables: stirring speed, impeller diameter, baffle width, and impeller height to obtain maximum mixing efficiency and minimum energy consumption values in stirred tanks. In recent years, multi-objective optimization methods have started to be used in building insulation. Gao et al. [26] took an office building in Chengdu as an example, and carried out multi-objective optimization of energy-saving measures and operating parameters for building renovation under future climate conditions. Hamooleh et al. [27] carried out multi-objective optimization to improve energy and thermal comfort by using insulation and phase change materials in residential buildings. Alimohamadi and Jahangir [28] studied multi-objective optimization of the energy consumption model using wall insulation, roof insulation, window type, cooling type, and heating type as design variables in order to ensure thermal comfort and reduce costs in a residential building. Researchers have also researched new algorithms to obtain optimum values faster and to obtain better values. Bi et al. [29] used a genetic algorithm method in the two-level principal-agent model for scheduling risk control of an IT outsourcing project. Antonio and Coello [30] presented a cooperative coevolution framework to optimize large-scale multi-objective optimization cases. De Farias and Araújo [31] presented MOEA/D, which uses a metric that detects improvements to determine when to adjust the set of weight vectors in multi-objective evolutionary algorithms (MOEA/D) based on decomposition and a procedure to divide the target space to increase diversity, with updates when needed (MOEA/D-UR). In another work, Liu et al. [32] proposed a decomposition-based MOEA driven by a growing neural network (DEA-GNG) that learns the topological structure of Pareto Fronts.

In conclusion, the studies on energy, cost, and ecological analysis of building insulation applications underscore the importance of optimizing insulation materials and thicknesses to enhance energy efficiency, reduce adverse environmental impact, and achieve sustainable building practices. By considering a range of factors, researchers aim to strike a balance between energy performance, cost-effectiveness, and environmental sustainability in building insulation applications. In this study, optimization is performed with four different multi-objective optimization methods, namely the fast and elitist multi-objective genetic algorithm (NSGA-II), which is one of the most widely used multi-objective optimization algorithms in the literature, and the recently presented methods, the third-generation cooperative coevolutionary differential evolution algorithm (CCGDE3), MOEA/D with update when required (MOEA/D-UR), and a decomposition-based multi-objective evolutionary algorithm guided by growing neural gas (DEA-GNG), and the algorithms are compared. Unlike other studies, optimum conditions have been determined for four different cases such as minimum cost point, minimum CO₂ point, cost-oriented knee point, and CO₂-oriented knee point. Optimum insulation thicknesses that minimize both objective functions (Cost and CO₂) simultaneously have been computed for four different climate zones considering the solar radiation effect. The study on multi-objective optimization investigated four design variables: wall thickness; wall materials including light concrete, reinforced concrete, and brick; insulation materials, such as expanded polystyrene (EPS), extruded polystyrene (XPS), mineral wool (MW), and polyurethane foam (PUR); and heating sources like natural gas, electricity, and fuel oil. Unlike previous studies that primarily focus on fuel-related emissions and insulation material-related emissions, this study includes a detailed analysis of the carbon footprint of all materials used in the wall structure, including insulation material, wall material, and plaster. This provides a more holistic understanding of the environmental impact. This study distinguishes itself by including all operational and embodied emissions, unlike other studies. The application of the NSGA-II method in optimization studies for thermal insulation introduces a novelty to the literature. Lastly, by taking a building’s exterior walls which are designed for thermal insulation as a base case scenario and analyzing the potential cost and emission improvements through optimized insulation strategies, this study offers practical insights that can be directly applied in real-world applications, particularly in diverse climatic conditions.

2. Mathematical Model

2.1. Degree-Day Method Incorporating Solar Radiation Effect

The degree-day method is a fundamental and practical tool for estimating heating and cooling energy demand in buildings. Its simplicity, coupled with its ability to provide valuable insights into energy consumption patterns and climate change impacts, makes it a valuable resource for energy analysis and building design. For these reasons, the degree-day method has been preferred in many studies in the literature [16,33,34,35,36]. This method involves calculating heating degree days (HDD) and cooling degree days (CDD) to assess the energy required for heating and cooling purposes. HDD quantifies the energy needed to heat a building to a comfortable level above a base temperature (T_b), while CDD represents the energy required to cool a building to maintain comfort below a specific threshold temperature [37]. HDD and CDD are calculated by summing the differences between the average temperature of a specific day (T₀) and the base temperature (T_b). A positive difference signifies the need for energy to cool the building, while a negative difference indicates the need for energy to heat the building. A difference of zero means no heating or cooling is required. Equations (1) and (2) can be used to determine the total annual HDD and CDD values during the warmer periods and colder months, respectively.

$$HDD=\sum _{d=1}^{365}(T_b-T_0) for T_b>T_0$$

(1)

$$CDD=\sum _{d=1}^{365}(T_0-T_b) for T_0>T_b$$

(2)

Solar radiation has not been mentioned in this section so far. In order to obtain more accurate results in practical applications, this effect should also be included in the calculations. Therefore, T_sol, which is called solar air temperature, should be used instead of average daily temperature (T₀) in the above equations. Solar air temperature can be determined using the following equation [38].

$${ T}_{sol}=T_0+{\displaystyle \frac{{{\dot{q}}_s\alpha }_s}{h_0}}+{\displaystyle \frac{\epsilon \sigma \left({T_{sky}}^4-{T_0}^4\right)}{h_0}}$$

(3)

In this equation, T₀ represents the daily average temperature value, as mentioned before. Additionally, ${\dot{q}}_s$ is the incident solar radiation, ${\alpha }_s$ is the solar absorptance of the surface, $h_0$ is the combined radiation and convection coefficient, $\epsilon$ is the radiative emission coefficient of the surface, $\sigma$ is the Stefan-Boltzmann constant, and $T_{sky}$ is the sky and surrounding surface temperature [33].

In Equation (3), the second term represents the heat impact from solar exposure on the opaque surface. Here, the incident solar radiation (${\dot{q}}_s$) needs to be determined, comprising reflected, direct, and diffuse solar radiations. This radiation value, which includes reflected, direct, and diffuse solar radiation components, is computed using Equation (4).

$${\dot{q}}_s={\dot{q}}_h\left(1-{\displaystyle \frac{{\dot{q}}_{h,d}}{{\dot{q}}_h}}\right)R_b+{\dot{q}}_h\rho \left({\displaystyle \frac{1-\mathrm{c}\mathrm{o}\mathrm{s}\beta }{2}}\right)+{\dot{q}}_{h,d}\left({\displaystyle \frac{1+\mathrm{c}\mathrm{o}\mathrm{s}\beta }{2}}\right)$$

(4)

Average daily diffuse radiation for the horizontal surface, denoted by the symbol (${\dot{q}}_{h,d}$) in Equation (4), is calculated with the help of Equation (5) [39]. In this formula, ${\dot{q}}_h$ represents the monthly average daily global solar radiation, while ${\dot{q}}_{0,h}$ denotes the monthly average daily extraterrestrial radiation. In addition, the $R_b$ value, which appears in Equation (4), can be calculated by dividing the azimuth angle by the zenith angle as shown in Equation (6). Azimuth angle and zenith angle are crucial parameters in the context of solar energy systems. The azimuth angle refers to the horizontal angle measured clockwise from true north to the direction of the sun. In contrast, zenith angle is the angle between the sun and the vertical, representing the angle of incidence of sunlight on a surface perpendicular to the sun’s rays [40].

$${\dot{q}}_{h,d}={\dot{q}}_h(0.703-{\displaystyle \frac{{\dot{q}}_h}{{\dot{q}}_{0,h}}}0.414-{\displaystyle \frac{{{\dot{q}}_h}^2}{{{\dot{q}}_{0,h}}^2}}0.428)$$

(5)

$$R_b=\mathrm{c}\mathrm{o}\mathrm{s}\theta /\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_z$$

(6)

As a result, HDD and CDD values, including the effect of solar radiation, are obtained using the abovementioned equations.

2.2. Determination of Annual Heat Loss and Gain through Building Walls

To calculate the building’s annual energy consumption, it is essential to determine the heat loss through the exterior walls in winter and the heat gain through the exterior walls in summer. This calculation requires knowledge of the Heating Degree Days (HDD) and Cooling Degree Days (CDD) values, as well as the thermophysical properties and thickness of the wall components and the heat transfer coefficients of both the internal and external environments. In the base case scenario, the wall structure is assumed to consist of 2-cm thick extruded polystyrene (XPS) as the insulation material, 20-cm thick brick as the wall material, and a total of 5-cm thick plaster, with 2.5 cm on both the inside and outside (Figure 1).

Heat loss ($q_{A,H})$through the walls in winter can be calculated using Equation (7), where $R_i$ represents the convective heat resistance on the inside, $R_o$ signifies the convective heat resistance on the outside, $R_w$ denotes the thermal resistance of the uninsulated wall, and $R_{ins}$ stands for the thermal resistance of the insulation material. Convective heat resistance is calculated using the formula $1/h$, where ℎ is the heat transfer coefficient. In the present study, interior and exterior heat transfer coefficients are chosen as 8.29 W/m²K and 28.35 W/m²K, respectively [33,41].

$$q_{A,H}={\displaystyle \frac{\mathrm{86,400} HDD}{\left(R_i+R_o+R_w+R_{ins}\right) }}$$

(7)

The amount of energy required to heat the building ($E_{A,H}$) is determined by dividing the annual heat loss by the efficiency of the heating source ($\eta )$. The efficiency values for each heating source are presented in Table 1 In the base case scenario, the heating source is assumed to be fuel oil.

$$E_{A,H} =q_{A,H}/\eta$$

(8)

With a similar approach, during summer months, heat gain ${(q}_{A,C})$ from the walls is calculated based on CDD with the help of Equation (9). The amount of energy required to cool the building ($E_{A,C}$) is determined by dividing the annual heat gain by the coefficient of cooling system performance (COP). In all scenarios, the cooling source is assumed to be air conditioning.

$$q_{A,C}={\displaystyle \frac{\mathrm{86,400} CDD}{\left(R_i+R_o+R_w+R_{ins}\right) }}$$

(9)

$$E_{A,C} =q_{A,C}/COP$$

(10)

2.3. Economic Assessment and CO₂ Emission Calculations

When calculating the total cost of such an investment, the heating-related fuel cost during the winter months, the cooling-related electricity cost during the summer months, and the insulation cost, depending on the applied thickness, are taken into account. Additionally, to obtain more realistic results, the cost of wall material and plaster, aside from the insulation material, are also considered (see Equation (14)).

The life-cycle cost (LCC) analysis method, which is frequently used in the literature, has been employed in economic analysis. In this method, a term defined as present worth factor (PWF) is used to discount future annual energy costs to present value. The PWF is calculated based on the lifespan of the investment (N), the inflation rate (g), and the interest rate (i) as shown in Equation (11) [33].

$$PWF={\displaystyle \frac{{\left(\frac{1+i}{1+g}\right)}^N-1}{{\left(\frac{i-g}{1+g}\right)\left(\frac{1+i}{1+g}\right)}^N}}$$

(11)

In this study, the inflation rate and interest rate are chosen as 17% and 20%, respectively. These financial parameters are selected based on published data from the Turkish Statistical Institute and the Central Bank of Türkiye [42,43].

The expense associated with applying insulation can be determined by the product of the cost of the insulation material ($C_{ins}$) and the thickness of the insulation ($x$). Similarly, the total cost of plaster is calculated by multiplying its unit price ($C_{plast}$) by its thickness, and the total cost of the wall material is determined by multiplying its unit price ($C_{wall}$) by its thickness. The installation costs, denoted as $C_{inst}$, are considered to be 9 USD/m². In addition to these items, the total cost also includes the energy expenses for heating ($C_{Heat}$) and cooling ($C_{Cool}$), as shown in Equations (12) and (13) [33]. The annual total cost ($C_{T,A}$) can be determined using Equation (14).

$$C_{Heat}={\displaystyle \frac{\mathrm{86,400}HDD{C}_{f}PWF}{\left(\frac{1}{h_i}+\frac{1}{h_o}+\frac{x_{plast}}{k_{plast}}+\frac{x_{wall}}{k_{wall}}+\frac{x_{ins}}{k_{ins}}\right)H_u\eta }}$$

(12)

$$C_{Cool}={\displaystyle \frac{\mathrm{86,400}CDD{C}_{e}PWF}{\left(\frac{1}{h_i}+\frac{1}{h_o}+\frac{x_{plast}}{k_{plast}}+\frac{x_{wall}}{k_{wall}}+\frac{x_{ins}}{k_{ins}}\right)COP}}$$

(13)

$$C_T=C_{ins}{x}_{ins}+C_{plast}{x}_{plast}+C_{wall}{x}_{wall}{+C}_{inst}+C_{Heat}+C_{Cool}$$

(14)

Within these equations, $C_f$ indicates the cost of fuel, while $C_e$ denotes the cost of electricity. The lower heating value of the heating source is represented by $H_u$, and the thermal conductivity of all wall components is symbolized by $k$. Table 1 and

Table 2. Emission factors, physical properties, and prices of wall components [45,46,47,48,49,50].

Wall Components	Emission Factor, f	Density, ρ	Conductivity, k	Price, C
	(kgCO2/kg)	(kg/m3)	(W/mK)	(USD/m3)
Expanded Polystyrene (EPS)	3.51	20	0.036	100
Extruded Polystyrene (XPS)	3.83	30	0.037	150
Mineral Wool (MW)	1.16	55	0.04	130
Polyurethane Foam (PUR)	4.47	40	0.036	200
Plaster	0.36	1800	0.87	90
Light Concrete	0.09	1700	0.71	85
Reinforced Concrete	0.12	2400	2.5	120
Brick	0.31	1200	0.45	45

present the relevant values

Table 1. Emission factors, lower heating values, efficiencies, and prices of heating sources [33,44].

Heating Source	Emission Factor, fh	Lower Heating Value, Hu	Efficiency, η	Price, Cf
	(kgCO2/kWh)		(%)
Natural Gas	0.194	34.526 × 106 J/m3	93	0.327 USD/m3
Electricity	0.588	3.599 × 106 J/kWh	99	0.1059 USD/kWh
Fuel Oil	0.268	40.594 × 106 J/kg	80	0.734 USD/kg

Table 1. Emission factors, lower heating values, efficiencies, and prices of heating sources [33,44].

Heating Source	Emission Factor, fh	Lower Heating Value, Hu	Efficiency, η	Price, Cf
	(kgCO2/kWh)		(%)
Natural Gas	0.194	34.526 × 106 J/m3	93	0.327 USD/m3
Electricity	0.588	3.599 × 106 J/kWh	99	0.1059 USD/kWh
Fuel Oil	0.268	40.594 × 106 J/kg	80	0.734 USD/kg

Another purpose of applying insulation in this study is to reduce carbon dioxide emissions released into the atmosphere. In this context, emissions are divided into two categories: operational and embodied emissions. Operational emissions refer to the CO₂ released into the environment from the fuel consumed during heating and cooling. Embodied emissions are related to the CO₂ released during processes such as production, transportation, and installation of wall materials. This study evaluates the environmental impact of insulation applications by analyzing both operational and embodied emissions. This approach ensures that the results are more comprehensive and realistic.

From Equations (15)–(19), allow for the calculation of annual CO₂ emissions for heating ($M_{{CO}_2,heat}$), cooling ($M_{{CO}_2,cool}$), insulation materials ($M_{{CO}_2,ins}$), wall materials ($M_{{CO}_2,wall}$), and plaster ($M_{{CO}_2,plast}$). Each emission source can be individually determined using these equations. Total amount of CO₂ released to the atmosphere from the building used throughout the year is presented in Equation (20).

$$M_{{CO}_2,ins}={\displaystyle \frac{{\rho }_{ins}{x}_{ins}{f}_{ins}}{N }}$$

(15)

$$M_{{CO}_2,plast}={\displaystyle \frac{{\rho }_{plast}{x}_{plast}{f}_{plast}}{N }}$$

(16)

$$M_{{CO}_2,wall}={\displaystyle \frac{{\rho }_{wall}{x}_{wall}{f}_{wall}}{N }}$$

(17)

$$M_{{CO}_2,heat}={\displaystyle \frac{0.024 HDD{f}_h}{\left(\frac{1}{h_i}+\frac{1}{h_o}+\frac{x_{plast}}{k_{plast}}+\frac{x_{wall}}{k_{wall}}+\frac{x_{ins}}{k_{ins}}\right)\eta }}$$

(18)

$$M_{{CO}_2,cool}={\displaystyle \frac{0.024 CDD{f}_c}{\left(\frac{1}{h_i}+\frac{1}{h_o}+\frac{x_{plast}}{k_{plast}}+\frac{x_{wall}}{k_{wall}}+\frac{x_{ins}}{k_{ins}}\right)COP }}$$

(19)

$$M_{{CO}_2}=M_{{CO}_2,ins}+M_{{CO}_2,plast}+M_{{CO}_2,wall}+M_{{CO}_2,heat}+M_{{CO}_2,cool}$$

(20)

Within these equations, $\rho$ indicates the density of the relevant materials, while $f$denotes the emission factor of heating sources and wall components. Table 1 and Table 2 present the relevant values.

2.4. Multi-Objective Optimization and Knee Point

Due to the increase in carbon emissions, it has become essential to create low-carbon emission designs in building insulation works, as in every field. As with every design, cost is an important element of building insulation. Considering the above information, a multi-objective optimization is carried out in this study, aiming to both reduce carbon emissions and reduce the total cost. In multi-objective optimizations, instead of a single optimum, values that optimize both objectives are obtained. At the same time, when one objective is optimized in the Pareto curve, it can be seen at what levels the other objective can be best. In this way, the optimum range in which the system can operate can be seen with a single optimization.

While the objectives of the multi-objective optimization study carried out in this study are to reduce carbon emissions and total cost, the design variables are four: insulation thickness, insulation material, wall material, and heating type. In these design variables, insulation thickness is defined as a continuous design variable, while other design variables are defined as discrete design variables. Therefore, the multi-objective optimization is given as follows:

$$\left\{\begin{array}{c}\mathrm{Min}\left(C_T, M_{{CO}_2}\right)\\ s.t. \left\{\begin{array}{c}0<Insulation Thickness (m)<0.5\\ Insulation Material \in \left(EPS, XPS, MW, PUR\right)\\ Wall Material\in \left(Light Concrete, Reinforced Concrete, Brick\right)\\ Heating Source\in (Natural Gas, Electricity, Fuel Oil)\end{array}\right.\end{array}\right.$$

(21)

In this study, four different multi-objective optimization methods are examined to determine the optimum points and compare different optimization methods. Multi-objective optimizations are performed in the MATLAB R2023a program via PlatEMO [51]. The first optimization algorithm compared is the fast and elitist multi-objective genetic algorithm (NSGA-II) [52] method, which is one of the most preferred methods. The general flow chart of the NSGA-II method is given in Figure 2. The second method is the third-generation cooperative coevolutionary differential evolution algorithm (CCGDE3) method [30]. Other methods examined in the study are MOEA/D with an update when required (MOEA/D-UR) [31] and a decomposition-based multi-objective evolutionary algorithm guided by growing neural gas (DEA-GNG) [32], which have been introduced to the literature in recent years. While summary information about the NSGA-II method is given below, detailed information about the CCGDE3, MOEA/D-UR, and DEA-GNG methods can be found in the related method reference.

The method first starts with determining the method parameters and then creating the first population. The fitness functions of each alternative are calculated. The fitness values of each individual are calculated, and the individuals are sorted in order of priority (non-dominated sorting). By calculating the crowding distance, diversity among individuals with the same priority is preserved. Parents are selected using selection methods. In this phase, fitness values and crowding distance are considered. New individuals are created by performing crossover and mutation operations on the selected parents. These new individuals create the next generation population. A large population is created by combining the old population and the newly created population. Non-dominated sorting is applied again on the large population. After the large population is sorted, the best individuals are selected when creating a new population. In this selection, diversity is preserved by using crowding distance. Depending on the stopping criterion, the algorithm is terminated when a certain number of generations is reached, or the stopping criterion is met. The final set of population solutions is presented as a Pareto front. For details of the NSGA-II method, the article presented by Deb et al. [52] can be reviewed.

In multi-objective optimizations, all points on the Pareto front are optimum points, as opposed to the single optimum value given by single-objective optimization. In other words, in multi-objective optimizations, the designer can directly see the entire optimum operating state of the model. Here, which point the design will take as optimum depends entirely on the importance the designer attaches to the objectives. While there are subjective situations in which the designer selects a determined value or makes a comparison according to the initial situation in order to select the optimum point, there are also objective selection methods such as knee point. In this study, in determining the optimum points in multi-objective optimization, in addition to selecting separate semi-optimal points for both CO₂ and Cost, the knee point method, which objectively gives the best situation for both CO₂ and cost objectives, is also used. The knee point method is to normalize the values obtained in both objective functions and then calculates the shortest distance to the “utopia point”. The “utopia point” represents the best solution where both objectives are combined. “Knee point” on the Pareto front is calculated with the following formulation [53,54]:

$$\min D=\sqrt{\left({\sum }_{\tau =1}^n{\left({\displaystyle \frac{f_{c\tau }}{\mathrm{m}\mathrm{i}\mathrm{n}(f_{\tau }\left(x\right))}}-1\right)}^2\right)}$$

(22)

where $n$ symbolizes the number of the objective functions, $f_{c\tau }$ indicates the $\tau$th objective value in the $c$th result, and $D$ displays the distance from the knee point to the utopia point.

3. Results and Discussion

According to the Turkish Standards Institution (TS 825) [55], Türkiye is divided into four different climatic zones, as shown in Figure 3. Among these regions, the first zone corresponds to the hottest climate region, while the fourth zone corresponds to the coldest climate region. In the present study, the cities of Osmaniye, Bursa, Isparta, and Erzurum, located in the first, second, third, and fourth zones, respectively, have been chosen to observe the influence of different climatic zones.

As mentioned earlier in the manuscript, the effect of solar radiation has been considered when calculating annual average heating (HDD) and cooling (CDD) degree days values to achieve more realistic results. Figure 4 presents the HDD and CDD values calculated for each province. Figure 4 illustrates that the cities with the highest HDD values, which correlate directly with heating energy requirements, are ranked in descending order: fourth zone, third zone, second zone, and first zone. Conversely, the cities with the highest CDD values, indicating cooling energy demands, are arranged as first zone, second zone, third zone, and fourth zone. The graph clearly demonstrates that the total (heating and cooling) annual energy needs, from greatest to least, are as follows: fourth zone > third zone > second zone > first zone.

As shown in

Table 3. Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone I).

	Insulation Thickness (m)	Insulation Material	Wall Material	Heating Source
Base Case Scenario	0.02	XPS	Brick	Fuel Oil
Optimum Cost	0.0470	EPS	Brick	Natural Gas
Optimum CO2	0.1961	EPS	Light concrete	Natural Gas
Cost-Oriented Knee Point	0.1312	EPS	Brick	Natural Gas
CO2-Oriented Knee Point	0.0790	EPS	Light concrete	Natural Gas

, in the base case scenario, the wall structure consists of 2 cm thick extruded polystyrene (XPS) as the insulation material, and brick as the wall material. The heating source used is fuel oil.

In the following section, multi-objective optimizations for zones are examined. When the Pareto fronts obtained for each zone are examined, it is seen that the four optimization methods overlap. Since the optimum points given in the tables are the same or very close to each other and, therefore, insignificantly low in terms of insulation cases, the examinations are made using the NSGA-II method. In the optimization methods, the population size is selected as 100, while the maximum iteration number is determined as 10,000. Other parameters are taken as the default values of the optimization methods without performing parameter optimization since the same results and the same values or very small differences occurred in all optimization methods.

In order to examine the effects of design variables on the objective functions’ Cost and CO₂, a stepwise analysis is performed. Here, the initial situation is kept constant, and each parameter is changed to examine its effects on the objective functions. When Figure 5 is examined, it is seen that the most negligible impact in terms of cost is in the change of heating source. The most significant effect is seen in insulation thickness and insulation material. When the CO₂ values in Figure 6 are examined, it is seen that the other parameters, except the insulation material, have a similar effect. As in cost, a sharp increase is observed in CO₂ at small values of the insulation material.

In the multi-objective optimization conducted for Zone I, when the value with the minimum cost is chosen as the optimum, an EPS insulation material with a thickness of 4.7 cm should be selected for optimal insulation, brick for the wall, and natural gas for heating. When the value with the minimum emission is chosen as the optimum, an EPS insulation material with a thickness of 19.61 cm should be selected for optimal insulation, light concrete for the wall, and natural gas for heating. Upon examining the Pareto front, it is observed that two distinct curves are formed, as shown in Figure 7. This is because the brick wall structure is more cost-effective, while the light concrete wall structure is more suitable in terms of emissions. In multi-objective optimizations, both subjective choices and objective approaches like the knee point method can be used to select the optimum state. In this study, the optimum points for the two distinct curves mentioned above are found using the knee point approach. In the cost-oriented section, the optimum point found using the knee point method includes an insulation thickness of 13.12 cm, EPS insulation material, brick wall material, and natural gas as the heating source. In the CO₂-oriented section, the optimum point found using the knee point method includes an insulation thickness of 7.9 cm, EPS insulation material, light concrete wall material, and natural gas as the heating source.

As presented in

Table 4. Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone I.

Method	Scenario	CT (USD/m2)	MCO2 (kg/m2)	% CT	% MCO2
	Base Case Scenario	42.60	20.14	-	-
CCGDE3	Optimum Cost	34.27	15.56	20%	23%
	Optimum CO2	52.44	9.18	−23%	54%
MOEA/D-UR	Optimum Cost	34.27	15.55	20%	23%
	Optimum CO2	52.41	9.18	−23%	54%
DEA-GNG	Optimum Cost	34.27	15.55	20%	23%
	Optimum CO2	52.45	9.18	−23%	54%
NSGA-II	Optimum Cost	34.27	15.50	20%	23%
	Optimum CO2	52.45	9.18	−23%	54%
	Cost-Oriented Knee Point	38.84	13.68	9%	32%
	CO2-Oriented Knee Point	43.56	10.17	−2%	50%

, for the base case scenario identified in the study, the total cost is calculated as 42.60 USD/m², and the total CO₂ emission is 20.14 kg/m² for Zone I. In the optimum cost scenario, the total cost has decreased to 34.27 USD/m², while the total CO₂ emission is determined to be 15.50 kg/m². In the optimum CO₂ scenario, although the cost has increased (52.45 USD/m²), a huge improvement is observed in the CO₂ amount (9.18 kg/m²). In the cost-oriented optimum scenario determined using the knee point approach, the total cost has decreased to 38.84 USD/m², and the total CO₂ emission to 13.68 kg/m². In the CO₂-oriented optimum scenario, the total cost has been determined to be 43.56 USD/m², and the total CO₂ emission is 10.17 kg/m².

Table 5. Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone II).

	Insulation Thickness (m)	Insulation Material	Wall Material	Heating Source
Base Case Scenario	0.02	XPS	Brick	Fuel Oil
Optimum Cost	0.0499	EPS	Brick	Natural Gas
Optimum CO2	0.2055	EPS	Light concrete	Natural Gas
Cost-Oriented Knee Point	0.1368	EPS	Brick	Natural Gas
CO2-Oriented Knee Point	0.0829	EPS	Light concrete	Natural Gas

and Figure 8 present the optimum conditions for various objectives for Zone II. When the option with the lowest cost is selected as optimal, an EPS insulation material with a thickness of 4.99 cm should be chosen for insulation, along with brick for the wall and natural gas for heating. Conversely, when the option with the lowest emission is selected as optimal, an EPS insulation material with a thickness of 20.55 cm should be used, paired with light concrete for the wall and natural gas for heating. In the cost-oriented scenario determined by the knee point method, the optimal configuration includes an EPS insulation material with a thickness of 13.68 cm, brick for the wall, and natural gas as the heating source. In the CO₂-oriented scenario identified using the same method, the optimal configuration consists of an EPS insulation material with a thickness of 8.29 cm, light concrete for the wall, and natural gas as the heating source.

As shown in

Table 6. Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone II.

Method	Scenario	CT (USD/m2)	MCO2 (kg/m2)	% CT	% MCO2
	Base Case Scenario	48.45	22.40	-	-
CCGDE3	Optimum Cost	34.84	15.79	28%	30%
	Optimum CO2	53.44	9.31	28%	30%
MOEA/D-UR	Optimum Cost	34.84	15.79	28%	30%
	Optimum CO2	53.44	9.31	28%	30%
DEA-GNG	Optimum Cost	34.84	15.80	28%	30%
	Optimum CO2	53.47	9.31	28%	30%
NSGA-II	Optimum Cost	34.84	15.79	28%	30%
	Optimum CO2	53.47	9.31	−10%	58%
	Cost-Oriented Knee Point	39.51	13.83	18%	38%
	CO2-Oriented Knee Point	44.16	10.36	9%	54%

, for the base case scenario identified in the study, the total cost for Zone II is calculated as 48.45 USD/m², with a total CO₂ emission of 22.40 kg/m². In the optimum cost scenario, the total cost decreases to 34.84 USD/m², while the total CO₂ emission is reduced to 15.79 kg/m². In the optimum CO₂ scenario, although the cost has slightly increased to 53.47 USD/m², the primary improvement is in the CO₂ emissions, which drop to 9.31 kg/m². In the cost-oriented optimum scenario identified using the knee point method, the total cost is reduced to 39.51 USD/m², and the total CO₂ emission to 13.83 kg/m². In the CO₂-oriented optimum scenario, the total cost is determined to be 44.16 USD/m², with a total CO₂ emission of 10.36 kg/m².

It is understood that for the same objective functions, only the insulation thickness varies, while the wall material, heating type, and insulation material remain unchanged. In the analyses conducted for Zone III, the optimum conditions determined for Zones I and II remain consistent. For Zone III, the insulation thicknesses for the optimum cost, optimum CO₂, cost-oriented knee point, and CO₂-oriented knee point scenarios are determined to be 5.6 cm, 22.45 cm, 14.93 cm, and 9.06 cm, respectively (see

Table 7. Optimum insulation thickness, insulation material, wall material and heating source for different objective functions (Zone III).

	Insulation Thickness (m)	Insulation Material	Wall Material	Heating Source
Base Case Scenario	0.02	XPS	Brick	Fuel Oil
Optimum Cost	0.056	EPS	Brick	Natural Gas
Optimum CO2	0.2245	EPS	Light concrete	Natural Gas
Cost-Oriented Knee Point	0.1493	EPS	Brick	Natural Gas
CO2-Oriented Knee Point	0.0906	EPS	Light concrete	Natural Gas

and Figure 9).

According to

Table 8. Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone III.

Method	Scenario	CT (USD/m2)	MCO2 (kg/m2)	% CT	% MCO2
	Base Case Scenario	54.52	25.10	-	-
CCGDE3	Optimum Cost	36.07	16.26	34%	35%
	Optimum CO2	55.62	9.58	−2%	62%
MOEA/D-UR	Optimum Cost	36.07	16.24	34%	35%
	Optimum CO2	55.50	9.58	−2%	62%
DEA-GNG	Optimum Cost	36.07	16.24	34%	35%
	Optimum CO2	55.57	9.58	−2%	62%
NSGA-II	Optimum Cost	36.07	16.25	34%	35%
	Optimum CO2	55.57	9.58	−2%	62%
	Cost-Oriented Knee Point	41.10	14.11	25%	44%
	CO2-Oriented Knee Point	45.42	10.74	17%	57%

, the base case scenario for Zone III yields a total cost of 54.52 USD/m² and a CO₂ emission of 25.10 kg/m². When optimizing for cost, a significant improvement is seen in the total cost, which drops to 36.07 USD/m², and CO₂ emissions are reduced to 16.25 kg/m². In the scenario optimized for CO₂, while the cost has slightly increased to 55.57 USD/m², CO₂ emissions fall to 9.58 kg/m², which is a substantial reduction. For the cost-oriented optimum scenario, the total cost is further reduced to 41.10 USD/m², with CO₂ emissions at 14.11 kg/m². For the CO₂-oriented optimum scenario, the total cost is 45.42 USD/m², and CO₂ emissions are 10.74 kg/m².

As mentioned before, for the same objective functions, only the insulation thickness changes, while the other design variables remain unchanged. In the analyses conducted for Zone IV, the optimum conditions determined for other zones remain constant. For Zone IV, the insulation thicknesses for the optimum cost, optimum CO₂, cost-oriented knee point, and CO₂-oriented knee point scenarios are determined to be 7.97 cm, 29.71 cm, 19.92 cm, and 12.98 cm, respectively (see

Table 9. Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone IV).

	Insulation Thickness (m)	Insulation Material	Wall Material	Heating Source
Base Case Scenario	0.02	XPS	Brick	Fuel Oil
Optimum Cost	0.0797	EPS	Brick	Natural Gas
Optimum CO2	0.2971	EPS	Light concrete	Natural Gas
Cost-Oriented Knee Point	0.1992	EPS	Brick	Natural Gas
CO2-Oriented Knee Point	0.1298	EPS	Light concrete	Natural Gas

and Figure 10).

As shown in

Table 10. Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone IV.

Method	Scenario	CT (USD/m2)	MCO2 (kg/m2)	% CT	% MCO2
	Base Case Scenario	79.66	36.58	-	-
CCGDE3	Optimum Cost	40.80	17.97	49%	51%
	Optimum CO2	63.64	10.60	20%	71%
MOEA/D-UR	Optimum Cost	40.80	17.97	49%	51%
	Optimum CO2	63.52	10.60	20%	71%
DEA-GNG	Optimum Cost	40.80	17.97	49%	51%
	Optimum CO2	63.84	10.60	20%	71%
NSGA-II	Optimum Cost	40.80	17.97	49%	51%
	Optimum CO2	63.60	10.60	20%	71%
	Cost-Oriented Knee Point	47.21	15.20	41%	58%
	CO2-Oriented Knee Point	50.71	11.93	36%	67%

, the base case scenario identified in the study for Zone IV has a total cost of 79.66 USD/m² and a total CO₂ emission of 36.58 kg/m². In the optimum cost scenario, the total cost has decreased to 40.80 USD/m², while the total CO₂ emission is determined to be 17.97 kg/m². In the optimum CO₂ scenario, although the cost has slightly decreased to 63.60 USD/m², the main improvement is observed in the CO₂ amount, which is 10.60 kg/m². In the cost-oriented optimum scenario determined using the knee point approach, the total cost has decreased to 47.21 USD/m², and the total CO₂ emission to 15.20 kg/m². In the CO₂-oriented optimum scenario, the total cost has been determined to be 50.71 USD/m², and the total CO₂ emission is 11.93 kg/m².

The degree-day method, mentioned before, is a widely accepted and well-established approach for estimating energy consumption in buildings. Annual energy consumption is analyzed to determine the optimal insulation thickness. In order to validate the energy consumption calculation model, this study compares the insulation thicknesses that minimize costs with those determined in other studies examining the city of Erzurum, which is also analyzed in this research. The comparative results are presented in

Table 11. Comparative analysis with other studies.

Study	Erzurum xopt (cm)
Present Study	7.97
Sisman et al. [56]	8.0
Ucar [57]	7.39
Ozbek et al. [58]	8.0
Kurekci [34]	7.8

. It can be observed that the results are close to each other. The slight differences may be due to the use of different fuel types, different insulation materials, or periodic changes in financial parameters.

Figure 11 shows the percentage improvements in cost (%C_T) and emissions (%MCO₂) when insulation is applied, based on the optimum insulation thicknesses obtained for four different objective functions across four different climate zones.

In the optimum cost scenario, the improvements in cost and CO₂ emissions are more balanced across all zones. Zone IV leads with the highest improvements, followed closely by Zone III, Zone II, and Zone I, which have relatively similar performance. This indicates that the optimum cost scenario leads to significant gains in both cost and CO₂ emissions, with consistent results across different climate zones. The optimum CO₂ scenario focuses on minimizing CO₂ emissions. Zone IV demonstrates the highest CO₂ reduction, exceeding 70%, while the cost reduction is around 20%. Zone I shows a deterioration in cost but still achieves a substantial CO₂ reduction of 54%.

Under the Cost-Oriented Multi Objective scenario there is a noticeable improvement in both cost and CO₂ emissions across all zones. Zone IV exhibits the biggest improvement in cost reduction, reaching close to 60%, while its CO₂ emission improvement is also significant, nearing 41%. Zone I has the lowest percentage improvements in both cost and CO₂ emissions compared to other zones, but the improvements are still meaningful. In the CO₂-Oriented Multi-Objective scenario, Zone IV exhibits the highest CO₂ improvement at around 67%, with cost improvement slightly lower at around 36%. Zone III and Zone II show similar patterns with high CO₂ improvements and significant cost reductions. Zone I has the lowest improvements in CO₂ emissions, and again, a deterioration is observed in cost.

Across all optimization objectives, Zone IV consistently shows the highest percentage improvements in both cost and CO₂ emissions, indicating the effectiveness of optimization strategies in this zone. Zones II and III also perform well, with significant gains in CO₂ emissions, though slightly lower than Zone IV. When the analyses are conducted based on the optimum CO₂ scenario, a deterioration in costs is observed in all Zones except Zone IV. The findings suggest that climate zone-specific strategies may be necessary to maximize benefits, especially for relatively warm zones like Zone IV, which shows the most significant potential for improvement.

Figure 12 illustrates the variation in cost components for different insulation thicknesses in the hottest (Zone I) and coldest (Zone IV) climate zones. In Zone I, the heating cost ($C_{heat}$) is initially significant but gradually decreases as insulation thickness increases, reflecting reduced energy consumption for heating. The cooling cost ($C_{cool}$) is relatively high at lower insulation thicknesses and shows a slight decrease as insulation thickness increases, indicating reduced energy use for cooling. The heating cost ($C_{heat}$) is significantly higher in the coldest zone compared to the hottest zone, especially at lower insulation thicknesses. This cost decreases substantially as insulation thickness increases, demonstrating the effectiveness of insulation in reducing heating demand. In Zone IV, the cooling cost ($C_{cool}$) is relatively lower due to the colder climate, and it shows minimal change with increasing insulation thickness. The overall pattern indicates that when increasing the insulation thickness, significant savings in heating costs can be achieved in colder climates, making it a cost-effective strategy. Figure 12 highlights the trade-off between the initial costs of insulation, plaster, and wall materials and the savings in heating and cooling costs achieved with increased insulation thickness. In Zone I, cooling cost savings are more pronounced, while in Zone IV, heating cost savings are more significant.

Figure 13 illustrates the variation in emission components for different insulation thicknesses in the hottest (Zone I) and coldest (Zone IV) climate zones. In Zone I, initially, emissions from heating ($M_{{CO}_2,heat}$) and cooling ($M_{{CO}_2,cool}$) are substantial but decrease sharply as insulation thickness increases, indicating reduced energy consumption for heating and cooling. Emissions from heating ($M_{{CO}_2,heat}$) are significantly higher in the coldest zone compared to the hottest zone, especially at lower insulation thicknesses. These emissions decrease substantially as insulation thickness increases, demonstrating the effectiveness of insulation in reducing heating demand. Emissions from cooling ($M_{{CO}_2,cool}$) are relatively low in Zone IV due to the colder climate and show minimal change with increasing insulation thickness. The overall trend shows that when insulation thickness rises, substantial reductions in heating emissions can be realized in colder climates, making it an environmentally advantageous approach. Figure 13 shows the balance between initial emissions from insulation, plaster, and wall materials, and the savings in heating and cooling emissions with increased insulation thickness. In the hottest zone, the focus is on reducing cooling emissions, while in the coldest zone, reducing heating emissions is more significant.

4. Conclusions

In this study, multi-objective optimization, whose objectives are minimum cost and minimum CO₂ emission, has been carried out with the NSGA-II method.

The analysis results indicate that for Zone I, the optimal insulation thickness for minimizing cost is 4.7 cm, while the optimal thickness for minimizing CO₂ emissions is 19.61 cm. In Zone II, the optimal cost is achieved with an insulation thickness of 4.99 cm, and the optimal CO₂ emissions occur at a thickness of 20.55 cm. For Zone III, the lowest cost is found with an insulation thickness of 5.6 cm, whereas the lowest CO₂ emissions are achieved at 22.45 cm. Lastly, in Zone IV, the optimal cost corresponds to an insulation thickness of 7.97 cm, and the optimal CO₂ emissions are attained at 29.71 cm.

In the multi-objective optimization analysis, the knee point method is used to determine the optimal insulation thicknesses for cost-oriented and CO₂-oriented approaches. For Zone I, the optimal thicknesses are 13.12 cm for the cost-oriented approach and 7.90 cm for the CO₂-oriented approach. In Zone II, the optimal thicknesses are 13.68 cm and 8.29 cm for the cost-oriented and CO₂-oriented approaches, respectively. For Zone III, the optimal insulation thicknesses are found to be 14.93 cm for the cost-oriented approach and 9.06 cm for the CO₂-oriented approach. Finally, in Zone IV, the optimal thicknesses are 19.92 cm for the cost-oriented approach and 12.98 cm for the CO₂-oriented approach.

When the primary objective is to reduce costs, EPS insulation material should be selected, with brick as the wall material and natural gas as the heating source. Conversely, when the main goal is to minimize CO₂ emissions, EPS insulation material should still be used but paired with light concrete for the wall material and natural gas for heating.

Across all optimization objectives, Zone IV consistently shows the highest percentage improvements in both cost and CO₂ emissions. However, when the analyses are conducted based on the optimum CO₂ scenario, a deterioration in costs is observed in all Zones except Zone IV. While a deterioration in costs of up to 23% has been observed in certain Zones and conditions, improvements of up to 49% have been seen in other cases. Besides, improvement in emissions ranges from 23% to 71%. These insights emphasize the importance of climate-specific insulation strategies to maximize environmental and economic benefits.

When examining the components that make up the total cost and total emissions individually, it is found that increasing insulation thickness can lead to significant heating cost savings in colder climates. It is also observed that in Zone I, cooling cost savings are more pronounced, while in Zone IV, heating cost savings are more significant. Since emissions released into the atmosphere are related to the amount of energy used, it is understood that increasing insulation thickness can substantially reduce heating emissions in colder climates, making it both an economically and environmentally advantageous approach.

Finally, four different multi-objective optimization methods (NSGA-II, CCGDE3, MOEA/D-UR, and DEA-GNG) are examined to determine the optimum points and compare different optimization methods. All four methods give very similar or the same results. It has been determined that all algorithms are highly effective for achieving optimal results in insulation applications that require the simultaneous optimization of two different objective functions.