## 1 Introduction
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. [PERSON] and [PERSON] [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, [PERSON] 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. [PERSON] 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. [PERSON] 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, saw-dust, and granular cork into the plaster improves thermal conductivity by approximately 57%, 38%, and 68%, respectively. [PERSON] 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. [PERSON] 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. [PERSON] et al. [6] and [PERSON] et al. [8] have focused solely on ecological impacts and have emphasized strategies for reducing CO\({}_{2}\) in the building sector. On the other hand, various researchers [3; 4; 7; 10; 11; 18] have considered both cost and CO\({}_{2}\) 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].