## 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. [PERSON] et al. [3] provided a comprehensive review of unconventional sustainable building insulation materials, shedding light on natural or recycled options that are not widely commercial. 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. [PERSON] and [PERSON] [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. [PERSON] [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. [PERSON] 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. [PERSON] 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. [PERSON] et al. [8] examined the embodied carbon dioxide emissions within China's building industry.