Development of Methodology for Estimation of Energy-Efficient Building Renovation Using Application of MINLP-Optimized Timber–Glass Upgrade Modules

Vertical addition to already-existing structures is an approach to energy-efficient building renovation. It presents an opportunity for the densification of built-up areas and the construction of new usable spaces. While many studies have dealt with the subject of renovating buildings with a focus on energy efficiency, far fewer studies have specifically examined the potential of vertically extending existing buildings, an approach which could be introduced in new sustainable building policies. The objective of this study is to redevelop optimal timber–glass upgrade modules, considering the ideal proportions of glazing for all cardinal directions, by using discrete Mixed-Integer Non-Linear Programming optimization. The novelty of the suggested method resides in the synchronous optimization of the upgrade modules’ daylighting and energy-efficiency performance, resulting in the creation of optimization methods that can determine the optimal glazing proportions for all cardinal directions and incorporate rational design and window measurement. The impact of the developed Mixed-Integer Non-Linear Programming-optimized upgrade modules is compared to previously designed optimized upgrade modules. Finally, a methodology for estimating the energy efficiency of building renovations incorporating vertical additions using the timber–glass upgrade modules was developed, supporting the quick assessment of the reduction in hybrid buildings’ energy consumption for heating and cooling according to boundary conditions, presuming that they undergo the suggested renovations. The findings are applicable (not exclusively) to Slovenia’s residential building stock, which makes up around 20% of the country’s current housing stock and was mainly constructed between 1946 and 1970. This offers a substantial opportunity to improve the overall sustainability and energy efficiency of the country’s housing stock. The proposed approach offers a holistic solution to drive sustainable development in the built environment by incorporating all three pillars of sustainability (environmental, social, and economic).