An Integer Linear Programming approach to minimize the cost of the refurbishment of a façade to improve the energy efficiency of a building

Abstract

[EN] Buildings account 40% of the EU's total energy consumption. Therefore, they represent a key potential source of energy savings to fight, among others, against climate change. Furthermore, around 54% of the buildings in Spain date back before 1980, when no thermal regulation was available. The refurbishment of a façade of an old building is usually the most effective way to improve its energy efficiency, by adding layers to the external envelope in order to reduce its thermal transmittance. This paper deals with the problem of minimizing costs for the thermal refurbishment of a façade with thickness and thermal ransmittance bounds and with an intervention both on the opaque part (wall) and the transparent part (windows). Among thousands, even millions of combinations of materials and thicknesses for the different layers to be added to the opaque part, types of frame, and combinations of glasses and air chambers for the transparent part, the aim is to choose the one that minimizes the cost without violating any restriction imposed to the thermal refurbishment, in particular the current energy efficiency regulations in the zone. To optimally solve this problem, it will be modelled as an Integer Linear Programming problem with binary variables. The case study will be Building 1B of the School for Building Engineering of the Polytechnic University of Valencia, Spain. It was built in the late 1960s and has had a very inefficient energy consumption record. The optimal solution will be found among more than 6 million feasible solutions.