Mathematical optimisation of location and design of windows by considering energy performance, lighting and privacy of buildings

Purpose: The Middle East and North Africa (MENA) region is known for its extreme weather conditions during Summer. A major determinant of the sustainability of the design of a building is its fenestrations. The purpose of this paper is to explore the problem of designing and locating windows on building facades such that a number of relevant criteria to the MENA region are optimised, including solar heat gain, privacy, daylighting and cost of installation. Design/methodology/approach: A multi-objective optimisation problem is proposed with the focus on capturing the requirements of residential dwellings in the MENA region. Since the problem contains conflicting objectives that need to be optimised, a lexicographic approach is adopted. In order to display the Pareto curve, a bi-objective analysis based on the ε-constraint method is utilised. Findings: The conflicting nature of the proposed problem is indicated via the Pareto optimal solutions yielded. Depending on the preference of criteria adopted in lexicographic optimisation, the location of the windows on the building façade tends to change. The bi-objective analysis indicates the importance of balancing out the daylight factor against each of privacy, solar heat gain and installation cost criteria. Furthermore, an analysis conducted in three major cities in the MENA region highlights the discrepancy in design alternatives generated depending on the local climatic condition. Originality/value: This work proposes a novel mathematical optimisation model which focuses on producing a sustainable design and layout for windows on the facades of residential dwellings located in the MENA region. The proposed model provides designers with guidance through an automated support tool that yields optimised window designs and layout to ensure the sustainability of their designed buildings.