Multi-Criteria Optimization for the Decision Making in Building Envelope Thermal Design

The increase of energy utilization reinforced the need of reducing the primary energy consumption based on fossil fuels and the limitation of carbon dioxide (CO₂) emissions to the atmosphere. Such goals aim at the provision of affordable and generally clean energy for the citizens. However, the final decision making is hard to be achieved, due not only to the multitude variety of such proposed technologies, but also to the consideration of different criteria and scenarios, that in many cases are conflicting with each other. This paper deals with the optimization of the building envelope design considering thermal insulation, economic, and environmental aspects. The Life Cycle Assessment perspective is implemented for the data of the environmental criterion, focusing on the CO₂ emissions and the cumulative energy demand. The decision making refers not only to the selection of the appropriate thermal insulation material and its width, but also to the choice of the window frame material. In that way, Mathematical Programming (MP) models for the optimization of such criteria were developed. The General Algebraic Modeling System (GAMS) was used to model these problems and the BARON solver was used to solve them. The respective MP models include mixed integer nonlinear programming problems, multiple objective functions, as well as multi-criteria techniques such as goal programming. According to the results, the increase of the envelope thermal protection implies that the economic and environmental costs are higher, displaying the importance of criteria compensation. For smoothing the conflicting criteria, a weighting sensitivity analysis was conducted, showing that reference optimal values are formed for certain ranges of weights, elaborating the framework of decision-making without having to precisely prescribe them beforehand. All in all, the use of the optimization models can improve and facilitate the building design process by analyzing the advantages and drawbacks of the various materials/technologies and allowing the comparative evaluation of the considered alternatives.

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