Design Optimization Energy with the Lagrange multipliers Method

Energy consumption of a building mainly depends on how the building architectural design factors are combined. As such, a good combination of these design factors is considerably important for effectively reducing building energy consumption. This means that determining the optimal combination of factors that consume the least amount of energy will require many alternative studies. Nonetheless, it is possible to identify the optimal combination of factors without requiring numerous alternatives by using Lagrange multipliers method in optimization. However, at present, the applicability of this theory should be verified before actively applying it to architectural design. In this study, a basic research is carried out to examine whether the optimal design obtained via Lagrange multipliers method is consistent with the design option identified through numerous alternative simulation studies. To this end, a standard model is established and two variables that affect energy are designed. Experiments 1 and 2 are carried out to identify the optimal design through simulation and the Lagrange multipliers method, respectively, in order to verify the consistency between the two experimental values.