A Kriging Constrained Efficient Global Optimization Approach Applied To Low-Energy Building Design Problems

Low-energy building design is constrained not only by the total cost but also by both the energy demand and the comfort requirements. However, the evaluation of these criteria may require the implementation of time-consuming tasks, such as the direct building thermal simulation, which leads to difficulties in the design process. Moreover, it is of interest in this field to provide the designer with a large range of acceptable solutions rather than some unique optimal design. In this article, the application of an efficient global optimization approach is proposed as a tool to analyse the response functions of a building design problem. The method is based on a Kriging metamodel, which provides the global prediction of the objective and constraint functions, and an evaluation of uncertainty of the prediction at each point. The criterion for the infill sample selection is a generalized expected improvement function with desirable properties for stochastic responses. This criterion is maximized according to different constraints. First, inexpensive constraints are used as boundary constraints. Then, the expected violation criterion is used as a penalty. We use a particle swarm optimization algorithm to maximize the infill sample criterion according to the constraints. This approach is shown to be efficient for the building design problem, since the optimization is performed with an important reduction of the number of objective and constraint function calls. The Kriging metamodel is used to evaluate the sensitivity and the possible range of variations of the design parameters near their optimal values.