No abstract

Climate change, resource depletion, and worldwide urbanization feed the demand for more energy and resource-efficient buildings. Increasingly, architectural designers and consultants analyze building designs with easy-to-use simulation tools. To identify design alternatives with good performance, designers often turn to optimization methods. Randomized, metaheuristic methods such as genetic algorithms are popular in the architectural design field. However, are metaheuristics the best approach for architectural design problems that often are complex and ill defined? Metaheuristics may find solutions for well-defined problems, but they do not contribute to a better understanding of a complex design problem. This paper proposes surrogate-based optimization as a method that promotes understanding of the design problem. The surrogate method interpolates a mathematical model from data that relate design parameters to performance criteria. Designers can interact with this model to explore the approximate impact of changing design variables. We apply the radial basis function method, a specific type of surrogate model, to two architectural daylight optimization problems. These case studies, along with results from computational experiments, serve to discuss several advantages of surrogate models. First, surrogate models not only propose good solutions but also allow designers to address issues outside of the formulation of the optimization problem. Instead of accepting a solution presented by the optimization process, designers can improve their understanding of the design problem by interacting with the model. Second, a related advantage is that designers can quickly construct surrogate models from existing simulation results and other knowledge they might possess about the design problem. Designers can thus explore the impact of different evaluation criteria by constructing several models from the same set of data. They also can create models from approximate data and later refine them with more precise simulations. Third, surrogate-based methods typically find global optima orders of magnitude faster than genetic algorithms, especially when the evaluation of design variants requires time-intensive simulations.

No abstract

No abstract

The performance of Branch-and-Bound algorithms is severely impaired by the presence of symmetric optima in a given problem. We describe a method for the automatic detection of formulation symmetries in MINLP instances. A software implementation of this method is used to conjecture the group structure of the problem symmetries of packing equal circles in a square. We provide a proof of the conjecture and compare the performance of spatial Branch-and-Bound on the original problem with the performance on a reformulation that cuts away symmetric optima.