A comparison of global optimization algorithms with standard benchmark functions and real-world applications using EnergyPlus

There is an increasing interest in the use of computer algorithms to identify combinations of parameters that optimize the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems. To shed light on this issue, we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimising standard benchmark functions and real-world building energy optimization problems of varying complexity. From this, we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence of the building energy system that does not represent actual practice, further reinforcing their utility.