A convergent optimization method using pattern search algorithms with adaptive precision simulation

Abstract

Thermal building simulation programs, such as EnergyPlus, compute numerical approximations to solutions of systems of differential algebraic equations. We show that the exact solutions of these systems are usually smooth in the building design parameters, but that the numerical approximations are usually discontinuous due to adaptive solvers and finite precision computations. If such approximate solutions are used in conjunction with optimization algorithms that depend on smoothness of the cost function, one needs to compute high precision solutions, which can be prohibitively expensive if used for all iterations. For such situations, we have developed an adaptive simulation–precision control algorithm that can be used in conjunction with a family of derivative free optimization algorithms. We present the main ingredients of the composite algorithms, we prove that the resulting composite algorithms construct sequences with stationary accumulation points, and we show by numerical experiments that using coarse approximations in the early iterations can significantly reduce computation time.