Assessment of the gradient of an objective function by analytical derivation for optimization-based design of ground-coupled heat pump systems

Abstract

Optimization-based design of ground heat exchangers requires derivation of the objective function with respect to the design parameters, which is usually done through finite-differentiation of the cost or utility function. The approach is however prone to approximation errors and can result in convergence issues or long optimization time. By deriving analytically the ground heat exchanger transfer function, it is possible to obtain an exact representation of the objective function gradient and avoid numerical instabilities. To illustrate the advantages of using analytical expressions, a common design task is expressed as an optimization problem. It is shown that by using an analytical derivation of the gradient in conjunction with strong Wolfe conditions during a line search may reduce significantly computation time by comparison to a finite-differentiation of the gradient.