Test and Assessment of Derivative Computation Architectures using OpenMDAO and its Application in a Real Airfoil Optimization Problem

Abstract: Optimization problems are widespread in everyday life and engineering science. In the engineering optimization domain, the problems are usually modelled with an objective function. To solve these kinds of optimization problems, there are two main classes of optimization algorithms that are used: gradient-based algorithms and gradient-free algorithms. We will focus on gradient-based algorithms where the computation of derivatives is a critical step in the process. In this thesis, we present five different methods for computing the derivatives. These are the finite-differences method (FD), the complex-step method (CS), the automatic-differentiation method (AD), and two analytical methods – the direct and adjoint methods. We demonstrate the procedures involved in these methods in a test case and show their implementation using NASA’s Open source framework for Multidisciplinary Analysis and Optimization (OpenMDAO). Finally, we test and assess their performance in OpenMDAO by modelling a real airfoil problem.