Improving the Performance of the Spectral Level Methodology

Abstract

nite Fourier series. The Fourier coecients become the design variables of the optimization problem. The spectral level set methodology has already produced excellent results in benchmark structural optimization, as well as in reinforced wing-box and morphing airfoil applications. In this paper, we discuss three improvements to the methodology to make it computationally cost eective under a multidisciplinary design framework. First, we study coupling it with a pattern search particle swarm optimization algorithm to avert local optima. Then we discuss the elimination of volume constraints by adequately choosing one of the Fourier coecients. Finally, to avoid parameter adjustment, we consider the methodology’s relaxation parameters to be design variables. We provide illustrative examples to evaluate the potential of each improvement. Although preventing local optima has proven to be a dicult task in need of further consideration, we were able to demonstrate the viability of eliminating volume constraints and parameter adjustment in reducing the computational cost of the spectral level set methodology.