Differential evolution-based topology optimization using Karhunen-Loève expansion

Abstract

Topology optimization is a widely adopted structural optimization approach that aims to maximize desired performance based on mathematical and physical principles. Gradient-based methods are common for obtaining optimal configurations; however, they struggle with problems involving numerous local optima and non-differentiable problems, which prevent the derivation of design sensitivity. To address these issues, this study explores the application of the Success History-Based Differential Evolution with Linear Population Size Reduction and Semi-Parameter Adaptation, which is regarded as LSHADE-SPA algorithm, known for its strong search capabilities. Nevertheless, its computational cost makes it impractical for topology optimization, especially as the number of design variables increases. To overcome this challenge, a novel structure representation method utilizing the Karhunen-Loève (KL) expansion is constructed. Applying truncated KL expansion instead of conventional density methods to represent structural configurations reduces the number of design variables. This article introduces a differential evolution-based topology optimization method utilizing truncated KL expansion and validates its effectiveness through applications in various structural and fluid problems. The method is particularly suited to highly nonlinear problems, such as negative Poisson's ratio structures and micro-mixer designs. The findings here indicate that differential evolution with truncated KL expansion can serve as an efficient and robust topology optimization method, proving particularly effective for solving optimization problems that are challenging for conventional gradient-based approaches. Notably, the proposed methodology not only delivers superior results but also alleviates computational burdens, thereby advancing the prospects of topology optimization in various engineering applications.