An Evolutional Topology Optimization Method Based on Kernel Level Set Function

Topology optimizations involving evolutionary algorithms are promising approaches to solve practical engineering design problems, since their use of derivation-free algorithms makes them applicable to any design problem. In some evolutional topology optimization methods, structures are determined through the use of spatially smooth parametric functions. This article, first, presents a new parametric level set function using kernel functions as a general formulation of spatially smooth function-based methods. It is called the kernel level set function, which is used to determine the distributions of materials in the design region. By using the evolutionary algorithm to modify the profile of the kernel level set function, topology optimizations can be realized for various design problems, and the shape expression ability of the kernel level set function can be customized by changing the kernel functions. Second, a multi-objective formulation considering an objective and structural complexity is introduced, and an optimization algorithm specialized for solving it is proposed. The combination of the kernel level set function and the present optimization algorithm makes it possible to solve various topology optimization problems, and Pareto fronts with respect to target performance and structural complexity can be obtained. The present method is applied to three topology optimization problems. The numerical results are used to examine the characteristics of the present method for various kernel functions. Furthermore, the present method is applied to an optimization problem of an interior permanent magnet motor for electric vehicles. It is shown that the present method can solve practical design problems that have various objectives and constraint conditions, thanks to the use of a derivation-free evolutionary algorithm.