A topology optimization method for electric machines and devices through submodular maximization

This paper presents a topology optimization method using a greedy algorithm for submodular maximization. This method is based on a shape representation using the normalized Gaussian network. The weight coefficients of Gaussians are discretized to +1/-1, and then their values are greedily inverted. Hence, the computational cost of the present method is relatively smaller than that of evolutionary algorithms. The present method is applied to a magnetic shield optimization problem. It is shown that Pareto solutions can be obtained by the present method. In addition, it can be found from the numerical results that the stochastic greedy algorithm can effectively reduce the computational time compared with the conventional greedy algorithm. As a result, it is shown that a 3-D optimization problem with over 3000 design variables can be solved within acceptable computational time.