Interior Point Method-Assisted Differential Evolution for Expensive Optimization of Secondary Source Deployment

In active noise control, the optimal deployment of secondary sources is a critical factor influencing the noise reduction performance due to the spatial inhomogeneity of the sound field. Traditional methods, which rely on finite element analysis to model the sound field, are accurate but computationally intensive, leading to high costs in solving the deployment optimization problem. To address this issue, this paper proposes an expensive optimization method for secondary source deployment based on Interior Point Method-assisted Differential Evolution with Weibull distribution (IPMDEW). During the optimization process, a Kriging model is employed to construct a response surface, i.e., a surrogate model, of the objective function. The surrogate model is used for the initial evaluation of the population, while the finite element model is utilized to verify promising individuals. A surrogate model update algorithm based on k-means clustering is designed to iteratively refine the model and enhance its accuracy. The IPMDEW algorithm utilizes the Weibull distribution-based weighted differential evolution for global exploration and switches to the gradient-based interior point method for refined local optimization when the population approaches convergence. The results demonstrate Kriging surrogate-assisted optimization method for secondary source deployment reduces the optimization time by 85.79%, i.e., by 347.64 h, significantly improving optimization efficiency. Furthermore, the accuracy of the Kriging model continuously improves during the optimization process. The proposed method achieves a noise reduction of 58.32 dB, ensuring high optimization accuracy while substantially increasing efficiency.