Radiation shielding is crucial for ensuring the environmental safety of personnel and nuclear facilities in the nuclear industry. As it usually consumes a long time in single simulation calculation, the optimization design of radiation shielding is a classical expensive optimization problem.

This study aims to reduce the number of sampling points required in the radiation shield optimization design and improve the efficiency of intelligent optimization algorithms.

A dynamic radial basis function based on particle flying (PF-DRBF) surrogate model was proposed in this study for radiation shielding optimization. Firstly, a radial basis neural network was used to build the initial surrogate model of the actual objective function, and the surrogate model was globally searched for optimality by a differential evolutionary (DE) algorithm. Thereafter new sample points were selected to join the original sample points based on the result of the surrogate model search and the particle flight sample update strategy, and the surrogate model was updated based on the new set of sample points and iterated until the convergence condition was satisfied. Since the flight speed of the original sample point to the random sample point and the optimal predicted sample point based on the fitting accuracy of the surrogate model were controlled by the model, the adaptive balance between the global exploration and the local exploration of the dynamic surrogate model was achieved. Finally, in order to verify the effectiveness of the method, the proposed method was applied to 12 numerical test functions and the optimization design for radiation shielding of marine reactors, and the calculation results of other optimization methods, i.e., mode pursuing sampling (MPS) method and dynamic radial basis function based on trust region (TR-DRBF) method, were compared.

The comparative results show that for numerical test functions, the proposed PF-DRBF method has significant advantages in search accuracy, search efficiency, and algorithm robustness. For the radiation shielding optimization, the neutron transmittance obtained by the proposed method is 48% and 8% of MPS and TR-DRBF methods, and the number of required sample points is 25% of the static surrogate model.

The results of this study indicate that by using the dynamic surrogate model based on the particle flying algorithm, the number of sample points needed to solve the expensive optimization problem is greatly reduced. The dynamic radial basis surrogate model with particle flight is an effective method for radiation shielding optimization.