Abstract
Like most evolutionary algorithms, particle swarm optimization (PSO) usually requires a large number of fitness evaluations to obtain a sufficiently good solution. This poses an obstacle for applying PSO to computationally expensive problems. This paper proposes a two-layer surrogate-assisted PSO (TLSAPSO) algorithm, in which a global and a number of local surrogate models are employed for fitness approximation. The global surrogate model aims to smooth out the local optima of the original multimodal fitness function and guide the swarm to fly quickly to an optimum or the global optimum. In the meantime, a local surrogate model constructed using the data samples near each particle is built to achieve a fitness estimation as accurate as possible. The contribution of each surrogate in the search is empirically verified by experiments on uni- and multi-modal problems. The performance of the proposed TLSAPSO algorithm is examined on ten widely used benchmark problems, and the experimental results show that the proposed algorithm is effective and highly competitive with the state-of-the-art, especially for multimodal optimization problems.