Surrogate-Assisted Hybrid Searching Method for High-Dimensional Expensive Optimization Problems

To address the challenges of intensive computation cost and poor convergence for high-dimensional expensive optimization problems, a surrogate-assisted hybrid searching method (SAHSM) is proposed in this paper. In SAHSM, the Leave-One-Out method is firstly carried out to adaptively choose the most promising radial basis function for the objective, which enhances the approximation performance of the surrogate. In order to enhance global exploration, the particle swarm optimization-based sampling mechanism is executed to generate offspring, and the best individual is selected as a global infill sample point. To accelerate convergence, a sequential quadratic programming method is adopted to find out the local optimum which is considered as a local infill sample point. During optimization, the surrogate is adaptively refined according to the global and local sampling mechanism, which improves the performance of the surrogate continuously. A number of high-dimensional benchmarks are used to illustrate the performance of SAHSM compared with ESAO a state-of-the-art optimization algorithm. Finally, SAHSM is applied to solve a 50-dimensional airfoil aerodynamic design optimization problem. The results show that the lift-drag ratio of the optimized airfoil has increased by 25.18% and 84.34% compared with ESAO and DE, which verifies the potential of SAHSM in engineering design.