Surrogate-adjoint refine based global optimization method combining with multi-stage fuzzy clustering space reduction strategy for expensive problems[Formula presented]

In engineering optimization, surrogate model (SM) is widely used to replace the involved time expensive model, due to the expensive model is complex and high precise requirement caused a long calculation cycle. In traditional process of engineering optimization, the separation of the surrogate model static construction stage and dynamic optimization stage depresses the optimization accuracy and efficiency. Moreover, in order to ensure the accuracy of the surrogate model, expensive model had to be intensively invoked to get enough representative samples in the design space for the SM training. In this paper, a surrogate model adjoint refine based global optimization method combining with the multi-stage fuzzy clustering space reduction strategy (MFCPR-SGO) is proposed to improve the optimization accuracy and efficiency. Firstly, the optimal Latin hypercube design method (OLHD) is used to sample in design space to assure the initial sample set with strong space filling property. Then, the design space is subdivided into three tiered subspaces by using the space reduction strategy of multi-stage fuzzy clustering, which has the ability of space focusing, space reduction and jumping out of local optimum. On this basis, the hierarchical optimization method with ADAM gradient descent is proposed to quickly and accurately search the local minimum value of the objective function in each subspaces. At the same time, combined with the extremum sampling and the gaussian process sampling, a dynamic sampling algorithm is given to realize the synchronization of optimization and surrogate model update. Finally, the benchmark test problems in 12 different dimensions are used to verify the proposed method. The results show that the optimization accuracy can be improved by 21.3% and expensive model invoking times are reduced by 31.5% compared with other three heuristic optimization methods and the three recent surrogate-based optimization (SGO) algorithms. It indicated that the optimization precision and efficiency can be greatly improved by synchronizing the dynamic updating of the surrogate model with the engineering optimization search.