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.

在工程优化中，由于昂贵的模型复杂，精度要求高导致计算周期长，代理模型（SM）被广泛用于替代所涉及的时间昂贵的模型。在传统的工程优化过程中，代理模型静态构建阶段和动态优化阶段的分离降低了优化的准确性和效率。此外，为了确保代理模型的准确性，必须密集调用昂贵的模型，以便在设计空间中为 SM 训练获得足够的代表性样本。本文提出了一种基于代理模型伴随细化的全局优化方法，结合多级模糊聚类空间缩减策略（MFCPR-SGO）来提高优化精度和效率。首先，在设计空间中采用最优拉丁超立方设计方法（OLHD）进行抽样，保证初始样本集具有很强的空间填充性。然后，利用多级模糊聚类的空间缩减策略将设计空间细分为三层子空间，具有空间聚焦、空间缩减和跳出局部最优的能力。在此基础上，提出了具有ADAM梯度下降的分层优化方法，以快速准确地搜索每个子空间中目标函数的局部最小值。同时，结合极值采样和高斯过程采样，给出动态采样算法，实现优化和代理模型更新的同步。最后，使用12个不同维度的基准测试问题来验证所提出的方法。结果表明，与其他三种启发式优化方法和最近的三种基于代理的优化（SGO）算法相比，优化精度可提高 21.3%，昂贵的模型调用次数减少 31.5%。表明将代理模型的动态更新与工程优化搜索同步，可以大大提高优化精度和效率。