Estimating a batch of parameter vectors of a nonlinear model is considered, where there exists a model interpreting the independent and the dependent variables, and the parameter vectors of the model are assumed to be sampled from a multivariate normal distribution. The mean vector and the covariance matrix of the parameter distribution can be assumed and such a parameter distribution is referred to as the hypothetical underlying distribution. A new framework is proposed, namely, the distribution-guided heuristic search framework, which uses the information of the hypothetical underlying distribution with the following two main concepts: (i) changing the coordinate of the parameter vectors via linear transformation and (ii) probabilistically filtering a parameter vector sampled by a heuristic algorithm. The framework is not a stand-alone algorithm, but it works with any heuristic algorithms to solve the target problem. The framework was tested in two simulation studies and was applied to a real example of measuring the critical dimensions of a 2-dimensional high-aspect-ratio structure of a wafer in semiconductor manufacturing. The test results show that a heuristic algorithm within the proposed framework outperforms the original heuristic algorithm as well as other existing algorithms.

考虑估计非线性模型的一批参数向量，其中存在一个解释自变量和因变量的模型，并且假定该模型的参数向量是从多元正态分布中采样的。可以假设参数分布的均值向量和协方差矩阵，并且将这样的参数分布称为假设的基础分布。提出了一种新的框架，即分布指导的启发式搜索框架，该框架使用具有以下两个主要概念的假设基础分布的信息：（i）通过线性变换更改参数向量的坐标，以及（ii）概率地过滤由启发式算法采样的参数向量。该框架不是独立的算法，但是它可以与任何启发式算法一起解决目标问题。该框架在两项仿真研究中进行了测试，并被应用于在半导体制造中测量晶圆的二维高纵横比结构的关键尺寸的实际示例。测试结果表明，所提出的框架内的启发式算法优于原始启发式算法以及其他现有算法。