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Abstract
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.
Acknowledgments
We appreciate the department editor, three anonymous referees, and Drs. Heeyoung Kim and Sungil Kim for their helpful comments.
Additional information
Funding
Notes on contributors
Hyungjin Kim
Hyungjin Kim is a Ph.D. candidate in the Department of Industrial Engineering at Hanyang University. He received a B.S. degree in industrial engineering from Hanyang University. His research interests are in the areas of nonlinear parameter estimation and machine learning.
Chuljin Park
Chuljin Park is an assistant professor in the Department of Industrial Engineering at Hanyang University. He received a B.S. in mechanical engineering from the Korea Advanced Institute of Science and Technology (KAIST) and an M.S. and Ph.D. in industrial and systems engineering from Georgia Institute of Technology. His research interest centers on simulation-based optimization, stochastic simulation, and applications of applied statistics and optimization techniques to semiconductor manufacturing and environmental management.
Yoonshik Kang
Yoonshik Kang is a senior engineer at SK Hynix. He received a Ph.D. in physics from Inha University. Prior to joining SK Hynix, he worked for the Korea Research Institute of Standards and Science as a post-doctoral researcher. His research interests are in the areas of quantum information and advanced metrology.