Heuristic Strategies of Modified Levenberg–Marquardt Algorithm for Fitting Transition Curves
Publication: Journal of Surveying Engineering
Volume 146, Issue 2
Abstract
Horizontal curve identification is important both for road safety management and railway maintenance. Parameters of a transition curve are introduced to perform an orthogonal least-squares fitting. During such a fitting process, the Gauss-Newton (GN) method may fail to converge because of an ill-conditioned Hessian matrix. A biobjective fitting model is introduced, and the Levenberg–Marquardt (LM) algorithm is specified to perform the fitting of transition curves. The LM parameter is updated heuristically during iterations according to the specific information explored instead of the standard preset way. Further, another heuristic strategy is proposed to search a path to the optimum instead of the traditional greedy strategy. The heuristic strategies were compared with traditional ones by fitting a transition curve of a railway to the measured points. Monte Carlo simulations were employed to test the robustness and efficiency of the modified LM algorithm, with different initial values, all converging to the same optimum. Results showed that the heuristic strategy for updating the LM parameter has a better robustness than the preset way, and the heuristic strategy for searching a path converges much faster than the traditional one, for which visual interpretations are provided.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant No. 51678574). The authors thank the anonymous reviewers for their constructive comments. The first author thanks the China Scholarship Council (Grant No. 201706375006) for financially supporting his studies at the University of Maryland.
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Published In
Journal of Surveying Engineering
Volume 146 • Issue 2 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Dec 1, 2018
Accepted: Oct 2, 2019
Published online: Jan 17, 2020
Published in print: May 1, 2020
Discussion open until: Jun 17, 2020
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