Multi-fidelity algorithms for the horizontal alignment problem in road design

Abstract

Multi-fidelity algorithms for solving the horizontal alignment problem in road design are considered. A multi-fidelity surrogate model is built and quantile regression is used to understand its accuracy at various fidelity levels. Two algorithms are compared: a generalized pattern search algorithm with adaptive precision control, and a trust-region algorithm for unconstrained problems with controlled error. To make a fair comparison, the parameters of each algorithm are tuned on five small roads using performance profiles. Then the algorithms are evaluated on 35 roads, ranging from small to very large roads. The results show that using multi-fidelity surrogates in optimization algorithms provide notable speed-up when compared to single-fidelity algorithms while preserving the quality of solutions (cost error $<1\mathrm{\%}$). On the longest roads, higher speed-up and better accuracy are observed.

Keywords:

• Multi-fidelity
• road design
• surrogate
• generalized pattern search
• trust region

Acknowledgements

Part of the computation in this research was carried out using a software library provided by Softree Technical System Inc.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Warren Hare http://orcid.org/0000-0002-4240-3903

Yves Lucet http://orcid.org/0000-0003-0349-6737

Notes

1 http://ggplot2.tidyverse.org/reference/geom_quantile.html and https://www.r-project.org/

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Collaborative Research and Development grant [#CRDPJ 479316-15] sponsored by Softree Technical Systems Inc.; the University of British Columbia under the Graduate Entrance Scholarship and the University Graduate Fellowship; the Canada Foundation for Innovation (CFI) under Leaders Opportunity Fund (LOF, John R. Evans Leaders Fund — Funding for research infrastructure for the Computer-Aided Convex Analysis (CA2) laboratory); and the province of British Columbia under British Columbia Knowledge Development Fund (BCKDF).