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

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 ). On the longest roads, higher speed-up and better accuracy are observed.