Robust Adaptive Routing Under Uncertainty

TL;DR

This paper develops a robust, adaptive routing strategy that minimizes risk under uncertain arc costs using distributionally robust optimization, demonstrated with Singapore road data.

Contribution

It introduces a novel distributionally robust approach for adaptive routing under uncertainty, handling limited distribution information.

Findings

The robust method reduces risk compared to non-robust strategies.

Numerical experiments show improved performance on Singapore road network data.

The algorithm efficiently computes near-optimal strategies under distributional ambiguity.

Abstract

We consider the problem of finding an optimal history-dependent routing strategy on a directed graph weighted by stochastic arc costs when the objective is to minimize the risk of spending more than a prescribed budget. To help mitigate the impact of the lack of information on the arc cost probability distributions, we introduce a robust counterpart where the distributions are only known through confidence intervals on some statistics such as the mean, the mean absolute deviation, and any quantile. Leveraging recent results in distributionally robust optimization, we develop a general-purpose algorithm to compute an approximate optimal strategy. To illustrate the benefits of the robust approach, we run numerical experiments with field data from the Singapore road network.