Neural Combinatorial Optimization for Robust Routing Problem with Uncertain Travel Times

We consider the robust routing problem with uncertain travel times under the min-max regret criterion, which represents an extended and robust version of the classic traveling salesman problem (TSP) and vehicle routing problem (VRP). The general budget uncertainty set is employed to capture the uncertainty, which provides the capability to control the conservatism of obtained solutions and covers the commonly used interval uncertainty set as a special case. The goal is to obtain a robust solution that minimizes the maximum deviation from the optimal routing time in the worst-case scenario. Given the significant advancements and broad applications of neural combinatorial optimization methods in recent years, we present our initial attempt to combine neural approaches for solving this problem. We propose a dual multi-head cross attention mechanism to extract problem features represented by the inputted uncertainty sets.