Abstract
This paper introduces a data-driven Distributionally Robust Optimization (DRO) framework to identify risk-averse Hamiltonian cycles in non-stationary stochastic networks subject to severe probabilistic uncertainty. Rather than relying on static nominal travel times, which suffer heavily from the optimizer's curse, we construct a distribution- free ambiguity set defined by a Type-1 Wasserstein metric ball centered on an empirical distribution of historical link latencies. The resulting minimax optimization model minimizes the worst-case expected routing cost over all probability distributions compatible with historical observations. To resolve the joint challenge of combinatorial hardness (NP-complete) and non-linear robust objectives, we synthesize this DRO formulation with an evolutionary computing engine governed by precise permutation set operators, deploying an Edge Recombination Crossover (ER) operator and an ergodic Swap Mutation mechanism. We evaluate our model on two structurally contrasting urban networks in Kazakhstan: the dense, topography-constrained grid of Almaty, and the expansive, bridge-dependent network of Astana. Our empirical findings demonstrate that the proposed framework prevents catastrophic out-of-sample routing delays by preserving edge adjacency maps and outperforming classical stochastic programming models.