A Hybrid Memetic Algorithm for Asymmetric Vehicle Routing with Topographic Constraints: Quantifying the Orographic Gap in Mountain Urban Networks

Classical vehicle routing models assume flat, symmetric road networks, yet mountain cities exhibit gravitational asymmetry and steep gradients that invalidate two-dimensional cost estimates and may produce mechanically infeasible routes. This study formalizes the Asymmetric Capacitated Vehicle Routing Problem with Topographic Constraints (ACVRP-TC) and introduces a generalized cost function (GCF) that linearizes direction-dependent energy consumption into an impedance metric within a mixed-integer linear programming (MILP) formulation. A hybrid memetic algorithm coupled with stochastic large neighborhood search (H-MA-LNS) is proposed to solve this NP-hard variant, combining evolutionary global exploration with structured local intensification. Benchmark validation yields a mean improvement of 9.4% over the state of the art on flat reference instances. An extensive computational evaluation on 24 real geospatial instances from Seoul (Republic of Korea), enriched with satellite elevation data, reveals a topographic gap of 14.1% for this urban network (Wilcoxon: p = 0.002), quantifying the cost underestimation that orography imposes on theoretical planning in the studied setting. Furthermore, the feasibility-based arc pruning reduces the search space by 51%, accelerating convergence and inducing a shift toward radial route structures in high-density environments.