Adaptive Quantum-Classical Routing under Dynamic Traveler Preferences

Quantum optimization algorithms for the Traveling Salesperson and Vehicle Routing Problems overwhelmingly treat the problem as static: constraints, demands, and objectives are fixed before the solver runs and never revisited. The one adaptive strand of prior work, Quantum Reinforcement Learning for VRP, responds to changes in the external environment, such as traffic or demand, but not to the traveler's own evolving priorities. This paper introduces a prototype system that re-solves a small routing problem each time a simulated traveler's preferences shift, using a Bayesian model to represent the traveler's evolving priorities and the Quantum Approximate Optimization Algorithm (QAOA) to re-solve the routing subproblem on a quantum circuit simulator. We describe the architecture, report preliminary results on a 4-stop instance comparing QAOA against an exact classical baseline, and discuss the current limitations of penalty-based QUBO encodings for this problem class. We conclude with a concrete extension for future work: representing the traveler's decision-making as a branching tree of possible preference trajectories rather than a single linear path, which would allow the system to be evaluated for path-dependence, i.e. whether small early differences in a traveler's mood compound into substantially different final routes.