Multi-Day Intermodal Travel Planning for Urban Cities Using Ising Machines

The multi-day intermodal travel planning problem (MITPP) is an optimization problem (OP) and it generates the optimal sequences of point-of-interests (POIs) and hotels while searching for the most suitable transport modes between POIs and hotels. Conventional methods and solvers using von Neumann computers provide good approximate solutions to the OPs, but the computation time grows exponentially dealing with large-scale or complex OPs. Meanwhile, Ising machines or quantum annealing machines are non-von Neumann computers that are designed to solve complex OPs. In this paper, we focus on solving the MITPP by a two-phase Ising-based method. The first POI clustering phase aims at generating POIs clusters for sightseeing days and the second POI routing phase generates travel routes for each day with the optimal transport modes. Practical factors such as POI satisfaction, POI duration, hotel fee, and transportation fee are included in the MITPP. We map these elements onto quadratic unconstrained binary optimization (QUBO) models. For evaluation, we use a real-world dataset in Sapporo, Japan. Empirical results confirm that the proposed method can effectively solve the MITPP both in terms of solution quality and execution time and outperforms a conventional solver, a conventional method, and the latest Ising-based method.