Ising-Machine-Assisted Large Neighborhood Search with Flexibly Tunable Subproblem Size

Ising machines are heuristic solvers for combinatorial optimization, but their solution quality can degrade when large-scale constrained problems are solved directly. Ising-machine-assisted large neighborhood search (LNS) instead repeatedly updates a feasible current solution by solving smaller subproblems. An existing feasibility-preserving method for the vehicle routing problem (VRP) re-optimizes the entire routes of selected vehicles and thus cannot adjust the subproblem size finely. We propose LNS-VT, which introduces the number of consecutive steps re-optimized per vehicle as a parameter to control the subproblem size finely while preserving feasibility. For a 300-site, 5-vehicle VRP, its best setting reduced the objective value by approximately 10\% relative to the existing method after 100 iterations, and the appropriate setting changed with the current solution quality. Applying the same principle to the quadratic multiple knapsack problem, we confirmed that an appropriate subproblem size also exists, indicating that subproblem-size control is important in Ising-machine-assisted LNS.