AI 中文总结
研究受限组合优化问题的大规模二次无约束二元优化，通过比较基于当前解车辆路线的LNS-K和基于QUBO变量及约束关系的LNS-Q构建方式，发现子问题设计应考虑多种因素。
AI 中文摘要
受限组合优化问题的大规模二次无约束二元优化（QUBO）公式常超出当前伊辛机输入大小限制或因二元变量数量增加导致解质量下降。大邻域搜索（LNS）通过顺序优化受限子问题缓解此困难，但除二元变量数量外区分子问题的结构因素仍未充分表征。本研究考察车辆路径问题……
英文摘要
Large-scale quadratic unconstrained binary optimization (QUBO) formulations of constrained combinatorial optimization problems often exceed the input-size limit of present Ising machines or suffer from degraded solution quality as the number of binary variables increases. Large neighborhood search (LNS) mitigates this difficulty by sequentially optimizing restricted subproblems, but the structural factors that distinguish subproblems beyond the number of binary variables remain insufficiently characterized. In this study, we examine vehicle routing problems and compare a construction based on the vehicle routes of the current solution, denoted by LNS-K, with a construction based on QUBO variables and constraint relations, denoted by LNS-Q, while controlling the number of binary variables in the subproblems. Under the tested conditions, LNS-K obtained shorter total distances than LNS-Q in the matched-size comparisons, and the position variance, a measure of the spatial spread of the selected customers, decreased during the iterations in LNS-K. These observations suggest that subproblem design for sequential optimization with Ising machines should consider not only subproblem size but also semantic and geometric structures inherited from the current solution.
Comments11 pages, 3 figures
