面向双目标旅行劫匪问题的高级量子退火：一种$\varepsilon$-约束方法

本文针对双目标旅行劫匪问题（BI-TTP），即需要同时优化旅行成本和物品利润的挑性多目标优化问题。BI-TTP的常规方法常因路由决策与装箱决策之间的复杂相互依赖以及问题规模的天然复杂性和庞大而面临严重的可扩展性问题。这些困难使得经典计算方法日益不可用。为此，我们提出了一种高级混合方法，将量子退火（QA）与$\varepsilon$-约束方法相结合。具体而言，我们通过可调的$\varepsilon$水平（在确定的上限和下限内）对第二个目标进行限制，将双目标问题重新表述为单目标问题。 resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting $\varepsilon$ parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.