发表机构
Moscow State University（莫斯科国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带现实约束的车辆路径问题，开发了Smart Routes平台，对比SCIP、LKH、JAMPR等方法，发现深度学习与经典启发式算法在大规模问题上比精确求解器SCIP更高效且解质量接近。
AI 中文摘要
面对全球城市人口增长，带现实约束的路径优化问题正变得极为重要。我们注意到，部分方法在理论上能提供精确最优解，但随着问题规模增大，由于指数级复杂度，其应用变得极具挑战。本文研究带时间窗的容量约束车辆路径问题（CVRPTW），对比精确求解器SCIP与启发式算法（如LKH、2-OPT、3-OPT）、ORTools框架及深度学习模型JAMPR所得到的解。结果表明，对于规模为50的问题，深度学习与经典启发式解已接近SCIP的精确解，但所需时间更少；此外，对于规模为100的问题，SCIP精确方法的运行速度约是神经与经典启发式算法的13倍，且在相同时间下得到的首个可行解的质量比后者差约50%。为开展实验，我们开发了Smart Routes平台，用于求解路径优化问题，该平台包含精确、启发式及深度学习模型，便于集成自定义算法与数据集。
英文摘要
The problem of route optimization with realistic constraints is becoming extremely relevant in the face of global urban population growth. While we are aware of approaches that theoretically provide an exact optimal solution, their application becomes challenging as the problem size increases because of exponential complexity. We investigate the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and compare solutions obtaining by exact solver SCIP with heuristic algorithms such as LKH, 2-OPT, 3-OPT, the ORTools framework, and the deep learning model JAMPR. We demonstrate that for problem of size 50 deep learning and classical heuristic solutions became close to SCIP exact solution but requires less time. Additionally for problems with size 100, SCIP exact methods around 13 times slower that neural and classical heuristics with the same route cost and on around 50% worse for the first feasible solution on the same time. To conduct experiments, we developed the Smart Routes platform for solving route optimization problems, which includes exact, heuristic, and deep learning models, and facilitates convenient integration of custom algorithms and datasets.
