AI 中文总结
研究基于链路的对数随机用户均衡求解难题，提出可微求解器DiLLSUE，无需路径枚举等，通过特定算法实现GPU运算，经多种求解器和滤波器测试，在多网络上表现良好，计算均衡收敛且精度高。
AI 中文摘要
对数随机用户均衡（SUE）考虑了不完美的路径成本感知，但其实际求解器依赖于路径枚举（在大型网络上成本过高）或基于链路的启发式方法（无收敛保证）。我们开发了DiLLSUE，一种用于基于链路的对数SUE的可微求解器，无需路径枚举、训练数据和特定于网络的调整。其内部加载算法将所有目的地批量处理为固定形状的张量运算，实现了首个基于链路的对数SUE的GPU实现。对四种外部求解器进行了基准测试，并使用了一族无环滤波器。在五个标准基准网络上，GPU和CPU执行结果在平均绝对百分比误差的$10^{-4}$%内一致，计算出的均衡单调收敛到独立计算的Wardrop均衡。
英文摘要
Logit stochastic user equilibrium (SUE) captures imperfect route cost perceptions, but its practical solvers rely on route enumeration, which becomes prohibitive on large networks, or on link-based heuristics without convergence guarantees. We develop DiLLSUE, a differentiable solver for the link-based logit SUE that requires no route enumeration, no training data, and no network-specific tuning. Its inner loading algorithm batches all destinations into fixed-shape tensor operations, yielding, to our knowledge, the first GPU implementation of link-based logit SUE. Four outer solvers -- successive averages, self-regulating averaging, Anderson mixing, and implicit-function-theorem Newton -- are benchmarked under identical settings, and a family of acyclicity filters provides fast approximations with a quantified speed-accuracy trade-off. On five standard benchmark networks, GPU and CPU executions agree to within $10^{-4}$\% mean absolute percentage error, and the computed equilibrium converges monotonically to the independently computed Wardrop equilibrium, reaching 0.33\% error on Sioux Falls, where the zero-training solver is more accurate than published trained surrogates.
