成本函數不可微時路網均衡解的敏感度分析

Abstract

路網均衡流量的敏感度分析在許多運輸問題中都扮演著中要角色，如：雙層路網設計問題、道 路壅擠訂價問題、號誌控制問題、起迄矩陣推估問題…等。在路網均衡流量分析中，常用來求取敏 感度資訊的方法包括梯度法及方向導數法兩大類，其中方向導數法具有較好的性質，可用於求解當 均衡解變化軌跡為不可微時的敏感度資訊。然而目前所發展之方法皆須符合成本函數具有連續可微 之限制，為了使敏感度分析可應用在更廣義的網路問題上，本研究將以方向導數法為基礎，對成本 函數為不可微的路網均衡解進行敏感度分析，探討其敏感度資訊的存在性及唯一性，並提出適當的 模式將其求解出來。

Sensitivity analysis of equilibrium network flows is useful in various fields, such as bilevel network design problems, road pricing, signal control problems and origin-destination matrix estimation. Gradient based method and directional derivative based method are two popular approaches in sensitivity analysis of traffic equilibria. Compared with the gradient based sensitivity method, directional derivative based method can deal with more general problem that the equilibrium solution is non-differentiable. In this study, the assumption of continuously differentiability for directional derivative based method is relaxed by non-differentiable cost functions. The existence and uniqueness of directional derivatives of traffic equilibria with non-differentiable cost functions are investigated. Finally, an appropriate model is proposed to solve the directional derivatives of traffic equilibria.