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Frank-Wolfe(FW)算法是一类广泛应用于求解交通分配问题的算法。它具有容易编程实现，所需内存少的特点。但是该算法收敛速度较慢，不能得到路径信息。为了提高算法的效率，本文研究三种流量更新策略(all-at-once, one-origin-at-a-time, one-OD-at-a-time)以及不同的步长搜索策略下的FW算法，其中步长搜索策略包括精确线性搜索方法(包括二分法、黄金分割法、成功失败法)和不精确的线性搜索方法(包括基于Wolfe-Powell收敛准则的搜索方法和Gao等提出的非单调线性搜索方法)。最后，本文将上述策略应用于四种不同规模的交通网络中，并给出较适合求解的组合。

Implementing Frank-Wolfe Algorithm for Traffic Assignment Problem under Different Flow Update Strategies and Line Search Technologies

Frank-Wolfe (FW) algorithm is widely used to solve traffic equilibrium assignment problems. It has the characteristics of simple implementing and modest memory requiring. However, it also faces some problems such as slow convergence, no providing path information, and so on.In order to improve its implementation efficiency, the FW algorithm is further studied from three flow update strategies (all-at-once, one-origin-at-a-time, one-OD-at-a-time) and different step search methods, which includes deterministic line search methods (bisection method, golden-section method, success-failure method) and non-deterministic line search methods (a search method based on the basis of Wolfe-Powell convergent criterion, and a nonmonotone line search method). Four different scales transportation networks are used to test the different update strategies finally.