吴方法在求解Beckmann交通平衡分配模型中的应用

On Application of Wu’s Method in Solving the Beckmann Traffic Assignment Model

摘要: 交通流分配中的Beckmann优化模型的广泛适用性越来越受到人们的关注。在通常解Beckmann模型时往往采用W-F算法，该算法得到的解为近似解，并非理想的精确解。本文采用吴方法对Beckmann交通平衡分配优化模型的求解方法进行了研究。首先，把问题等价的转化为求解多元多项式组特征列集零点集的问题。其次，对后者用吴方法处理获得零点集，进而获得优化问题的解。作为方法的应用，我们用该方法求解了具体的Beckmann优化模型的解，说明了提出方法的有效性。该方法也提供了用吴方法探索交通问题的一个新的思路。

Abstract: The Beckmann optimization model of traffic equilibrium assignment has drawn more and more attention of researchers because of its wide application in transportation science and engineering. The model is usually solved by W-F algorithm. In the present paper, the Beckmann Traffic equili-brium assignment model is investigated by Wu’s Method. Using Mathematics-Mechanization ideal and symbolic computation, we equivalently transform the model to finding the zero set problem of the characteristic sets of a multivariable polynomials and realize the algorithm on computer by computer algebra system. As an application of Wu’s Method, we use it to solve the specific Beck-mann optimization model. As a result, we prove the efficiency of Wu’s method and provide a new research idea for such kind of the transportation problems.