基于Groebner基的Beckmann交通平衡分配模型新解法

A New Method Based on Groebner Bases for Solving the Beckmann Traffic Equilibrium Assignment Model

摘要: Beckmann交通平衡分配模型是研究交通分配问题的基础，然而目前该模型的求解主要依赖于F-W迭代算法和智能优化算法，无法求得精确解。为了寻找Beckmann交通平衡分配模型的精确解，本文借助Groebner基理论在求解多维多项式方程方面的优势，将Beckmann模型转化为多项式方程，通过引入新的变量和映射将一般多项式转化为单项式，给出了精确求解Beckmann交通平衡分配模型的方法。最后给出算例验证了该方法的有效性。

Abstract: Beckmann traffic equilibrium assignment model is the basis of the study of traffic assignment problem. However, at present, the solution of Beckmann traffic equilibrium assignment model is still dependent on the F-W iterative algorithm and intelligent optimization methods, which can’t obtain the exact solution. In order to find the exact solution of the Beckmann traffic equilibrium assignment model, this paper uses the advantage of Groebner bases theory in solving multidimen-sional polynomial equations, transforms the Beckmann model into a polynomial equation, then introduces the new variables and mapping to make the general polynomial into monomial, and then a method for solving the traffic equilibrium assignment model of Beckmann exactly is given. Finally, an example is given to show the effectiveness of the proposed method.