基于极大熵模型的交通出行矩阵解法研究

Study of solving origin-destination matrix based on maximum-entropy model

引入拉格朗日乘子,对由路段观测流量反推交通出行矩阵的极大熵模型进行变换,将优化问题转换为非线性方程组的求解,并提出一种遗传算法求解方法.该方法以非线性方程组的待求量为决策变量,方程组两端向量的均方差最小值为目标函数,初值在决策变量可行域内随机产生.通过实例验证,遗传算法较之牛顿法改进了其对初始值要求严格、易产生局部收敛并含有矩阵求逆的不足,且当初始值偏离真实值较大时,遗传算法求解成功率远远高于牛顿法,证明了遗传算法在多种交通网络中求解交通出行矩阵是可行的.

The maximum-entropy model, estimating origin-destination （OD） matrix from observed traffic link flows, was transformed by the introduction of I.agrange multiplier, and the optimization problem was transformed into solving the systems of non-linear equations, then the calculation method of OD matrix by genetic algorithm （GA） was proposed. In this method, the GA decision-making variable was the unknown value of the systems of non-linear equations, the target function for optimization was the minimum of the root-mean-square error between the left computational value and the right real value in equations, and the initial value was generated randomly in the feasible field of decision-making variables. A practical example showed that GA overcomes the imperfection of Newton＇s method that strictly depends on initial values, does not easily converge and must calculate inverse matrices. When the initial value is far from the real value, there are more probabilities of solving OD matrix successfully by GA than by Newton＇s method. Comparison between the results of the two methods showed the feasibility of solving OD matrix by GA in different traffic network.