Abstract: In order to reflect route choice behavior considering the reliability in traffic network, a mathematic model of shortest path problem in stochastic network was developed based on the mathematical programming and a penalty function algorithm was constructed to solve the constrained optimization problem. Firstly, a mathematical model of mathematical programming was established to reflect the reliable shortest path selection in stochastic network through defining the standard deviation as the part of the objective function; Secondly, the nonlinear constrained optimization problem was transformed into unconstrained optimization problem through introduction of penalty function and penalty factor; Thirdly, a quasi-Newton method is developed to solve the proposed problem; Finally, numerical experiments was carried out on the actual traffic network and the numerical results were analyzed. Numerical results show that the proposed algorithm is able to get exact solution of the optimal path.

Key words: traffic and transportation engineering, stochastic network, optimal path, penalty function, quasi-Newton method

摘要： 为了反映交通网络中考虑可靠性的路径选择行为，基于数学规划理论建立随机交通网络环境下最优路径问题的数学模型并构造罚函数法求解该约束优化问题。首先，在路径目标函数中 加入了均方差以反映路径的可靠性，建立随机网络环境下最小期望-均方差路径问题的数学规划模型；其次，引入罚函数和罚因子，把非线性约束优化问题转换为无约束优化问题；第三，构造 拟牛顿法求解无约束优化问题，最终获得原问题的精确解；最后，针对实际交通网络开展了数值实验并对数值结果进行了分析。数值结果表明：提出的算法是能获得最优路径的精确解。

关键词: 交通运输工程, 随机网络, 最优路径, 罚函数, 拟牛顿法