随机交通网络最小期望-均方差路径问题罚函数解法

发布时间：2018-05-21 16:29

  本文选题：交通运输工程 + 随机网络　； 参考：《重庆交通大学学报(自然科学版)》2017年04期

【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。
[Abstract]:In order to reflect the path selection behavior considering reliability in traffic network, the mathematical model of optimal path problem in stochastic traffic network environment is established based on mathematical programming theory and the penalty function method is constructed to solve the constrained optimization problem. Firstly, the mean-variance is added to the path objective function to reflect the reliability of the path, and the mathematical programming model of the minimum expected mean-variance path problem in the stochastic network environment is established. Secondly, the penalty function and penalty factor are introduced. The nonlinear constrained optimization problem is transformed into the unconstrained optimization problem. Thirdly, the quasi-Newton method is constructed to solve the unconstrained optimization problem, and the exact solution of the original problem is obtained. Numerical experiments are carried out on the actual traffic network and the numerical results are analyzed. Numerical results show that the proposed algorithm can obtain the exact solution of the optimal path.
【作者单位】： 南京林业大学汽车与交通工程学院;
【基金】：国家自然科学基金青年基金项目(51508280) 南京林业大学高学历人才基金项目(GXL2014031) 江苏省高等学校大学生创新创业训练计划项目(201610298037Z)
【分类号】：U491
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本文编号：1919944