航线网络中非参数需求非限化估计的MM算法

MM Algorithm for Nonparametric Demand Unconstraining Estimation in Airline Network

尽管非参数离散选择模型可灵活地对航线网络替代效应和顾客策略行为进行建模,但其在历史顾客初始需求非限化估计中的应用会受到顾客到达过程分布假设的影响。为提高精确度,针对基于顾客偏好排序列表的网络型非参数离散选择模型,使用泊松分布对航线网络中短视型和策略型顾客需求的到达过程进行描述,并提出MM算法对泊松到达率和偏好排序概率质量函数进行联合估计。考虑到似然函数的非凹性,将极大似然估计问题重构为凹差(DC)规划问题,并应用凹-凸过程(CCCP)算法和Frank-Wolfe(F-W)算法对具有收敛性特征的凹优化问题进行求解。最后,通过数值模拟对所提方法的有效性和准确性进行了比较分析。结果表明,在综合考虑网络替代效应、顾客策略行为和模型需求分布假设等因素的情况下,本文所提方法相较于现有方法能够更加有效地控制非限化估计误差,避免对历史顾客初始需求的高估。

Although the nonparametric discrete choice model can flexibly model the substitution effects in the airline network and the customer strategic behavior,its application in the unconstraining estimation for historical customer primary demand will be affected by the assumption of customer arrival process distribution.To improve accuracy,based on the network nonparametric discrete choice model using customer rank-based preference lists,the Poisson distribution was used to describe the arrival process of both myopic and strategic customer demand in the airline network.The MM algorithm was proposed to jointly estimate the Poisson arrival rate and the probability mass function of preference rankings.Considering the non-concave feature of the likelihood function,the maximum likelihood estimation problem was reformulated to a difference-of-concave(DC)programming problem.Meanwhile,the concave optimization problem with convergence characteristics was solved by using the concave-convex procedure(CCCP)algorithm and the Frank-Wolfe(F-W)algorithm.Finally,the effectiveness and accuracy of the proposed method were compared and analyzed through numerical simulations.The results show that under the comprehensive consideration of substitution effects in network,customer strategic behavior,demand distribution assumptions of choice model,the proposed method can more effectively control the unconstraining estimation error and prevent overestimating the primary demand of historical customers.