考虑双重不确定性的公交时刻表分布鲁棒优化模型

城市公交系统由于受外界干扰,其需求和运行环境在时空上呈现高度不确定性,给日常运营组织带来了巨大挑战.为增强公交系统对于客流需求和运行场景双重不确定性的应对能力,提出一种权衡服务质量和服务鲁棒性的单一线路时刻表优化方法.方法采用离散场景集刻画需求的不确定性,并以滞留人数的期望值和条件风险值最小化为目标,综合考虑多方面约束,构建多场景耦合的分布鲁棒优化模型(DRO).为方便模型求解,运用模糊集描述场景发生概率的不确定性,再借助对偶理论和常规线性化方法将原模型转化为等价的混合整数线性规划形式.最后通过实际案例对方法进行分析,结果表明:等价转换得到的线性形式可由GUROBI优化软件快速求得最优解; DRO模型所得时刻表能有效应对双重不确定性;随着不确定性的上升,分布鲁棒优化方法相较于传统随机规划方法体现出更强的鲁棒性,可以切实改善公交系统运营的稳定性.     

考虑多重覆盖的应急设施多级协同布局鲁棒优化

应急设施的合理布局是灾后实现物资高效、公平和稳定供应的重要保障.针对突发自然灾害的不确定性,研究基于多重覆盖的应急设施多级协同布局鲁棒优化问题.首先,提出多级设施选址下的多重覆盖水平函数,以最小覆盖水平和期望总成本最优为目标,建立应急设施多级协同选址双目标优化模型;其次,应用基数不确定集和p-鲁棒方法构建两类鲁棒优化模型,分别研究场景内不确定需求和随机场景对设施布局的影响;最后,以湖南省救灾备荒种子储备库选址为例进行实证分析,验证所提出优化模型的有效性.研究结果表明:多级协同布局相比传统布局方案更具优势;鲁棒优化模型能够有效应对不确定情形和随机场景下的物资需求;决策者的风险偏好程度和预算水平对设施协同布局有重要影响,需对二者进行综合权衡.     

基于均衡性和可达性的高速铁路列车停站方案优化

为了兼顾高速铁路的速度优势和旅客出行的方便,从列车停站数量的均衡性和区间的可达性出发,建立高速铁路列车停站方案的非线性多目标优化模型。结合模型的特点,设计了具有自适应性的遗传退火算法。自适应遗传算法控制全局的寻优方向,模拟退火的Metropolis邻域搜索策略提高算法的邻域搜索能力,可以快速搜索高质量的解。最后用2015年京沪高速铁路数据进行验证,并用得到的停站方案与原停站方案进行对比。结果表明：优化方案中开行列车的停站数量更加集中,停9站和停10站列车占开行列车总数的71.8%,显著提高了停站方案的均衡性;可达性提高约2.32%。     

基于分布鲁棒优化的城市轨道交通网络末班车衔接研究

随着我国城市轨道交通网络规模快速扩张,线路间协调配合的高度复杂性给城市轨道交通的运营组织与管理带来极大挑战.针对客流需求及其分布双重不确定条件下的城市轨道交通网络末班车衔接优化问题,提出一种分布鲁棒机会约束规划模型,即在给定容忍度下最小化最坏条件下的换乘失败客流量.通过分析分布鲁棒优化模型与其对应鲁棒优化模型之间的联系,证明该模型为鲁棒优化模型的推广形式.基于有限的期望和方差信息构造高斯分布非精确集,采用对偶理论将原模型转化为可利用CPLEX求解的混合整数二阶锥规划形式,并通过数值实验验证所构建模型的有效性.算例结果表明:分布鲁棒模型对于小规模网络可利用CPLEX快速求得精确解;相比鲁棒模型可有效避免产生过于保守的优化结果;相比随机模型可有效降低极端情况下换乘失败客流量,具有较强的鲁棒性.     

考虑区域协调性的城际列车开行方案优化

针对城际列车开行方案没有有效匹配城市轨道交通运能的问题，提出一种考虑区域协调性的城际列车开行方案优化方法。首先，以旅客出行费用最小和铁路运输效益最大为优化目标，考虑城际列车载客能力、出发地目的地（Original Destination，OD）客流需求和通过能力等约束；然后，在此基础上增加运能匹配度的限制，构建了考虑区域协调性的城际列车开行方案多目标非线性规划模型，并设计改进的模拟退火算法求解模型；最后，以广深城际铁路为例并进行两组对比分析。实验结果表明:考虑区域协调性的列车开行方案可以使旅客出行总广义费用降低约4.06%，铁路部门的效益提高约9.58%，旅客和铁路的系统总成本降低约23.27%；与遗传算法相比，改进的模拟退火算法在求解质量与收敛速度上均有较大提高。所提模型和算法可充分兼顾旅客和铁路双方利益，能够为城际列车开行方案优化问题提供有效解决方法。     

基于混合粒子群算法的列车停站方案优化

列车停站方案影响着旅客服务质量和运行效率,是列车开行方案的重要环节.本文建立了旅客列车停站方案的多目标规划模型以最大化区段可达性从而减少旅客旅行时间.针对传统的粒子群优化算法在处理复杂多维问题时,算法效率不高,易陷进局部最优,且无法有效处理离散问题等缺点,提出了一种将量子遗传算法引入到MPSO中的方法.算法整体采用粒子群算法,结合量子遗传算法的概率幅编码,并使用粒子群的速度更新公式来更新量子旋转门.算法引入量子遗传算法的全局探索和粒子群算法的种群智能体系,不仅提高了算法的收敛速度,同时增加了粒子多样性.最后,将改进的量子遗传粒子群算法（QGA_PSO）应用于ZDT函数优化和停站方案模型优化,证明了算法的有效性.     

考虑高铁与其它运输方式竞争的停站方案优化

为提升高速铁路在综合运输市场的竞争力,考虑快速性、方便性、舒适性和经济性指标构造效用函数.以高铁部门营业收入和效用函数值最大为目标,将短途运输高铁与公路的平均效用对比函数、长途运输高铁与航空的平均效用对比函数、客流需求、车站最低停站率、列车最大停站次数等作为主要约束条件,建立高速铁路停站方案的0-1多目标优化模型,设计...     

面向负载均衡的高铁路网列车开行方案优化方法

针对当前高速铁路运营过程中存在的运输需求与运力资源不匹配现象,面向负载均衡原理研究了路网条件下运能可适配的高速铁路旅客列车开行方案优化与评估方法.首先,针对路网条件下列车开行方案优化,构建以提升经济效益、社会效益和网络负载均衡为目标的非线性混合整数规划模型,并设计基于遗传算法和粒子群算法的两阶段混合搜索求解算法.在此基础上,考虑开行列车在高速铁路网中的抗干扰能力,建立了面向网络化运营场景的开行方案综合评估指标体系,揭示了故障场景下高速铁路网络性能的演化规律.最后,以实际高速铁路线路数据和运营数据为场景进行仿真实验,本文提出方法在保证运输需求和路局收益的同时能够有效地提升8.66%网络整体负载均衡性,增强发生故障时网络的抗干扰能力.     

面向负载均衡的高铁路网列车开行方案优化方法

针对当前高速铁路运营过程中存在的运输需求与运力资源不匹配现象,面向负载均衡原理研究了路网条件下运能可适配的高速铁路旅客列车开行方案优化与评估方法.首先,针对路网条件下列车开行方案优化,构建以提升经济效益、社会效益和网络负载均衡为目标的非线性混合整数规划模型,并设计基于遗传算法和粒子群算法的两阶段混合搜索求解算法.在此基础上,考虑开行列车在高速铁路网中的抗干扰能力,建立了面向网络化运营场景的开行方案综合评估指标体系,揭示了故障场景下高速铁路网络性能的演化规律.最后,以实际高速铁路线路数据和运营数据为场景进行仿真实验,本文提出方法在保证运输需求和路局收益的同时能够有效地提升8.66%网络整体负载均衡性,增强发生故障时网络的抗干扰能力.     

考虑车数限制的城市轨道交通非对称时刻表优化

在城市轨道交通中,优化时刻表是提高能效、改善乘客体验的重要手段.潮汐客流给时刻表的优化带来了较大的困难.此外,地铁建设期购置多少列车、运营期如何在有限车数下制定时刻表也是常常被忽视的问题.对此,以列车发车间隔为决策变量,构建列车运行模型以及乘客行为模型,考虑车数限制条件,设计列车能效与乘客体验的优化目标,建立一个非线性多目标优化问题.该问题采用NSGA-II算法进行求解.以某城市某条地铁线路为算例,通过放宽车数限制最多可以节能11.1%,同时增加车辆储备带来的边际效益递减;通过设计非对称的时刻表,可以在列车能效上最多得到4.6%的优化.当客流具有潮汐特征时,通过设计非对称时刻表可以带来显著的收益.     

基于灵活编组的城轨车底运用计划及鲁棒客流控制策略

针对通勤客流需求的动态性、不均衡性和随机性等复杂特征,提出基于灵活编组的城轨车底运用计划及鲁棒客流控制策略两阶段随机规划模型.第1阶段为编组类型指派和车底运用计划优化模型,以极小化系统运营成本为目标;第2阶段为车站协同限流鲁棒优化模型,以极小化乘客等待时间为目标.通过线性化方法将原模型重构为可被CPLEX等优化软件直接求解的混合整数线性规划模型.算例结果表明,灵活编组模式在仅增加0.5%乘客等待时间的基础上,可降低约30.2%的系统运营费用,表明灵活编组方案在满足客流需求的同时可合理地降低运营费用.此外,所提出鲁棒客流控制策略能够避免传统鲁棒优化方法过于保守的问题,对于实际运营过程中随机客流需求具有较好的适应性.     

Rescheduling trains with scenario-based fuzzy recovery time representation on two-way double-track railways

Severe weather conditions and inherent uncertainties in various components of railway traffic systems can lead to equipment breakdown and reduced capacity on tracks and stations. This paper formulates a two-stage fuzzy optimization model to obtain a robust rescheduling plan under irregular traffic conditions, and a scenario-based representation is adapted to characterize fuzzy recovery time durations on a double-track railway line. The model aims to minimize the expected total delay time in the rescheduled train schedule with respect to the original timetable. Two decomposed sub-models are further developed corresponding to the trains in different directions, and then GAMS optimization software is used to obtain the robust rescheduling plan. The numerical experiments demonstrate the effectiveness of the proposed approaches.     

A stochastic dual dynamic programming method for two-stage distributionally robust optimization problems

This paper studies a class of two-stage distributionally robust optimization (TDRO) problems which comes from many practical application fields. In order to set up some implementable solution method, we first transfer the TDRO problem to its equivalent robust counterpart (RC) by the duality theorem of optimization. The RC reformulation of TDRO is a semi-infinite stochastic programming. Then we construct a conditional value-at-risk-based sample average approximation model for the RC problem. Furthermore, we analyse the error bound of the approximation model and obtain the convergent results with respect to optimal value and optimal solution set. Finally, a so-called stochastic dual dynamic programming approach is proposed to solve the approximate model. Numerical results validate the solution approach of this paper.     

A two-stage programming approach for water resources management under randomness and fuzziness

In this study, a fuzzy stochastic two-stage programming (FSTP) approach is developed for water resources management under uncertainty. The concept of fuzzy random variable expressed as parameters’ uncertainties with both stochastic and fuzzy characteristics was used in the method. FSTP has advantages in uncertainty reflection and policy analysis. FSTP integrates the fuzzy robust programming, chance-constrained programming and two-stage stochastic programming (TSP) within a general optimization framework. FSTP can incorporate pre-regulated water resources management policies directly into its optimization process. Thus, various policy scenarios with different economic penalties (when the promised amounts are not delivered) can be analyzed. FSTP is applied to a water resources management system with three users. The results indicate that reasonable solutions were generated, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and different levels of constraint-violation probability. The developed FSTP was also compared with TSP to exhibit its advantages in dealing with multiple forms of uncertainties.     

Train scheduling and circulation planning in urban rail transit lines

This paper proposes a two-stage optimization approach to optimize the train schedule and circulation plan with consideration of passenger demand for an urban rail transit line. A train scheduling model is based on the operation of train services, which results a mixed integer nonlinear programming problem. Moreover, a train circulation model is formulated to adjust the departure and arrival times obtained by the train scheduling model to reduce the number of trains required, which results in a mixed integer linear programming problem. The case study based on the Beijing Yizhuang line illustrates the effectiveness of the proposed model and solution approach.     

The distributionally robust complementarity problem

We investigate the linear complementarity problem with uncertain parameters (ULCP) which affect the linear mapping affinely or quadratically. Assuming that the distribution of the uncertain parameters belongs to some ambiguity set with prescribed partial information, we formulate the ULCP as a distributionally robust optimization reformulation named as the distributionally robust complementarity problem (DRCP), which minimizes the worst case of an expected complementarity measure with a joint chance constraint that the probability of the linear mapping being nonnegative is not less than a given level. Applying the cone dual theory and S-procedure, we conservatively approximate the DRCP as a nonlinear semidefinite programming (NSDP) with bilinear matrix inequalities, which can be solved by the NSDP solver PENLAB. The preliminary numerical test on a constrained stochastic linear quadratic control problem shows that the DRCP as well as the corresponding solution method is promising.     

Urban rail transit planning using a two-stage simulation-based optimization approach

In urban metro systems, stochastic disturbances occur repeatedly as a result of an increment of demands or travel time variations, therefore, improving the service quality and robustness through minimizing the passengers waiting time is a real challenge. To deal with dwell time variability, travel time and demand uncertainty, a two-stage GA-based simulation optimization approach is proposed in order to minimize the expected passenger waiting times. The proposed method here has the capability of generating robust timetables for a daily operation of a single-loop urban transit rail system. The first stage of the algorithm includes the evaluation of even-headway timetables through simulation experiments. In the second stage, the search space is limited to the uneven-headway patterns in such a manner where the algorithm keeps the average of headways close to the best even-headway timetable, obtained from the first stage. The optimization is intended to adjust headways through simulation experiments. Computational experiments are conducted on Tehran Metropolitan Railway (IRAN) and the outcomes of optimized timetable obtained by this proposed method are demonstrated. This newly proposed two-stage search approach could achieve to a more efficient solution and speed up the algorithm convergence.