Robust user equilibrium model based on cumulative prospect theory under distribution-free travel time

The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.

Traffic assignment problem under tradable credit scheme in a bi-modal stochastic transportation network: A cumulative prospect theory approach

The traffic equilibrium assignment problem under tradable credit scheme(TCS) in a bi-modal stochastic transportation network is investigated in this paper. To describe traveler’s risk-taking behaviors under uncertainty, the cumulative prospect theory(CPT) is adopted. Travelers are assumed to choose the paths with the minimum perceived generalized path costs, consisting of time prospect value(PV) and monetary cost. At equilibrium with a given TCS, the endogenous reference points and credit price remain constant, and are consistent with the equilibrium flow pattern and the corresponding travel time distributions of road sub-network. To describe such an equilibrium state, the CPT-based stochastic user equilibrium(SUE) conditions can be formulated under TCS. An equivalent variational inequality(VI) model embedding a parameterized fixed point(FP) model is then established, with its properties analyzed theoretically. A heuristic solution algorithm is developed to solve the model, which contains two-layer iterations. The outer iteration is a bisection-based contraction method to find the equilibrium credit price, and the inner iteration is essentially the method of successive averages(MSA) to determine the corresponding CPT-based SUE network flow pattern. Numerical experiments are provided to validate the model and algorithm.

Cumulative prospect theory-based user equilibrium model with stochastic perception errors

The cumulative prospect theory(CPT) is applied to study travelers' route choice behavior in a degradable transport network. A cumulative prospect theory-based user equilibrium(CPT-UE) model considering stochastic perception error(SPE) within travelers' route choice decision process is developed. The SPE is conditionally dependent on the actual travel time distribution, which is different from the deterministic perception error used in the traditional logit-based stochastic user equilibrium. The CPT-UE model is formulated as a variational inequality problem and solved by a heuristic solution algorithm. Numerical examples are provided to illustrate the application of the proposed model and efficiency of the solution algorithm. The effects of SPE on the reference point determination, cumulative prospect value estimation, route choice decision and network performance evaluation are investigated.

The Evaluation of Alternative Risk Control Schemes Based on Cumulative Prospect Theory

Based on the analysis of the evaluation problems associated with the risk control scheme for major engineering projects,the evaluation method of the risk control scheme considering the irrational behavior of evaluation members in fuzzy random environment is proposed.Firstly,a maximum entropy model corresponding to any evaluation member is es-tablished by using triangular fuzzy random variables and grey correlation coefficient in order to obtain the weight of each risk factor of the member.Secondly,a nonlinear programming model is established according to the principle of minimiz-ing deviation to estimate the weight of different evaluation members on the evaluation of alternative risk control schemes.Lastly,the cumulative entropy model is used to calculate the weight of risk control schemes.Cumulative prospect theory obtains the comprehensive prospect utility value of each alternative to determine the optimal alternative.

基于CPT的异质通勤者多维出行决策模型

为了准确描述异质通勤者的风险态度及出行决策行为,假设通勤者的到达时间符合偏态分布,根据不同的可靠性要求计算偏好到达时间,综合考虑出行费用的影响,构建参照点与风险偏好系数函数,建立了基于累积前景理论(CPT)的异质通勤者多维出行决策模型.结果表明,在参照点与风险偏好系数异质的情况下,通勤者表现出不同的风险态度,从而采取不同的出行决策行为,多维出行决策模型得到的结果更符合实际.在单维出行决策时,风险偏好系数对出行决策结果的影响不显著;而在多维出行决策时,风险偏好系数对出行决策结果的影响显著.

包容性属性价值函数与近CPT前景价值模型

为克服累积前景理论(CPT)不能同时解释Allias选择行为与强选择行为的内在缺陷并解决已有相关研究在价值函数上的学术分歧,在借鉴需要层次理论的基础上通过整合CPT与范围-频率理论,给出了一个能够包容(或近似包容)学术界迄今所提出的各种价值函数的新函数即包容性属性价值函数.然后,以CPT价值函数仅是包容性属性价值函数的近似为立足点,给出了包容性属性价值模型及内含性依赖该模型的近CPT包容性属性价值函数.之后,以该函数为基础给出了关于前景价值评价的近CPT前景价值模型.数值分析表明:近CPT前景价值模型既有能力同时解释Allias选择行为与强选择行为,又能够在输入信息可比的条件下给出与CPT前景价值模型保持高度一致的选择结论,从而直接证实了近CPT前景价值模型较之于原模型的相对合理性,间接证实了包容性属性价值函数较之于CPT价值函数的相对合理性.

基于CPT-UE模型的城市道路施工顺序优化

合理的城市道路施工顺序对缓解施工期间的道路拥堵有着积极的作用。现有对城市道路施工顺序优化问题的研究主要集中在短时施工范畴,并且多数研究者主要利用交通仿真软件来计算因施工造成的交通延误,这些研究手段并不适用我国目前出现的大量长期施工现象。而现有对长期施工顺序优化的研究在适用性及精确性等方面还有一定的不足,对于所研究的施工问题也要求施工区的施工周期是月的整数倍,显然与实际有一定的差别。鉴于此,针对长期施工问题提出了一个城市道路施工顺序优化的双层规划模型。其中上层规划模型以路网上施工引起的总交通阻抗增加量最小为目标,下层规划模型以网络上的出行者都试图选择累积前景值最大的路径出行为目标。随后利用遗传算法对该双层规划模型进行求解,最后通过算例对出行者的心理参考点、网络上的施工队数量等影响最优施工顺序变化的因素进行了分析。研究发现,不同的参考点取值对整个网络总旅行时间增加量的影响不大,但对出行者在出行时的主观认知有着重要的影响;增加施工队的数量可以在一定程度上缩短总施工周期,但可能会增加网络的出行总成本,因此,在实际中存在一个最优的施工顺序,可以最小化施工对交通造成的不利影响。

基于改进CPT的矿工HVB变化分析

为探究矿工习惯性违章行为(HVB)的变化路径,从演化博弈的角度,基于改进的累积前景理论(CPT),构建矿工与安全监管人员间的收益感知矩阵;在综合考虑双方利益的基础上,引入薪酬激励作为变量,构建奖酬变动对矿工HVB变化的影响模型;以王庄煤矿为例,运用Matlab仿真软件模拟验证改进措施。结果表明:以改进的CPT为基础的演化博弈能有效探究矿工HVB的变化过程;只有当4个约束不等式同时被满足时,安全程度才能达到最高;在一定条件下,薪酬激励程度越高,矿工违章行为发生概率越低。提高薪酬水平和矿工风险感知能力有利于降低矿工HBV的发生概率,提升煤矿安全管理水平。

基于MA-CPT模型的出行方式选择模型优化

为提高累积前景理论在出行方式选择建模应用中的准确性,考虑个体对于时间与费用货币态度的不同,优化原始累积前景理论(cumulative prospect theory,CPT)模型的时间值函数和时间权重函数.首先,针对时间压力下出行方式偏好发生转变的现象,将出行方式分为刚性出行和弹性出行,改进刚性出行情景下的时间值函数形式,并根据出行时间特性求出时间权重函数中吸引力参数的取值范围,构建MA-CPT (mental accountingcumulative prospect theory)模型;其次,根据实证数据标定时间权重函数中辨别力参数和吸引力参数的取值;最后,标定MA-CPT模型结果并检验其拟合优度,对比MA-CPT模型和CPT模型的命中率.实证分析结果表明:刚性出行和单行出行场景下,时间权重函数的吸引力参数值均大于1.00;MA-CPT模型在刚性出行和弹性出行情境下的拟合优度分别为0.17和0.18;相比于CPT模型,MA-CPT模型在弹性出行和刚性出行情景下的命中率分别提高了12.2%和19.8%.

Multi-Objective Optimization of Urban Bus Network Using Cumulative Prospect Theory

Multi-objective optimization of urban bus network can help improve operation efficiency of the transit system and develop strategies for reducing urban traffic congestion in China. The work used cumulative prospect theory, currently the most influential model for decision under uncertainty,to optimize urban bus network. To achieve the research objective, the work developed the theoretical framework of urban bus network optimization, including optimization principle, optimization objectives and constraints. Furthermore, optimization objectives could comprehensively reflect expectations of passengers and bus companies from the dimension of time, space and value. It is more scientific and reasonable compared with only one stakeholder or dimension alone in the previous studies. In addition,the technique for order preference by similarity to ideal solution(TOPSIS) was used to determine the positive and negative ideal alternative. The correlations between the optimization alternatives and the ideal alternatives were estimated by grey relational analysis simultaneously. The cumulative prospect theory(CPT) was used to determine the best alternative by comparing comprehensive prospect value of every alternative, accurately describing decision-making behavior compared with expected utility theory in actual life. Finally, Case of Xi'an showed that the method can better adjust the bus network,and the optimization solution is more reasonable to meet the actual needs.

The Park-and-Ride Behavior in a Cumulative Prospect Theory-Based Model

As an effective travel demand management means,park-and-ride(P&R)mode is an important part of urban traffic.In a traffic corridor with P&R service,suppose that the travel time on highway is uncertain,a cumulative prospect theory(CPT)-based travel decision-making model is established with two travel modes of driving all the way and(P&R).With this setting,the effect of various factors such as the transit fare rate,the parking fee and the total travel demand on the CPT-based and expected utility theory(EUT)-based equilibrium results are compared.In addition,the sensitivity analysis focus on CPT-related parameters are also performed.The numerical results in our case show that the equilibrium flow on P&R mode is always underestimated in an EUT-based model,especially for a low total travel demand.Also,it is found that reducing the transit fare rate or parking fee for P&R station and raising the parking fee for CBD has the same effect on promoting more commuters transfer to P&R mode,whatever CPT-based or EUT-based model is employed.Furthermore,commuter’s reference dependence characteristic is also observed in a CPT-based model,and it is especially noticeable when the road uncertainty is large.

A New Method of Portfolio Optimization Under Cumulative Prospect Theory

In this paper, the portfolio selection problem under Cumulative Prospect Theory （CPT） is investigated and a model of portfolio optimization is presented. This model is solved by coupling scenario generation techniques with a genetic algorithm. Moreover, an Adaptive Real-Coded Genetic Algorithm （ARCGA） is developed to find the optimal solution for the proposed model. Computational results show that the proposed method solves the portfolio selection model and that ARCGA is an effective and stable algorithm. We compare the portfolio choices of CPT investors based on various bootstrap techniques for scenario generation and empirically examine the effect of reference points on investment behavior.

A Cumulative Prospect Theory Based Counterterrorism Resource Allocation Method under Interval Values

Strategic resource allocation into decision-making model plays a valuable role for the defender in mitigating damage and improving efficiency in military environments.In this paper,we develop a defensive resource allocation model based on cumulative prospect theory (CPT),which considers terrorists' psychological factors of decision-making in reality.More specifically,we extend existing models in the presence of multiple attributes and terrorists' deviations from rationality using a multi-attribute cumulative prospect theory.In addition,interval values are used to cope with uncertainties regarding gain and loss.Comparative studies are also carried out to demonstrate the differences among minmax,Nash equilibrium (NE),and traditional probability risk analysis (PRA) strategies.Results show that the defender's optimal defensive resource allocation will change along with terrorists' behaviors and the proposed model makes more sense compared with other traditional resource allocation strategies.

An Improved Group Decision-Making Model for the Investment Options of Small-Scale Photovoltaic Systems Based on Cumulative Prospect Theory and Choquet Integral

With the development of photovoltaic(PV) industry, installing small-scale PV systems which are integrated into the buildings becomes popular. Therefore, it is important to make optimal investment decisions for investors and consumers. This paper proposes an improved group decision-making method which integrates the cumulative prospect theory and Choquet integral for the investment options of small-scale PV systems. From the perspective of sustainability, the alternatives are evaluated by four criteria, including economic benefits, solar energy condition, carbon emissions and social benefits. Since the performances of criteria are given by decision makers as linguistic variables, the proposed method measures the criteria values by intuitionistic trapezoidal fuzzy numbers. Then the alternatives are evaluated and ranked to determine the optimal option. Finally, the proposed method is implemented in a case study to illustrate its feasibility and effectiveness.

基于ED-GRA和CPT的图书馆供应商选择的决策方法

为了解决高校图书馆图书供应商选择问题中的决策者认知复杂问题,反应决策者的心理与行为特征,本文提出一种基于认知复杂的多属性决策方法。首先,采用欧式距离(ED)和灰色关联分析法(GRA)确定专家权重和图书供应商评价指标体系的权重;然后,提出基于累积前景理论(CPT)的多属性决策方法,计算图书供应商的综合前景值。

基于云模型和累积前景理论的山区铁路绿色低碳线路优选

铁路作为一种绿色的交通方式,在我国的交通强国战略和双碳目标中扮演重要角色,开展绿色低碳研究势在必行。铁路选线设计统领项目全局的阶段,对后续的建设、运营具有决定性作用。然而,设计比选易受到专家和决策者的影响,专家评价存在不确定性和模糊性,而决策者存在主观偏好,难以定性评判方案优劣。此外,项目初期需要反复修改优化设计方案,难以获得全面的方案数据,而目前贯彻绿色低碳理念的选线设计研究较少,缺少相应的工程案例做参考,定量描述线路设计低碳设计水平存在挑战。为了解决上述问题,提出一种基于云模型和累积前景理论的山区铁路绿色低碳线路设计优选方法。结合山区铁路特征和绿色低碳设计理念构建评价体系,用熵权法和CRITIC法获取指标权重。采用云模型综合考虑专家评语中的不确定性和模糊性,借助累积前景理论考虑决策者的主观偏好。提出在设计阶段估算铁路线路碳排放量和车站光伏发电潜力的公式,实现了对线路低碳设计水平的定量描述。以中老铁路孟阿至班普亚一段为例进行分析,所得结论与专家一致,验证了方法的有效性。这将为山区铁路线路设计提供决策支持,为交通碳排放计算和光伏潜力评估提供一种新的思路,有助于我国的绿色低碳转型和经济高质量发展。

有限理性条件下多层次轨道交通客流拥堵传播机理研究

多层次轨道交通系统通过融合不同制式轨道交通,实现了运输能力的灵活配置和互补,但也增加了客流拥堵传播的不确定性,极易出现客流拥堵的跨层级传播。在分析乘客出行有限理性选择行为的基础上,通过引入心理账户理论,建立了广义出行时间账户和拥堵程度账户,并利用改进的价值函数与决策权重函数,刻画了乘客出行路径的综合交易效用。通过考虑出行方式与出行路径双因素,建立了基于巢式Logit-心理账户-累积前景理论(Nested Logit-mental Accountingcumulative Prospect Theory, NL-MA-CPT)的乘客出行方式选择预测模型。在此基础上,通过引入改进的易感-感染-恢复(Upgraded Susceptible-infected-recovered, USIR)模型,提出了考虑乘客选择行为的多层次轨道交通客流拥堵传播模型,并刻画了有限理性条件下的传播速率和恢复速率。最后,以北京市多层次轨道交通为例,验证模型的有效性,并通过灵敏度分析,揭示相关关键因素对拥堵传播的影响机理。研究结果表明:多层次轨道交通网络客流拥堵传播具有显著的波动性和收敛性特征,而传播速率和恢复速率直接影响拥堵传播的强度及影响范围,且随着网络层数的增加,乘客出行选择决策的有限理性特征对拥堵传播的影响更加显著。本研究可为运营企业制定客流拥堵控制策略提供一定的理论参考依据。

基于累积前景理论的共享停车泊位匹配模型

为缓解停车资源紧缺问题,合理利用现有泊位资源,在充分考虑商业区停车用户的出行目的和个体异质性的基础上构建基于累积前景理论(cumulative prospect theory,CPT)的共享停车泊位匹配模型。通过累积前景理论分析商业区用户的停车选择行为,在考虑停车资源利用情况和用户对泊位满意程度的基础上,以泊位利用率和综合前景价值综合最大为目标函数,采用遗传算法对模型进行求解。通过算例分析模型泊位分配方案差异,发现相较于泊位利用率最大(maximum parking utilization rate,MPUR)模型的分配方案,CPT方案的泊位利用率与MPUR方案相同,但用户平均满意度提升了4.6%。为进一步验证模型的有效性和适用性,分别在不同供需情况和不同停车规模下对模型进行仿真实验,结果表明:在供大于求、供需平衡和供不应求3种情况下,CPT模型能在保证泊位利用率的基础上,使用户平均满意度分别提升了10.72%、8.64%和24.62%。模型可根据不同用户个体特性和泊位选择心理,为用户分配该停车场景下更符合用户心理预期的泊位,提升用户对停车分配方案的满意度,为泊位管理者提供了更加人性化的泊位分配方案参考。

基于累积前景理论的轨道交通非常态乘客出行方式选择行为研究

当城市轨道交通系统出现异常,乘客容易产生盲目、恐慌、从众等心理,并做出非完全理性的决策。现有MNL模型基于信息完备假设与完全理性假设,在面对非常态情景时的适应性较差。为刻画非常态情况下乘客的不完全理性并考虑乘客个体差异,解决MNL模型的不适用性,本文针对轨道交通非常态情景,通过累积前景理论进行建模。首先,综合考虑时间、费用、舒适度与便捷性4个对乘客出行行为有直接影响的因素,构建基于累积前景理论的轨道交通非常态乘客出行方式选择模型,刻画乘客的不完全理性行为。然后,开展问卷调查用以标定模型参数,并结合调查结果构建服从泊松分布的差异化参考点,描述模型的参考点依赖现象,差异化参考点的泊松分布检验值满足大于等于0.05的检验标准,解释了乘客出现不同决策结果的本质,使综合前景呈现随参考点波动的态势。最后,将引入差异化参考点的基于累积前景理论的轨道交通非常态乘客出行方式选择模型与多项Logit(multinomial logit,MNL)模型进行对比。研究结果表明:针对非常态情景,本文模型体现了乘客面对非常态时的有限理性与个体差异性,宏观角度下的交通方式划分率计算结果总体偏差较MNL模型减小了4.9%,微观角度下乘客个体决策结果预测准确率较MNL模型提升了25.4%,整体效果优于MNL模型,验证了模型的合理性。研究成果可以为轨道交通非常态下的交通需求预测与应急响应提供理论支撑。

基于改进多属性决策的铁路车站改建方案评价研究

为进一步提升铁路车站改建项目方案决策的科学性和有效性,首先在对铁路车站改建方案的主要影响因素进行全面梳理的基础上,构建改建方案评价体系,涵盖地区枢纽适应性与协调性、运输组织及能力、既有营运线干扰、工程可实施性、经济与社会效益5个指标层;然后,提出基于改进多属性决策的铁路车站改建方案评价方法,即区间直觉模糊环境下基于累积前景理论的改进MABAC算法,并考虑在属性权重未知的情况下采用熵权法确定属性权重,以更准确地刻画决策者的心理偏好;随后,给出铁路车站改建方案评价的具体步骤;最后,以某枢纽车站改建为例,采用所提方法对其改建方案进行评价,并将评价结果与实际采用方案以及其他决策方案评价结果对比,对比结果的一致性证明该方法具有实用性和有效性,而且在逻辑上更加贴近现实决策因素,可为铁路车站改建方案的优劣评判提供依据。