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。

中国中老年人C反应蛋白累积升高次数与躯体和非躯体抑郁症状的关系:前瞻性队列研究

背景 C反应蛋白(CRP)升高的累积效应及抑郁症状的不同维度是既往中老年人CRP与抑郁症状关联研究结论不一致的可能原因。目前中国关于CRP与抑郁症状的研究缺乏探索CRP累积升高次数对抑郁症状不同维度的影响。目的 探索中国中老年人CRP在2次连续测量中累积升高次数与抑郁症状及其躯体和非躯体症状之间的纵向关联。方法 本研究采用2011—2018年中国健康与养老追踪调查(CHARLS)公开数据,共纳入3 868名研究对象。依据CRP在2次连续测量中(2011年、2015年)的累积升高次数(CRP>3 mg/L)将研究对象分为累积升高0次组(n=2 918)、累积升高1次组(n=763)、累积升高2次组(n=187)。分别于2011年、2015年、2018年采用10项流行病学研究中心抑郁量表(CESD-10)评估抑郁症状,该量表分为躯体抑郁症状和非躯体抑郁症状。采用多重线性回归模型分析CRP在2次连续测量中累积升高次数与2018年抑郁症状总分/躯体抑郁症状得分/非躯体抑郁症状得分之间的纵向关联。采用Logistic回归模型分析CRP在2次连续测量中累积升高次数与2018年抑郁症状患病情况(是/否)之间的关联性。结果 多重线性回归分析结果显示,在调整所有协变量后,CRP在2次连续测量中升高2次相比于0次,是抑郁症状总分(β=1.22,P<0.05)、躯体抑郁症状得分(β=0.51,P<0.05)及非躯体抑郁症状得分(β=0.71,P<0.05)的影响因素。Logistic回归分析结果显示,在调整所有协变量后,CRP在2次连续测量中升高2次相比于0次,抑郁症状的患病风险更高(OR=1.64,95%CI=1.18~2.29)。结论 中国中老年人CRP累积升高次数与抑郁症状及其躯体和非躯体抑郁症状之间存在正向关联,及时治疗可能存在的慢性炎性疾病,避免其长期处于慢性炎症状态,可以降低抑郁的发生风险。

基于毕达哥拉斯模糊—累积前景理论的抽水蓄能容量规划综合决策

针对含新能源接入的电网中抽蓄电站容量规划问题,提出一种综合考虑定量、定性指标及决策者主观偏好的综合决策方法,旨在达到经济、技术性最优,生态影响最小的目的。首先构造了抽蓄容量规划评价指标体系,建立了火—风—抽蓄联合出力模型,优化抽蓄电站出力;然后采用毕达哥拉斯模糊数描述专家主观判断的模糊性;最后利用累积前景理论处理模糊数矩阵,考虑决策者的风险偏好类型。针对改进的IEEE30节点联合出力系统中不同的规划方案进行决策。结果表明,所提方法可体现决策者主观偏好对方案支持度的影响,为抽蓄容量规划的综合决策问题提供了参考。

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.

The prediction of exit choice using cumulative prospect value

Exit choice is essential for pedestrian safety and evacuation efficiency during the context of an emergency. Cumulative prospect theory is a widespread realistic decision-making theory that can transform choice outcomes and probabilities into subjective terms and integrate them as a parameter of cumulative prospect value (CPV), which determines the decision. The main contribution of this paper is the use of the CPV to predict exit choice. Furthermore, the different decision-making rules including Max, exponential(Expo), and Ratio (i.e., the three variable choice functions) were summarized and examined. This study used a confusion matrix to compare the predicted results with experimental data. Consequently, the parameters of Accuracy and F1-score showed that the predictions from Max and Expo were significantly more realistic while the results from Ratio were much more robust.

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。

基于累积前景理论的混合型多属性决策方法

针对带有决策者期望的混合型多属性决策问题,提出一种基于累积前景理论的决策分析方法.首先考虑了决策者的心理行为因素,以决策者对各属性的期望作为参照点,然后将具有清晰数、区间数和语言短语三种信息形式的决策矩阵转化为相对于参照点的益损决策矩阵,在此基础上,考虑决策者对待收益和损失的不同风险态度,依据累积前景理论计算每个方案的综合前景值,并依据综合前景值的大小对所有方案进行排序.最后,通过一个算例说明了该方法的可行性和有效性.

不确定性条件下的多目标多路径选择

不确定性条件下,综合多种性能指标,提供多条合理候选路径的路径选择方法还未得到有效解决.介绍一种利用累积前景理论进行多目标多路径选择的方法.为此,首先分析路段的不确定性属性和出行者的路径选择特性,基于路段广义出行费用定义参考点和值函数,建立多目标路径选择的累积前景理论;然后基于累积前景值定义合理替换路径,建立合理多路径选择模型;将改进的克隆选择算法与节点删除法相结合,设计了多路径选择模型的求解算法;最后,将该法和节点删除法、传统k-最短路算法应用于示范网络,比较分析了本文算法的有效性和快捷性.

基于累积前景理论的联盟企业知识转移演化博弈分析

知识转移过程是一个复杂的博弈过程,演化博弈论可以很好地解释转移主体行为。考虑到传统的演化博弈模型不能对知识转移主体非理性心理因素及风险偏好问题进行有效解释,本文将累积前景理论与演化博弈相结合,运用前景价值函数完善支付矩阵的部分参数,分析博弈模型的演化稳定策略。通过仿真模拟得出如下结论:知识转移存在两个演化稳定策略;转移策略由直接收益、转移成本及前景损益等因素决定;转移方的风险损失对转移策略影响较大,而接收方潜在收入对知识转移策略影响较小。