Bi-level programming model for reconstruction of urban branch road network

Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network.

Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion

An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.

An Alternative Approach for Solving Bi-Level Programming Problems

An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

An Uncertain Programming Model for Competitive Logistics Distribution Center Location Problem

We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.

Bilevel Programming Model for Joint Scheduling of Arrival and Departure Flights Based on Traffic Scenario

In order to meet the needs of collaborative decision making,considering the different demands of air traffic control units,airlines,airports and passengers in various traffic scenarios,the joint scheduling problem of arrival and departure flights is studied systematically.According to the matching degree of capacity and flow,it is determined that the traffic state of arrival/departure operation in a certain period is peak or off-peak.The demands of all parties in each traffic state are analyzed,and the mathematical models of arrival/departure flight scheduling in each traffic state are established.Aiming at the four kinds of joint operation traffic scenarios of arrival and departure,the corresponding bi-level programming models for joint scheduling of arrival and departure flights are established,respectively,and the elitism genetic algorithm is designed to solve the models.The results show that:Compared with the first-come-firstserved method,in the scenarios of arrival peak&departure off-peak and arrival peak&departure peak,the departure flight equilibrium satisfaction is improved,and the runway occupation time of departure flight flow is reduced by 38.8%.In the scenarios of arrival off-peak&departure off-peak and departure peak&arrival off-peak,the arrival flight equilibrium delay time is significantly reduced,the departure flight equilibrium satisfaction is improved by 77.6%,and the runway occupation time of departure flight flow is reduced by 46.6%.Compared with other four kinds of strategies,the optimal scheduling method can better balance fairness and efficiency,so the scheduling results are more reasonable.

新能源电力系统不确定优化调度方法研究现状及展望

风电场和光伏电站出力的不确定性给电力系统优化调度带来很大技术挑战。文中主要介绍了考虑新能源不确定性的电力系统优化调度方法的研究现状及后续研究方向展望。首先,重点论述了各种不确定优化调度(UOD)方法,包括随机优化方法、鲁棒优化方法、随机鲁棒优化结合方法和基于人工智能技术的方法。其中,随机优化方法包括场景法、机会约束规划法和近似动态规划法;鲁棒优化方法包括传统鲁棒优化法和分布鲁棒优化法;随机鲁棒优化结合方法包括采样鲁棒优化法和分布鲁棒机会约束规划法。然后,介绍了每一种方法的优化模型形式、模型的转化和求解原理及其优缺点。最后,对UOD的后续重点研究方向进行展望,包括兼顾多个目标的UOD问题及多目标不确定优化方法、输配系统UOD问题及分布式不确定优化方法、考虑稳定性约束的UOD问题及含常微分方程约束的不确定优化方法、考虑管道传输动态的综合能源系统UOD问题及含偏微分方程约束的不确定优化方法。

不确定需求条件下考虑风险公平的危险品运输网络设计问题

危险品运输事故具有低概率、高后果的特征,降低事故风险是危险品运输研究的重点。危险品运输产生风险的同时伴随着风险在空间上的分布不均衡,此前研究关注总风险最小和风险公平的权衡,但较少考虑不确定需求下的运输网络。运输需求波动可能引起风险增加,为了解决不确定需求下考虑风险公平的危险品网络设计问题,构建了危险品多起点-终点(OD)对运输网络设计的双层混合整数规划模型,上层和下层问题分别为监管者选择关闭路段以及承运人选择最优路径,并通过自适应遗传算法和局部搜索算法进行求解。通过实例分析发现,不同需求情景特别是部分OD对中断时产生不同的最优网络设计方案,采用的遗传算法相比局部搜索算法运行时间稍长情况下获得的解更优。

不确定网络环境中任务卸载和资源分配联合优化方法

在不确定的无线网络环境中,由于任务到达、用户移动的随机性以及无线信道状态的时变性,导致出现不确定的任务云端排队时延、设备网络连接时间等网络环境特征,极大影响计算卸载效率和网络资源利用率。针对这一问题,建立了算网协同的动态任务卸载和资源联合分配模型,以最小化系统总能耗为目标,提出了基于随机模拟的任务卸载和算网资源联合分配多阶段随机规划优化算法(SS-MSSP),采用多阶段随机规划理论制定多阶段策略,并以后验算网资源分配的方式来追索补偿不确定网络环境的影响。仿真结果表明,在不确定的网络环境中,SS-MSSP算法保证了用户的计算时延需求,同时有效降低了系统能耗。

基于逐层试验设计的多维不确定参数对水资源配置结果的影响研究

不确定参数对水资源配置结果有着重要影响,相关研究较少定量评估不确定参数输入带来的系统响应情况变化。以区间数表示水资源配置涉及的不确定参数,构建了含多维不确定参数的不精确两阶段随机规划模型,然后采用逐层试验设计方法,量化不确定参数对目标值、配置决策等配置结果关键边界特征(上界、中值、下界)的主效应、交互效应和贡献率,最后以南渡江流域为实例验证本方法的实用性。结果表明,在规划年2030年,南渡江流域管理者可以按照预先定义的供水目标上限供水,预期供水总收益为[213.11,305.89]亿元。逐层试验设计能够定量分析多维不确定参数对配置结果的影响,中游、下游的农业和市政供水效益系数对供水总效益下界、中值、上界的贡献率可达60%以上,中游农业供水效益系数变化造成的供水总收益变化最大,对供水总效益的下界、中值、上界的主效应分别为44.22、48.28、43.01;P=95%特别枯水年来水量对总缺水量下界、中值、上界的贡献率可达50%以上,其主效应分别为-11.04、-22.30、-24.12,其变化造成的总缺水量变化最大;供水总效益或总缺水量下界、中值和上界的主要影响参数类型一致,但是不同界限上贡献率值不同,且交互效应影响很低。研究结果可为南渡江流域水资源配置方案制定和水安全保障分析提供科学依据。

基于鲁棒软时间窗和箱种代用的铁路集装箱空箱调运优化

传统的空箱调运问题多是研究箱种之间的彼此独立性,而忽略实际运输中箱种代用的情况,针对这一普遍现象,同时考虑需求站对集装箱空箱到达有时间窗约束,以及运输走行时间不确定性会对时间窗产生影响,建立了鲁棒软时间窗和箱种代用的集装箱空箱调运模型。首先,依据走行时间不确定性特点,建立鲁棒软时间窗模型;其次,通过等价变换和对偶变换,将鲁棒软时间窗模型转换为线性规划模型,简化了模型;最后,将集装箱调运模型转换为一般的整数线性规划模型,使模型更易于求解。研究结果表明,将箱种代用引入模型,有效地配置了空箱调运,提高了运输效率,降低了运输成本;对不确定走行时间p的个数进行灵敏度分析,结果表明箱种代用和不代用情况下p都存在一个较小的上界。

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Project Scheduling Problem with Uncertain Variables

Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.

Optimal Consumption under Uncertainties: Random Horizon Stochastic Dynamic Roy’s Identity and Slutsky Equation

This paper extends Slutsky’s classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes and life span. Utility maximization leading to a set of ordinary wealth-dependent demand functions is performed. A dual problem is set up to derive the wealth compensated demand functions. This represents the first time that wealth-dependent ordinary demand functions and wealth compensated demand functions are obtained under these uncertainties. The corresponding Roy’s identity relationships and a set of random horizon stochastic dynamic Slutsky equations are then derived. The extension incorporates realistic characteristics in consumer theory and advances the conventional microeconomic study on consumption to a more realistic optimal control framework.

A Lagrange Relaxation Based Approach to Solve a Discrete-Continous Bi-Level Model

In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.

基于不确定优化模型的滞销农产品逆向供应链网络分析与构建

文章基于农产品供应链网络的内涵价值,围绕以不确定优化数学模型构建滞销农产品逆向供应链网络为中心,建立了同时考虑网络总成本最小化和碳排放量最小化的多目标混合整数非线性规划模型,并借助三角模糊数、Lingo等工具优化了网络中设施的数量、位置和流量。研究表明:通过分析农产品滞销率在0.15~0.20范围内以及模糊参数增减10%的情况可知,模糊参数的变动会影响滞销农产品逆向供应链网络的经济效益,但设施选址方案是一致的,证明了模型的稳健性。此外,文章系统梳理农产品供应链网络研究现状、不确定优化模型刻画情况的意义在于,一方面为构建数学模型打实理论基础,另一方面为滞销农产品网络的构建研究提供了重要参考。

基于互联网出行数据的停车设施选址规划方法

为解决不确定需求下的停车设施选址问题,提出了基于互联网出行数据的停车设施选址规划方法。该方法基于居民通勤数据估计停车需求、识别备选停车设施点,并以停车设施的建设维护成本、停车设施到停车需求点的步行距离最小化为目标,构建不确定需求下的停车设施选址优化模型。为验证模型的可行性,基于北京市2021年9月—11月的居民通勤数据,针对海淀区中关村附近区域,构建并求解模型,并对建设维护总成本变化与停车需求不确定性之间的关系进行研究。研究结果表明:停车设施点的最优配置数量及其车位规模会随着停车需求被满足的置信水平(即实际停车需求小于或等于停车设施容量的概率)的提高而增加,且当置信水平达到0.9时,建设维护总成本变化显著提高,此时停车设施点的数量为30个,停车位总数为28862个。此外,建设维护总成本对停车需求不确定性水平较敏感,会随着停车需求不确定性的提升而增大,在停车需求不确定性水平分别为0.4,0.5,0.6时,停车设施建设和维护的相对总成本变化率分别为1.25,1.75,2.25,而在同一置信水平下,停车需求不确定性越高,相对总成本变化率越大,相对总成本对需求不确定性也较敏感。本研究对停车设施选址规划者,通过掌控设施点的停车容量与需求波动的情况,来有效地控制系统总成本,保证选址方案的鲁棒性。

A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.

Efficient Origin-Destination Estimation Using Microscopic Traffic Simulation with Restricted Rerouting

Traffic simulators are utilized to solve a variety of traffic-related problems.For such simulators,origin-destination(OD)traffic volumes as mobility demands are required to input,and we need to estimate them.The authors regard an OD estimation as a bi-level programming problem,and apply a microscopic traffic simulation model to it.However,the simulation trials can be computationally expensive if full dynamic rerouting is allowed,when employing multi-agent-based models in the estimation process.This paper proposes an efficient OD estimation method using a multi-agent-based simulator with restricted dynamic rerouting to reduce the computational load.Even though,in the case of large traffic demand,the restriction on dynamic rerouting can result in heavier congestion.The authors resolve this problem by introducing constraints of the bi-level programming problem depending on link congestion.Test results show that the accuracy of the link traffic volume reproduced with the proposed method is virtually identical to that of existing methods but that the proposed method is more computationally efficient in a wide-range or high-demand context.

考虑激励相容的不确定再制造绿色供应链研究

【目的/意义】在市场需求和废旧品回收质量水平不确定下,研究了激励相容理论下政府补贴对再制造绿色供应链的影响,以期寻找最优补贴政策和产品绿色度水平。【设计/方法】构建了考虑政府差异化补贴和产品绿色度的不确定再制造供应链系统成本模型,运用模糊机会约束法解决模型不确定因素,并运用粒子群算法和遗传算法寻找模型的近似最优解。【结论/发现】研究表明,再制造绿色供应链上的企业可以根据不同的需求制定最优的回收策略;当无政府补贴时,提高再制造绿色供应链的绿色度水平会增加成本,此时企业环保意愿较低;当政府基于激励相容理论实行差异化补贴时,提高再制造绿色供应链的绿色度水平的成本相对较低,从而有效提升企业环保意愿,实现政府和企业的目标相容,优化再制造绿色供应链。