基于电子路票征收及补偿的新型离散路网设计与算法

在城市交通网络设计中,可交易电子路票系统是一种新型且更加公平的拥挤收费方法。本文将具有征收与补偿机制的0分配可自由交易电子路票和路网离散改造设计结合起来共同研究城市道路交通网络设计与管理问题。建立的新型路网设计与管理模型同时考虑了0分配电子路票系统与离散路网设计。采用Logit随机用户均衡原理模拟出行者的路线选择行为,并设计具有路段容量和电子路票可行约束的随机均衡问题的有效算法。由于该模型是一个具有不动点约束的数学规划问题,求解比较困难,因此采用常见的群体智能优化算法求解该模型,数值实验验证了模型和算法的有效性和可行性。     

A Train Dispatching Model Under a Stochastic Environment: Stable Train Routing Constraints and Reformulation

After major capacity breakdown(s) on a railway network, train dispatchers need to generate appropriate dispatching plans to recover the impacted train schedule from perturbations and minimize the expected total train delay time under stochastic scenarios. In this paper, we propose a cumulative flow variables-based integer programming model for dispatching trains under a stochastic environment on a general railway network. Stable Train Routing (STR) constraints are introduced to ensure that trains traverse on the same route across different capacity breakdown scenarios, which are further reformulated to equivalent linear inequality constraints. Track occupancy and safety headways are modelled as side constraints which are dualized through a proposed Lagrangian relaxation solution framework. The original complex train dispatching problem is then decomposed to a set of single-train and single-scenario optimization subproblems. For each subproblem, a standard label correcting algorithm is embedded for finding the time dependent least cost path on a space-time network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted to demonstrate the efficiency and effectiveness of the proposed solution approach.     

Logistical support scheduling under stochastic travel times given an emergency repair work schedule

Stochastic factors during the operational stage could have a significant influence on the planning results of logistical support scheduling for emergency roadway repair work. An optimal plan might therefore lose its optimality when applied in real world operations where stochastic disturbances occur. In this study we employ network flow techniques to construct a logistical support scheduling model under stochastic travel times. The concept of time inconsistency is also proposed for precisely estimating the impact of stochastic disturbances arising from variations in vehicle trip travel times during the planning stage. The objective of the model is to minimize the total operating cost with an unanticipated penalty cost for logistical support under stochastic traveling times in short term operations, based on an emergency repair work schedule, subject to related operating constraints. This model is formulated as a mixed-integer multiple-commodity network flow problem and is characterized as NP-hard. To solve the problem efficiently, a heuristic algorithm, based on problem decomposition and variable fixing techniques, is proposed. A simulation-based evaluation method is also presented to evaluate the schedules obtained using the manual method, the deterministic model and the stochastic model in the operation stage. Computational tests are performed using data from Taiwan’s 1999 Chi-Chi earthquake. The preliminary test results demonstrate the potential usefulness of the proposed stochastic model and solution algorithm in actual practice.     

Computation and application of the paired combinatorial logit stochastic user equilibrium problem

The paired combinatorial logit (PCL) model is one of the recent extended logit models adapted to resolve the overlapping problem in the route choice problem, while keeping the analytical tractability of the logit choice probability function. However, the development of efficient algorithms for solving the PCL model under congested and realistic networks is quite challenging, since it has large-dimensional solution variables as well as a complex objective function. In this paper, we examine the computation and application of the PCL stochastic user equilibrium (SUE) problem under congested and realistic networks. Specifically, we develop an improved path-based partial linearization algorithm for solving the PCL SUE problem by incorporating recent advances in line search strategies to enhance the computational efficiency required to determine a suitable stepsize that guarantees convergence. A real network in the city of Winnipeg is applied to examine the computational efficiency of the proposed algorithm and the robustness of various line search strategies. In addition, in order to acquire the practical implications of the PCL SUE model, we investigate the effectiveness of how the PCL model handles the effects of congestion, stochasticity, and similarity in comparison with the multinomial logit stochastic traffic equilibrium problem and the deterministic traffic equilibrium problem.     

Stochastic structural topology optimization: discretization and penalty function approach

We consider structural topology optimization problems, including unilateral constraints arising from, for example, non-penetration conditions in contact mechanics or non-compression conditions for elastic ropes. To construct more realistic models and to circumvent possible failures or inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be stochastic. The resulting non-smooth stochastic optimization problem is an instance of stochastic mathematical programs with equilibrium constraints (MPEC), or stochastic bilevel programs. We propose a solution scheme based first on the approximation of the given topology optimization problem by a sequence of simpler sizing optimization problems, and second on approximating the probability measure in the latter problems. For stress-constrained weight-minimization problems, an alternative to -perturbation based on a new penalty function is proposed.     

Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations,Comparisons and Extensions

In this paper we formulate a network design model in which the traffic flows satisfy dynamic user equilibrium conditions for a single destination. The model presented here incorporates the Cell Transmission Model (CTM); a traffic flow model capable of capturing shockwaves and link spillovers. Comparisons are made between the properties of the Dynamic User equilibrium Network Design Problem (DUE NDP) and an existing Dynamic System Optimal (DSO) NDP formulation. Both network design models have different objective functions with similar constraint sets which are linear and convex. Numerical demonstrations are made on multiple networks to demonstrate the efficacy of the model and demonstrate important differences between the DUE and DSO NDP approaches. In addition, the flexibility of the approach is demonstrated by extending the formulation to account for demand uncertainty. This is formulated as a stochastic programming problem and initial test results are demonstrated on test networks. It is observed that not accounting for demand uncertainty explicitly, provides sub-optimal solution to the DUE NDP problem.     

Stabilization of stochastic nonlinear systems driven by noise ofunknown covariance

This paper poses and solves a new problem of stochastic (nonlinear) disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise. This is a natural stochastic counterpart of the problem of input-to-state stabilization in the sense of Sontag (1989). Our development starts with a set of new global stochastic Lyapunov theorems. For an exemplary class of stochastic strict-feedback systems with vanishing nonlinearities, where the equilibrium is preserved in the presence of noise, we develop an adaptive stabilization scheme (based on tuning functions) that requires no a priori knowledge of a bound on the covariance. Next, we introduce a control Lyapunov function formula for stochastic disturbance attenuation. Finally, we address optimality and solve a differential game problem with the control and the noise covariance as opposing players; for strict-feedback systems the resulting Isaacs equation has a closed-form solution     

Neural network approach for allocation with capacity

In this paper we discuss neural network approach for allocation with capacity constraints problem. This problem can be formulated as zero-one integer programming problem. We transform this zero-one integer programming problem into an equivalent nonlinear programming problem by replacing zero-one constraints with quadratic concave equality constraints. We propose two kinds of neural network structures based on penalty function method and augmented Lagrangian multiplier method, and compare them by theoretical analysis and numerical simulation. We show that penalty function based neural network approach is not good to combinatorial optimization problem because it falls in the dilemma whether terminating at an infeasible solution or sticking at any feasible solution, and augmented Lagrangian multiplier method based neural network can alleviate this suffering in some degree.     

Bilevel stochastic linear programming problems with quantile criterion

We propose a setting for a bilevel stochastic linear programming problem with quantile criterion. We study continuity properties of the criterial function and prove the existence theorem for a solution. We propose a deterministic equivalent of the problem for the case of a scalar random parameter. We show an equivalent problem in the form of a two-stage stochastic programming problem with equilibrium constraints and quantile criterion. For the case of a discrete distribution of random parameters, the problem reduces to a mixed linear programming problem. We show results of numerical experiments.     

Optimization-based scheduling for the single-satellite,multi-ground station communication problem

In this paper, we develop models and algorithms for solving the single-satellite, multi-ground station communication scheduling problem, with the objective of maximizing the total amount of data downloaded from space. With the growing number of small satellites gathering large quantities of data in space and seeking to download this data to a capacity-constrained ground station network, effective scheduling is critical to mission success. Our goal in this research is to develop tools that yield high-quality schedules in a timely fashion while accurately modeling on-board satellite energy and data dynamics as well as realistic constraints of the space environment and ground network. We formulate an under-constrained mixed integer program (MIP) to model the problem. We then introduce an iterative algorithm that progressively tightens the constraints of this model to obtain a feasible and thus optimal solution. Computational experiments are conducted on diverse real-world data sets to demonstrate tractability and solution quality. Additional experiments on a broad test bed of contrived problem instances are used to test the boundaries of tractability for applying this approach to other problem domains. Our computational results suggest that our approach is viable for real-world instances, as well as providing a strong foundation for more complex problems with multiple satellites and stochastic conditions.     

A high-performance nonlinear dynamic scheme for the solution of equilibrium constrained optimization problems

In this paper, a feedback neural network model is proposed to compute the solution of the mathematical programs with equilibrium constraints (MPEC). The MPEC problem is altered into an identical one-level non-smooth optimization problem, then a sequential dynamic scheme that progressively approximates the non-smooth problem is presented. Besides asymptotic stability, it is proven that the limit equilibrium point of the suggested dynamic model is a solution for the original MPEC problem. Numerical simulation of various types of MPEC problems shows the significance of the results. Moreover, the scheme is applied to compute the Stackelberg–Cournot–Nash equilibria.     

Bus-based park-and-ride system: a stochastic model on multimodal network with congestion pricing schemes

This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users’ route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users’ generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit (bus) flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.     

Stochastic and semidefinite optimization for scheduling in orthogonal frequency division multiple access networks

In this paper, we propose stochastic binary quadratic programs for the scheduling resource allocation process of a wireless orthogonal frequency division multiple access network. More precisely, we formulate a two-stage stochastic model, then we further extend the two-stage model by introducing a knapsack probabilistic constrained approach, and finally we propose a multi-stage stochastic program for this problem. The models are aimed at minimizing the total power consumption of the network at each time slot of the scheduling process subject to user bit rates, sub-carrier and modulation linear constraints. In order to compute lower bounds, we derive linear and semidefinite programming relaxations for each of the proposed models. The bounds are also compared with a basic variable neighborhood search metaheuristic approach. Numerical results show tight lower bounds for the semidefinite relaxations when compared to the linear ones and with the metaheuristic. Moreover, near optimal solutions are found with the semidefinite relaxations for the two-stage model without using probabilistic constraints and for the multi-stage program as well.     

Efficient computation of evacuation routes on a three-dimensional geometric network

We consider a real-time emergency evacuation problem that seeks to compute a set of rapid evacuation routes in a building. Given a three-dimensional geometric structure of the evacuation network, an emergency evacuation route is a sequence of movements of people away from the threat or actual occurrence of a hazard (such as a fire, a hidden bomb) to a safe exit in the network. In such a network each room/crossing/exit in the building is designated as a node and the corridors/staircases/links between the rooms are edges. The evacuation times assigned to the edges are normally distributed random variables. This stochastic routing problem subject to deadline constraints is NP-hard. We provide a new pseudo-polynomial-time dynamic programming algorithm to solve this problem. Based on this algorithm, we construct two types of approximation algorithm, namely a fully polynomial-time approximation scheme providing “almost-optimal” solutions and a fully polynomial-time approximately feasible scheme yielding a best “almost feasible” solution. We present a case study and results of computational experiments to illustrate the working and efficacy of the proposed solution methods, respectively.     

A Dual Approach for Solving the Combined Distribution and Assignment Problem with Link Capacity Constraints

In this paper, we consider the combined distribution and assignment (CDA) problem with link capacity constraints modeled as a hierarchical logit choice problem based on random utility theory. The destination and route choices are calculated based on the multi-nominal logit probability function, which forms the basis for constructing the side constrained CDA (SC-CDA) problem as an equivalent mathematical programming (MP) formulation. A dual MP formulation of the SC-CDA problem is developed as a solution algorithm, which consists of an iterative balancing scheme and a column generation scheme, for solving the SC-CDA problem. Due to the entropy-type objective function, the dual formulation has a simple nonlinear constrained optimization structure, where the feasible set only consists of nonnegative orthants. The iterative balancing scheme explicitly makes use of the optimality conditions of the dual formulation to analytically adjust the dual variables and update the primal variables, while a column generation scheme is used to iteratively generate routes to the working route set as needed to satisfy the side constraints. Two numerical experiments are conducted to demonstrate the features of the SC-CDA model and the computational performance of the solution algorithm. The results reveal that imposing link capacity constraints can have a significant impact on the network equilibrium flow allocations, and the dual approach is a practical solution algorithm for solving the complex SC-CDA problem.     

Opportunistic scheduling for streaming multimedia users in high-speed downlink packet access (HSDPA)

High-speed downlink packet access (HSDPA) achieves high data rates and high spectral efficiency by using adaptive modulation and coding schemes and employing multicode CDMA. In this paper, we present opportunistic algorithms for scheduling HSDPA users and selecting modulation/coding and multicode schemes that exploit channel and buffer variations to increase the probability of uninterrupted media play-out. First, we introduce a stochastic discrete event model for a HSDPA system. By employing the discrete event model, we transform the scheduling problem of providing uninterrupted play-out to a feasibility problem that considers two sets of stochastic quality-of-service (QoS) constraints: stability constraints and robustness constraints. A methodology for obtaining a feasible solution is then proposed by starting with a so-called stable algorithm that satisfies the stability QoS constraints. Next, we present stochastic approximation algorithms that adapt the parameters of the stable algorithm in a way that a feasible point for the robustness QoS is reached within the feasibility region of the stability QoS.     

A Nash equilibrium solution in an oligopoly market: The search for Nash equilibrium solutions with replicator equations derived from the gradient dynamics of a simplex algorithm

The present analysis applies continuous time replicator dynamics to the analysis of oligopoly markets. In the present paper, we discuss continuous game problems in which decision-making variables for each player are bounded on a simplex by equalities and non-negative constraints. Several types of problems are considered under conditions of normalized constraints and non-negative constraints. These problems can be classified into two types based on their constraints. For one type, the simplex constraint applies to the variables for each player independently, such as in a product allocation problem. For the other type, the simplex constraint applies to interference among all players, creating a market share problem. In the present paper, we consider a game problem under the constraints of allocation of product and market share simultaneously. We assume that a Nash equilibrium solution can be applied and derive the gradient system dynamics that attain the Nash equilibrium solution without violating the simplex constraints. Models assume that three or more firms exist in a market. Firms behave to maximize their profits, as defined by the difference between their sales and cost functions with conjectural variations. The effectiveness of the derived dynamics is demonstrated using simple data. The present approach facilitates understanding the process of attaining equilibrium in an oligopoly market.     

Aprojected gradient based game theoretic approach for multi-user power control in cognitive radio network

The fifth generation (5G) networks have been envisioned to support the explosive growth of data demand caused by the increasing traditional high-rate mobile users and the expected rise of interconnections between human and things. To accommodate the ever-growing data traffic with scarce spectrum resources, cognitive radio (CR) is considered a promising technology to improve spectrum utilization. We study the power control problem for secondary users in an underlay CR network. Unlike most existing studies which simplify the problem by considering only a single primary user or channel, we investigate a more realistic scenario where multiple primary users share multiple channels with secondary users. We formulate the power control problem as a non-cooperative game with coupled constraints, where the Pareto optimality and achievable total throughput can be obtained by a Nash equilibrium (NE) solution. To achieve NE of the game, we first propose a projected gradient based dynamic model whose equilibrium points are equivalent to the NE of the original game, and then derive a centralized algorithm to solve the problem. Simulation results show that the convergence and effectiveness of our proposed solution, emphasizing the proposed algorithm, are competitive. Moreover, we demonstrate the robustness of our proposed solution as the network size increases.     

基于机会约束规划的无线Mesh网跨层优化算法

以无线Mesh网的联合拥塞控制与功率控制为优化目标,针对网络中的不可控数据流与无线传播环境的时变随机性两类随机性因素,结合随机网络效用最大化理论,建立了无线Mesh网的跨层联合优化模型。将无线Mesh网络中的不可控数据流和时变无线传播的干扰建模为随机变量,采用机会约束规划方法进行分析,最后利用遗传算法求解该随机优化问题,并进行了仿真验证。仿真结果反映了网络速率、节点发射功率与链路置信水平三者之间的定量制约关系。