Multiclass Combined Models for Urban Travel Forecasting

Progress in formulating, solving and implementing models with multiple user classes that combine several travel choices into a single, consistent mathematical formulation is reviewed. Models in which the travel times and costs on the road network are link flow-dependent are considered; such models seek to represent congestion endogenously. The paper briefly summarizes the origins of this field in the 1950s and its evolution through the development of solution algorithms in the 1970s. The primary emphasis of the review is on the implementation and application of multiclass models. The paper concludes with a brief discussion of prospects for improved solution algorithms.     

Dynamic Traffic Assignment with More Flexible Modelling within Links

Traffic network models tend to become very large even for medium-size static assignment problems. Adding a time dimension, together with time-varying flows and travel times within links and queues, greatly increases the scale and complexity of the problem. In view of this, to retain tractability in dynamic traffic assignment (DTA) formulations, especially in mathematical programming formulations, additional assumptions are normally introduced. In particular, the time varying flows and travel times within links are formulated as so-called whole-link models. We consider the most commonly used of these whole-link models and some of their limitations.In current whole-link travel-time models, a vehicle's travel time on a link is treated as a function only of the number of vehicles on the link at the moment the vehicle enters. We first relax this by letting a vehicle's travel time depend on the inflow rate when it enters and the outflow rate when it exits. We further relax the dynamic assignment formulation by stating it as a bi-level program, consisting of a network model and a set of link travel time sub-models, one for each link. The former (the network model) takes the link travel times as bounded and assigns flows to links and routes. The latter (the set of link models) does the reverse, that is, takes link inflows as given and finds bounds on link travel times. We solve this combined model by iterating between the network model and link sub-models until a consistent solution is found. This decomposition allows a much wider range of link flow or travel time models to be used. In particular, the link travel time models need not be whole-link models and can be detailed models of flow, speed and density varying along the link. In our numerical examples, algorithms designed to solve this bi-level program converged quickly, but much remains to be done in exploring this approach further. The algorithms for solving the bi-level formulation may be interpreted as traveller learning behaviour, hence as a day-to-day traffic dynamics. Thus, even though in our experiments the algorithms always converged, their behaviour is still of interest even if they cycled rather than converged. Directions for further research are noted. The bi-level model can be extended to handle issues and features similar to those addressed by other DTA models.     

Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models

The historical origins, development and application of traffic network equilibrium models with variable origin–destination flows are examined in this review. The original formulation and analysis of this model during 1952–1955 by Beckmann, McGuire and Winsten at the Cowles Commission for Research in Economics is the starting point for the review. Subsequent research building upon the original formulation is described, and contrasted with urban travel forecasting practice stemming from the same period. Additional model developments through the end of the twentieth century are then summarized, followed by a brief discussion of travel forecasting practice and software development stimulated by the original formulation.     

Integrated Network Capacity Expansion and Traffic Signal Optimization Problem: Robust Bi-level Dynamic Formulation

This paper presents a robust optimization formulation, with an exact solution method, that simultaneously solves continuous network capacity expansion, traffic signal optimization and dynamic traffic assignment when explicitly accounting for an appropriate robustness measure, the inherent bi-level nature of the problem and long-term O-D demand uncertainty. The adopted robustness measure is the weighted sum of expected total system travel time (TSTT) and squared up-side deviation from a fixed target. The model propagates traffic according to Daganzo’s cell transmission model. Furthermore, we formulate five additional, related models. We find that when evaluated in terms of robustness, the integrated robust model performs the best, and interestingly the sequential robust approach yields a worse solution compared to certain sequential and integrated approaches. Although the adopted objective of the integrated robust model does not directly optimize the variance of TSTT, our experimental results show that the robust solutions also yield the least-variance solutions.     

A decomposition approach for the probabilistic maximal covering location-allocation problem

The maximal covering location problem (MCLP) maximizes the population that has a facility within a maximum travel distance or time. Numerous extensions have been proposed to enhance its applicability, like the probabilistic model for the maximum covering location-allocation with a constraint in waiting time or queue length for congested systems, with one or more servers per service center. This paper presents a solution procedure for that probabilistic model, considering one server per center, using a column generation and covering graph approaches. The computational tests report interesting results for network instances up to 818 vertices. The column generation results are competitive solving the instances in reasonable computational times, reaching optimality for some and providing good bounds for the difficult instances.     

A compact model and tight bounds for a combined location-routing problem

This paper considers a combined location-routing problem. We define an auxiliary network and give a compact formulation of the problem in terms of finding a set of paths in the auxiliary network that fulfill additional constraints. The LP solution to the considered model provides an initial lower bound and is also used in a rounding procedure that provides the initial solution for a Tabu search heuristic. Additionally, we propose a different lower bound based on the structure of the problem. The results of computational testing on a set of randomly generated instances are promising.     

Study on continuous network design problem using simulated annealing and genetic algorithm

In general, a continuous network design problem (CNDP) is formulated as a bi-level program. The objective function at the upper level is defined as the total travel time on the network, plus total investment costs of link capacity expansions. The lower level problem is formulated as a certain traffic assignment model. It is well known that such bi-level program is non-convex and non-differentiable and algorithms for finding global optimal solutions are preferable to be used in solving it. Simulated annealing (SA) and genetic algorithm (GA) are two global methods and can then be used to determine the optimal solution of CNDP. Since application of SA and GA on continuous network design on real transportation network requires solving traffic assignment model many times at each iteration of the algorithm, computation time needed is tremendous. It is important to compare the efficacy of the two methods and choose the more efficient one as reference method in practice. In this paper, the continuous network design problem has been studied using SA and GA on a simulated network. The lower level program is formulated as user equilibrium traffic assignment model and Frank–Wolf method is used to solve it. It is found that when demand is large, SA is more efficient than GA in solving CNDP, and much more computational effort is needed for GA to achieve the same optimal solution as SA. However, when demand is light, GA can reach a more optimal solution at the expense of more computation time. It is also found that increasing the iteration number at each temperature in SA does not necessarily improve solution. The finding in this example is different from [Karoonsoontawong, A., & Waller, S. T. (2006). Dynamic continuous network design problem – Linear bilevel programming and metaheuristic approaches. Network Modeling 2006 Transportation Research Record (1964) (pp. 104–117)]. The reason might be the bi-level model in this example is nonlinear while the bi-level model in their study is linear.     

Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.     

Efficient solution of the 3G network planning problem

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time (St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method (St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.     

Efficient solution of the 3G network planning problem

The 3G universal mobile telecommunications system (UMTS) planning problem is combinatorially explosive and difficult to solve optimally, though solution methods exist for its three main subproblems (cell, access network, and core network planning). We previously formulated the entire problem as a single integrated mixed-integer linear program (MIP) and showed that only small instances of this global planning problem can be solved to optimality by a commercial MIP solver within a reasonable amount of time ( St-Hilaire, Chamberland, & Pierre, 2006). Heuristic methods are needed for larger instances. This paper provides the first complete formulation for the heuristic sequential method ( St-Hilaire, Chamberland, & Pierre, 2005) that re-partitions the global formulation into the three conventional subproblems and solves them in sequence using a MIP solver. This greatly improves the solution time, but at the expense of solution quality. We also develop a new hybrid heuristic that uses the results of the sequential method to generate constraints that provide tighter bounds for the global planning problem with the goal of reaching the provable optimum solution much more quickly. We empirically evaluate the speed and solution accuracy of four solution methods: (i) the direct MIP solution of the global planning problem, (ii) a local search heuristic applied to the global planning problem, (iii) the sequential method and (iv) the new hybrid method. The results show that the sequential method provides very good results in a fraction of the time needed for the direct MIP solution of the global problem, and that optimum results can be provided by the hybrid heuristic in greatly reduced time.     

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.     

计算机博弈中序贯不完美信息博弈求解研究进展

计算机博弈是人工智能的果蝇和通用测试基准.近年来,序贯不完美信息博弈求解一直是计算机博弈研究领域的前沿课题.围绕计算机博弈中不完美信息博弈求解问题展开综述分析.首先,梳理计算机博弈领域标志性突破的里程碑事件,简要介绍4类新评估基准,归纳3种研究范式,提出序贯不完美信息博弈求解研究框架;然后,着重对序贯不完美信息博弈的博弈模型和解概念进行调研,从博弈构建、子博弈和元博弈、解概念以及评估3方面进行简要介绍;接着,围绕离线策略求解,系统梳理算法博弈论、优化理论和博弈学习3大类方法,围绕在线策略求解,系统梳理对手近似式学习、对手判别式适变和对手生成式搜索3大类方法;最后,从环境、智能体(对手)和策略求解3个角度分析面临的挑战,从博弈动力学和策略空间理论、多模态对抗博弈和序贯建模、通用策略学习和离线预训练、对手建模(剥削)和反剥削、临机组队和零样本协调5方面展望未来研究前沿课题.对于当前不完美信息博弈求解问题进行全面概述,期望能够为人工智能和博弈论领域相关研究带来启发.     

Dual search procedures for the exact formulation of the simple plant location problem with spatial interaction

We present an exact formulation of the simple plant location problem with spatial interaction. The formulation is based on the derivation of the spatially interactive travel behavior, often described through a spatial “gravity” model. By using techniques from separable programming, we can derive an exact formulation of the problem, i.e. without using any approximation of the function that describes the spatially interactive travel behavior. The resulting model is a pure zero-one location model. We also present a dual ascent and adjustment procedure for the linear programming relaxation of the exact formulation of the simple plant location problem with spatial interaction. Furthermore, we present a solution method based on Lagrangean relaxation and subgradient optimization. The two dual search procedures are computationally tested on problems with a maximal size of 50 × 100.     

基于随机演化的最小反馈弧集的改进算法

最小反馈弧集问题是一类组合优化问题,在实践中具有广泛的应用。随机演化是解决组合优化问题的一种通用的迭代随机过程。提出了一种基于随机演化的最小反馈弧集问题的改进算法。实验结果表明,改进之后的算法不仅提高了解的质量而且还减少了运行时间。     

Heuristic solutions to multi-depot location-routing problems

This paper presents a method for solving the multi-depot location-routing problem (MDLRP). Since several unrealistic assumptions, such as homogeneous fleet type and unlimited number of available vehicles, are typically made concerning this problem, a mathematical formulation is given in which these assumptions are relaxed. Since the inherent complexity of the LRP problem makes it impossible to solve the problem on a larger scale, the original problem is divided into two sub-problems, i.e., the location-allocation problem, and the general vehicle routing problem, respectively. Each sub-problem is then solved in a sequential and iterative manner by the simulated annealing algorithm embedded in the general framework for the problem-solving procedure. Test problems from the literature and newly created problems are used to test the proposed method. The results indicate that this method performs well in terms of the solution quality and run time consumed. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.Scope and purposeIn many logistic environments managers must make decisions such as location for distribution centers (DC), allocation of customers to each service area, and transportation plans connecting customers. The location-routing problems (LRPs) are, hence, defined to find the optimal number and locations of the DCs, simultaneously with the vehicle schedules and distribution routes so as to minimize the total system costs. This paper proposes a decomposition-based method for solving the LRP with multiple depots, multiple fleet types, and limited number of vehicles for each different vehicle type. The solution procedure developed is very straightforward conceptually, and the results obtained are comparable with other heuristic methods. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.     

Dynamic User Equilibrium Model for Combined Activity-Travel Choices Using Activity-Travel Supernetwork Representation

Integrated urban transportation models have several benefits over sequential models including consistent solutions, quicker convergence, and more realistic representation of behavior. Static models have been integrated using the concept of Supernetworks. However integrated dynamic transport models are less common. In this paper, activity location, time of participation, duration, and route choice decisions are jointly modeled in a single unified dynamic framework referred to as Activity-Travel Networks (ATNs). ATNs is a type of Supernetwork where virtual links representing activity choices are added to augment the travel network to represent additional choice dimensions. Each route in the augmented network represents a set of travel and activity arcs. Therefore, choosing a route is analogous to choosing an activity location, duration, time of participation, and travel route. A cell-based transmission model (CTM) is embedded to capture the traffic flow dynamics. The dynamic user equilibrium (DUE) behavior requires that all used routes (activity-travel sequences) provide equal and greater utility compared to unused routes. An equivalent variational inequality problem is obtained. A solution method based on route-swapping algorithm is tested on a hypothetical network under different demand levels and parameter assumptions.     

Sequential decision models for expert system optimization

Sequential decision models are an important element of expert system optimization when the cost or time to collect inputs is significant and inputs are not known until the system operates. Many expert systems in business, engineering, and medicine have benefited from sequential decision technology. In this survey, we unify the disparate literature on sequential decision models to improve comprehensibility and accessibility. We separate formulation of sequential decision models from solution techniques. For model formulation, we classify sequential decision models by objective (cost minimization versus value maximization) knowledge source (rules, data, belief network, etc.), and optimized form (decision tree, path, input order). A wide variety of sequential decision models are discussed in this taxonomy. For solution techniques, we demonstrate how search methods and heuristics are influenced by economic objective, knowledge source, and optimized form. We discuss open research problems to stimulate additional research and development     

Shortest paths in stochastic networks with correlated link costs

The objective is to minimize expected travel time from any origin to a specific destination in a congestible network with correlated link costs. Each link is assumed to be in one of two possible conditions. Conditional probability density functions for link travel times are assumed known for each condition. Conditions over the traversed links are taken into account for determining the optimal routing strategy for the remaining trip. This problem is treated as a multistage adaptive feedback control process. Each stage is described by the physical state (the location of the current decision point) and the information state (the service level of the previously traversed links). Proof of existence and uniqueness of the solution to the basic dynamic programming equations and a solution procedure are provided.     

The strong network orientation problem

This study presents models and heuristics for solving the strong network orientation problem (SNOP), which can model several tactical optimization problems of setting directions in urban networks. The objective is to set an orientation for each edge in an undirected graph such that the resulting digraph is strongly connected and the total travel distance between any pair of nodes is minimized (or maximized). Investigating tactical optimization problems such as SNOP is motivated by several challenges in urban networks due to the growth of population in urban areas, large number of daily trips, increasing price of maintaining urban networks, and the need to reduce air pollution and passive noise. Thus, a new trend is to utilize the urban networks better. In this context, we first use a multicommodity flow formulation to model the minimization problem. The maximization version is modeled by using the dual formulation of the shortest path problem. Then, scalable heuristic strategies for solving SNOP are investigated. For such purpose, we first propose basic components such as constructive heuristics, perturbations and local searches. They are combined into several metaheuristics based on local searches, multi-start and evolutionary schemes, i.e. Multistart Local Search, Iterated Local Search (ILS), Relaxed ILS, Evolutionary Local Search (ELS), Relaxed ELS, and Variable Neighborhood Search. Computational experiments have been performed to analyze the proposed methods in terms of efficiency and quality of solutions, using grid instances and a graph from downtown Clermont-Ferrand in France.     

Computer tutors can reduce student errors and promote solution efficiency for complex engineering problems

An ability to solve complex problems, for which a variety of solution paths are possible, is an important goal in engineering education. While feedback is critical to learning, hand grading of homework rarely provides effective, timely feedback on attempts to solve complex problems. Such feedback is also unfeasible in distance education contexts. A technology, based on the approach of cognitive tutors, is presented as a generally applicable method of providing automated feedback on complex problem solving, with truss problems studied in engineering as an example. The tutor maintains a cognitive model of problem solving for this class of problems, and associates various solution steps with distinct skills or knowledge components. One can determine whether students learn individual skills by measuring the error rate as a function of practice. Prior work has shown that for many skills the error rate indeed decreases with practice. New insight into the tutor׳s effectiveness, pertaining to the efficiency of student solution paths, is presented in this paper. While no explicit feedback is given regarding solution efficiency, it is found that students using the tutor become more efficient with practice. Furthermore, more efficient paths are found to be associated with making fewer errors.