A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks

In this paper we study the problem of finding Origin–Destination (O–D) shortest paths in urban multimodal transportation networks, aiming at minimizing the overall cost, time and users' discommodity associated with the required paths. We present an approach based on the classical shortest path problem on a network representing the urban multimodal transportation system, i.e. the private, the public and the pedestrian modalities. Our idea is to make use of an ad hoc utility function for weighing the arcs both with their cost and time and considering at the same time the preference of the users related to all the possible transportation modalities. In particular, a utility measure is presented taking into a proper account the different users' propensities. The proposed approach has been developed for analysing the urban transportation network of an Italian city; the first experimental results are given in the paper.     

Multimodal K-shortest viable path problem in Tehran public transportation network and its solution applying ant colony and simulated annealing algorithms

This paper treats with K-shortest viable path problem in a transportation network including multiple modes. The considered modes are metro, rapid-bus, private and walking. In this network, a viable path is one that the number of mode changes is limited and the traverse time and also the walking, metro and private usage are restricted subjected to some constraints. The traverse time is defined dependent on congestion level. Because constrained shortest path is NP-hard, we extend two metaheuristic algorithms namely GASA and BACS for the given problem. GASA is a Greedy Algorithm Simulated Annealing and BACS is a bi-direction searching Ant Colony System made by two colonies of ants. We evaluate the validation of these algorithms applying several multimodal random networks. In addition, their results are compared with CPLEX 12.1. We find that GASA is appropriate for small networks and BACS has better performance in median and large-scale networks. Our results on Tehran network also demonstrate that BACS provides better objective values than BACS ones because Tehran public transportation is sparse.     

Evaluation and optimization of urban public transportation networks

So far, not much attention has been given to the problem of improving public transportation networks. In many cities these networks have been built sequentially and do not fit to the needs of the users any more. The results are long travel times and an unnecessarily high number of people who have to transfer. Compared to other investments for improving the service level of public transportation systems, the costs of rerouting the public vehicles are low and can, yet, highly improve the performance of the system.To evaluate a public transportation network, the shortest distance and the shortest route from node x to node y, taking the waiting times for a vehicle into account, must be known.It is shown in this paper, how to compute distances and routes efficiently for large networks. Using this algorithm it is described how to evaluate the average transportation cost of the passengers in a public transportation network.In the second part of the paper a heuristic algorithm is stated that improves a public transportation network using the average transportation cost as the objective.Finally, some experiences with real world problems are reported.     

Exact algorithms for multi-criteria multi-modal shortest path with transfer delaying and arriving time-window in urban transit network

This paper investigates the solution algorithms for the multi-criteria multi-modal shortest path problem (M-SPP), which belongs to the set of problems known as NP-hard, in urban transit network (UTN). The related M-SPP is one of the important and practical problems in several fields such as urban transportation system and freight transportation. The UTN is composed of multiple modes (e.g., automobile, bus, subway, light rail, pedestrian and so on). To get their destination, the passengers can alternate between different modes. As a special demand, the time-window is usually associated with the M-SPP. Because of the service time-limit of modes, the available modes at a stop are varied with the time. So the optimal M-SPP with arriving time-window cannot be simply obtained by finding the optimal M-SPP firstly and then reversely deducing the leaving time-window of the origin according to the arriving time-window of destination. In this paper, the M-SPP with arriving time-window is firstly proposed. To solve the multi-criteria M-SPPs (MM-SPP) with transfer delaying, an improved exact label correcting algorithm (LCA) is designed and, to solve the proposed MM-SPPs with both of transfer delaying and arriving time-window, an exact reverse LCA is designed. Finally, some computing examples are given to test the effectiveness of the designed algorithms.     

Steady state results for the M/M(a,b)/c batch-service system

The transportation system considered in this paper has a number of vehicles with capacity constraint, which take passengers from a source terminal to various destinations and return to the terminal. The trip times are considered to be independent and identically distributed random variables with a common exponential distribution. Passengers arrive at the terminal in accordance with a Poisson process. The system is operated under the following policy: when a vehicle is available and there are at least ‘a’ passengers waiting for service, then a vehicle is dispatched immediately. A recursive algorithm is derived to obtain the steady-state probability P(m, j) that there are m idle vehicles and j waiting passengers in the queue. Analytical expressions have been derived for passenger queue length distribution, average passenger queue length, the r-th moment of passenger waiting time in the queue, service batch size distribution and the average service batch size, all in terms of P(0,0).     

The 1-median and 1-highway problem

In this paper we study a facility location problem in the plane in which a single point (median) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L₁ or Manhattan metric. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. We represent the highway by a line segment with fixed length and arbitrary orientation. This problem was introduced in [Computers & Operations Research 38(2) (2011) 525–538]. They gave both a characterization of the optimal solutions and an algorithm running in O(n³logn) time, where n represents the number of clients. In this paper we show that the previous characterization does not work in general. Moreover, we provide a complete characterization of the solutions and give an algorithm solving the problem in O(n³) time.     

On some methods for entropy maximization and matrix scaling

We describe and survey in this paper iterative algorithms for solving the discrete maximum entropy problem with linear equality constraints. This problem has applications e.g. in image reconstruction from projections, transportation planning, and matrix scaling. In particular we study local convergence and asymptotic rate of convergence as a function of the iteration parameter. For the trip distribution problem in transportation planning and the equivalent problem of scaling a positive matrix to achieve a priori given row and column sums, it is shown how the iteration parameters can be chosen in an optimal way. We also consider the related problem of finding a matrix X, diagonally similar to a given matrix, such that corresponding row and column norms in X are all equal. Reports of some numerical tests are given.     

An equilibrium model for urban transit assignment based on game theory

The urban public transport system is portrayed as a special commodity market where passenger is consumer, transit operator is producer and the special goods is the service for passenger’s trip. The generalized Nash equilibrium game is applied to describe how passengers adjust their route choices and trip modes. We present a market equilibrium model for urban public transport system as a series of mathematical programmings and equations, which is to describe both the competitions among different transit operators and the interactive influences among passengers. The proposed model can simultaneously predict how passengers choose their optimal routes and trip modes. An algorithm is designed to obtain the equilibrium solution. Finally, a simple numerical example is given and some conclusions are drawn.     

碳排放限制下的冷藏集装箱多式联运路径优化

为了降低碳排放限制下的冷藏集装箱多式联运成本,实现节能减排的目的,高效的路径选择至关重要.该文基于碳排放限制的视角,针对多式联运网络中铁路和水路运输具有发班时间限制,以及冷藏集装箱需要考虑制冷费用、货损货差的特点,建立了在碳排放限制下以总成本最低为目标的优化模型.构建总成本时不仅考虑了运输费用和转运费用,还考虑了受发班时间影响而动态变化的冷藏费用和货损费用.设计了遗传算法求解,并进行了算例分析.结果表明:通过该模型和算法,可根据决策者的要求快速地选出成本最少的运输方案,为决策者提供决策支持.     

An effective algorithm for the two-stage location problem on a tree-like network

A two-stage facility location problem on a tree-like network is considered under the restriction that the transportation costs for a unit of production from one node to another is equal to the sum of the edges in the path connecting these nodes. Some exact algorithm with time complexity O(nm ³) is suggested for this problem, where n is the number of the production demand points and, m is an upper bound on the number of possible facility location sites of each stage.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

Alternative formulations of a combined trip generation,trip distribution,modal split,and trip assignment model

The traditional four-step model has been widely used in travel demand forecasting by considering trip generation, trip distribution, modal split and traffic assignment sequentially in a fixed order. However, this sequential approach suffers from the inconsistency among the level-of-service and flow values in each step of the procedure. In the last two decades, this problem has been addressed by many researchers who have sought to develop combined (or integrated) models that can consider travelers’ choice on different stages simultaneously and give consistent results. In this paper, alternative formulations, including mathematical programming (MP) formulation and variational inequality (VI) formulations, are provided for a combined travel demand model that integrates trip generation, trip distribution, modal split, and traffic assignment using the random utility theory framework. Thus, the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness. Qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution. Particularly, the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model. Furthermore, a self-adaptive Goldstein–Levitin–Polyak (GLP) projection algorithm is adopted for solving this special case.     

A continuous whole-link travel time model with occupancy constraint

The continuous dynamic network loading problem (CDNLP) aims to compute link travel times and path travel times on a congested network, given time-dependent path flow rates for a given time period. A crucial element of CDNLP is a model of the link performance. Two main modeling frameworks have been used in link loading models: The so-called whole-link travel time (WTT) models and the kinematic wave model of Lighthill–Whitham–Richards (LWR) for traffic flow.In this paper, we reformulate a well-known whole-link model in which the link travel time, for traffic entering a time t, is a function of the number of vehicles on link. This formulation does not require the satisfying of the FIFO (first in, first out) condition. An extension of the basic WTT model is proposed in order to take explicitly into account the maximum number of vehicles that the link can accommodate (occupancy constraint). A solution scheme for the proposed WTT model is derived.Several numerical examples are given to illustrate that the FIFO condition is not respected for the WTT model and to compare the travel time predictions effected by LWR and WTT models.     

Application of network theory and AHP in urban transportation to minimize earthquake damages

Network theory and Saaty's analytic heirarchy process (AHP) are considered to be effective methods for estimating a city's traffic pattern during the emergency period of an earthquake, and for evaluating the urban transportation network of that city. A graph is created in which the nodes are land uses (or a group of land uses), crossroads or junctions represent the city, and the arcs are the streets. AHP is used to determine the priority of trips, and shortest path techniques identify the fastest routes for daily trips, and the safest ones during earthquakes. A pareto diagram then shows those streets that play an important role in satisfying both criteria. On the basis of the trip patterns obtained, the accessibility of a city may be estimated. This methodology helps to identify the weak points of the transportation network after an earthquake. However, it can also be used to analyse plans for the expansion of existing cities. The methodology was employed in the city of Rasht after the devastating earthquake in northern Iran in 1990.     

Methods for routing with time windows

Consider a set of trips where each trip is specified a priori by a place of origin, a destination, a duration, a cost and a time interval within which the trip must begin. The trips may include visits to one or more specific points. Our problem is to determine the number of vehicles required together with their routes and schedules, so that each trip begins within his given time interval, while the fixed costs related to the number of vehicles, and the travel costs between trips are minimized. The problem is a generalization of the m-travelling salesman problem.We compare numerical results for 3 algorithms developed by our research team:

• 1.(1) Column generation on a set partitioning problem solved by simplex and branch-and-bound; columns are generated by a shortest path algorithm with time constraints on the nodes.
• 2.(2) Adaptation of the Carpaneto-Toth algorithm for the asymmetric travelling salesman problem: solution of network problems by relaxing scheduling constraints, and branch-and-bound on flow variables.
• 3.(3) Solution of network problems by relaxing scheduling constraints and branch-and-bound based on dividing the time windows.

     

An N-path user equilibrium for transportation networks

The traditional trip-based approach to transportation modeling has been employed for the past decade. The last step of the trip-based modeling approach is traffic assignment, which has been typically formulated as a user equilibrium (UE) problem. In the conventional perspective, the definition of UE traffic assignment is the condition that no road user can unilaterally change routes to reduce their travel time. An equivalent definition is that the travel times of all the used paths between any given origin–destination pair are equal and less than those of the unused paths. The underlying assumption of the UE definition is that road users have full information on the available transportation paths and can potentially use any path if the currently used path is overly congested. However, a more practical scenario is that each road user has a limited path set within which she/he can choose routes from. In this new scenario, we call the resulting user equilibrium an N-path user equilibrium (NPUE), in which each road user has only N paths to select from when making route choices in the network. We introduce a new formulation of the NPUE and derive optimality conditions based on this formulation. Different from traditional modeling framework, the constraints of the proposed model are of linear form, which makes it possible to solve the problem with conventional convex programming techniques. We also show that the traditional UE is a special case of an NPUE and prove the uniqueness of the resulting flow pattern of the NPUE. To efficiently solve this problem, we devise path-based and link-based solution algorithms. The proposed solution algorithms are empirically applied to networks of various sizes to examine the impact of constrained user path sets. Numerical results demonstrate that NPUE results can differ significantly from UE results depending on the number of paths available to road users. In addition, we observed an interesting phenomenon, where increasing the number of paths available to road users can sometimes decrease the overall system performance due to their selfish routing behaviors. This paradox demonstrates that network information should be provided with caution, as such information can do more harm than good in certain transportation systems.     

Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design

Freight transport has undesirable effects on the environment. The most prominent of these is greenhouse gas emissions. Intermodal freight transport, where freight is shipped from origin to destination by a sequence of at least two transportation modes, offers the possibility of shifting freight (either partially or in full) from one mode to another in the hope of reducing the greenhouse emissions by appropriately scheduling the services and routing the freight. Traditional planning methods for scheduling services in an intermodal transportation network usually focus on minimizing travel or time-related costs of transport. This article breaks away from such an approach by addressing the issue of incorporating environment-related costs (greenhouse gases, to be specific) into freight transportation planning and proposes an integer program in the form of a linear cost, multicommodity, capacitated network design formulation that minimizes the amount of greenhouse gas emissions of transportation activities. Computational results based on an application of the proposed approach on a real-life rail freight transportation network are presented.     

Dynamic journeying under uncertainty

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.     

Multimodal admittance method in waveguides and singularity behavior at high frequencies

This work presents a multimodal method for the propagation in a waveguide with varying height and its relation to trapped modes or quasi-trapped modes. The coupled mode equations are obtained by projecting the Helmholtz equation on the local transverse modes. To solve this problem we integrate the Riccati equation governing the admittance matrix (Dirichlet-to-Neumann operator). For many propagating modes, i.e. at high frequencies, the numerical integration of the Riccati equation shows that the rule is that this matrix has quasi-singularities associated to quasi-trapped modes.