Transit network design for small-medium size cities

This paper proposes a novel heuristic to solve the network design problem for public transport in small-medium size cities. Such cities can be defined as those with a diameter of a few kilometers with up to a few hundred thousand residents. These urban centers present a specific spatial configuration affecting the land use and mobility system. Transportation demand is widespread in origin and concentrated in a small number of attraction points close to each other. This particular structure of demand (‘many-to-few’) suggests the need for specific methodologies for the design of a transit system at a network level. In this paper, such design methodologies are defined in terms of models and solution procedures and tested on a selected case study. The solution methods show promising results. The key variables of the model are the routes and their frequencies. The constraints of the problem affect the overall demand to be served, the quality of the proposed service (transfer, load factors) and the definition of routes.     

Transit network design based on travel time reliability

This paper presents a transit network optimization method, in which travel time reliability on road is considered. A robust optimization model, taking into account the stochastic travel time, is formulated to satisfy the demand of passengers and provide reliable transit service. The optimization model aims to maximize the efficiency of passenger trips in the optimized transit network. Tabu search algorithm is defined and implemented to solve the problem. Then, transit network optimization method proposed in this paper is tested with two numerical examples: a simple route and a medium-size network. The results show the proposed method can effectively improve the reliability of a transit network and reduce the travel time of passengers in general.     

Transit network design by genetic algorithm with elitism

The transit network design problem is concerned with the finding of a set of routes with corresponding schedules for a public transport system. This problem belongs to the class of NP-Hard problem because of the vast search space and multiple constraints whose optimal solution is really difficult to find out. The paper develops a Population based model for the transit network design problem. While designing the transit network, we give preference to maximize the number of satisfied passengers, to minimize the total number of transfers, and to minimize the total travel time of all served passengers. Our approach to the transit network design problem is based on the Genetic Algorithm (GA) optimization. The Genetic Algorithm is similar to evolution strategy which iterates through fitness assessment, selection and breeding, and population reassembly. In this paper, we will show two different experimental results performed on known benchmark problems. We clearly show that results obtained by Genetic Algorithm with increasing population is better than so far best technique which is really difficult for future researchers to beat.     

Transit network design with allocation of green vehicles: A genetic algorithm approach

The use of fossil fuels in transportation generates harmful emissions that accounts for nearly half of the total pollutants in urban areas. Dealing with this issue, local authorities are dedicating specific efforts to seize the opportunity offered by new fuels and technological innovations in achieving a cleaner urban mobility. In fact, authorities are improving environmental performances of their public transport fleet by procuring cleaner vehicles, usually called low and zero emission vehicles (LEV and ZEV, respectively). Nevertheless there seems to be a lack of methodologies for supporting stakeholders in decisions related to the introduction of green vehicles, whose allocation should be performed since the network design process in order to optimize their available green capacity.In this paper, the problem of clean vehicle allocation in an existing public fleet is faced by introducing a method for solving the transit network design problem in a multimodal, demand elastic urban context dealing with the impacts deriving from transportation emissions.The solving procedure consists of a set of heuristics which includes a routine for route generation and a genetic algorithm for finding a sub-optimal set of routes with the associated frequencies.     

Geographic information system design for network equilibrium-based travel demand models

Travel demand analyses are useful for transportation planning and policy development in a study area. However, travel demand modeling faces two obstacles. First, standard practice solves the four travel components (trip generation, trip distribution, modal split and network assignment) in a sequential manner. This can result in inconsistencies and non-convergence. Second, the data required are often complex and difficult to manage. Recent advances in formal methods for network equilibrium-based travel demand modeling and computational platforms for spatial data handling can overcome these obstacles. In this paper we report on the development of a prototype geographic information system (GIS) design to support network equilibrium-based travel demand models. The GIS design has several key features, including: (i) realistic representation of the multimodal transportation network, (ii) increased likelihood of database integrity after updates, (iii) effective user interfaces, and (iv) efficient implementation of network equilibrium solution algorithms.     

Bus network design

This paper describes the bus network design problem, summarizes the different approaches that have been proposed for its solution and proposes a new approach incorporating some of the positive aspects of prior work. The proposed approach is intended to be easier to implement and less demanding in terms of both data requirements and analytical sophistication than previous methods. An algorithm is presented that can be used to design new bus routes taking account of both passenger and operator interests; however, this algorithm focuses on only a single component of the overall bus operations planning process described in this paper.     

Sustainable urban transit network design

Sustainability is a requirement for modern public transportation networks, as these are expected to play a critical role in environment-friendly transportation systems. This paper focuses on developing an efficient model for solving a sustainable oriented variant of the Transit Route Network Design Problem. The model incorporates sustainable design objectives, considers emission-free (electric) vehicles and introduces a direct route design approach with route structure and directness control. An application in a real world case, highlights the performance and benefits of the proposed model.     

On activity-based network design problems

This paper examines network design where OD demand is not known a priori, but is the subject of responses in household or user itinerary choices to infrastructure improvements. Using simple examples, we show that falsely assuming that household itineraries are not elastic can result in a lack in understanding of certain phenomena; e.g., increasing traffic even without increasing economic activity due to relaxing of space–time prism constraints, or worsening of utility despite infrastructure investments in cases where household objectives may conflict. An activity-based network design problem is proposed using the location routing problem (LRP) as inspiration. The bilevel formulation includes an upper level network design and shortest path problem while the lower level includes a set of disaggregate household itinerary optimization problems, posed as household activity pattern problem (HAPP) (or in the case with location choice, as generalized HAPP) models. As a bilevel problem with an NP-hard lower level problem, there is no algorithm for solving the model exactly. Simple numerical examples show optimality gaps of as much as 5% for a decomposition heuristic algorithm derived from the LRP. A large numerical case study based on Southern California data and setting suggest that even if infrastructure investments do not result in major changes in link investment decisions compared to a conventional model, the results provide much higher resolution temporal OD information to a decision maker. Whereas a conventional model would output the best set of links to invest given an assumed OD matrix, the proposed model can output the same best set of links, the same daily OD matrix, and a detailed temporal distribution of activity participation and travel from which changes in peak period OD patterns can be observed.     

Continuous equilibrium network design models

It is known that the network design problem with the assumption of user optimal flows can be modeled as a 0–1 mixed integer programming problem. Instead, we formulate the network design problem with continuous investment variables subject to equilibrium assignment as a nonlinear optimization problem. We show that this optimization problem is equivalent to an unconstrained problem which we solve by direct search techniques. For convex investment cost functions, the performance of both Powell's method and the method of Hooke and Jeeves is approximately the same with respect to computational requirements for a 24 node, 76 arc network. For the case of concave investment functions, Hooke and Jeeves was superior. The solution to the concave continuous model was very similar to that of the 0–1 model. Furthermore, the required solution time was far less than that required by the corresponding discrete model of the same network. The advantages and disadvantages of the continuous approach as well as the computational requirements are discussed.     

Fixed‐route taxi system: route network design and fleet size minimization problems

This paper introduces the taxi route network design problem (TXRNDP) for a fixed‐route taxi service operating in Iran and, in similar form, in various other developing countries. The service operates fairly similar to regular transit services in that vehicles are only permitted to follow a certain predetermined route on the network. The service is provided with small size vehicles and main features are that vehicles only depart if full and that there are no intermediate boarding stops. In Iran the service attracts a high modal share but requires better coordination which is the main motivation for the present study. We develop a mathematical programming model to minimize the total travel time experienced by passengers while constraining the number of taxi lines, the trip transfer ratio and the length of taxi lines. A number of assumptions are introduced in order to allow finding an exact rather than heuristic solution. We further develop a linear programming solution to minimize the number of taxis required to serve the previously found fixed‐route taxi network. Results of a case study with the city of Zanjan, Iran, illustrate the resulting taxi flows and suggest the capability of the proposed model to reduce the total travel time, the total waiting time and the number of taxi lines compared to the current taxi operation. Copyright © 2016 John Wiley & Sons, Ltd.     

A multi-commodity flow network design problem

There exist systems which can be usefully described by a network containingarcs through which a commodity of one type flows. This paper is concerned with finding a solution procedure for a particular multi-commodity flow network design problem. The problem is to identify a set of arcs in the network such that if travel is prohibited in them all flow travels by feasible paths and its total cost is minimal. The total flow in each arc may not exced its capacity, which is a known constant. Each arc and each node of the network has a non-negative constant unit traversal cost. Between each pair of distinct nodes there is a given non-negative rate of flow from the first vertex to the second which may be split up among a number of paths according to some constant traversal cost flow assignment process. The optimality criterion is the total traversal cost of all flow, which is to be minimized. Previous work on network design problems of this type is surveyed. The principal contribution of this paper is the presentation of a solution procedure for the above problem based on branch and bound enumeration. An illustrative numerical example is included. Computational experience gained in using the procedure with a FORTRAN IV program on an IBM 370 is favourable.     

The design of electric vehicle charging network

The promotion of Electric Vehicles (EVs) has become a key measure of the governments in their attempt to reduce greenhouse gas emissions. However, range anxiety is a big barrier for drivers to choose EVs over traditional vehicles. Installing more charging stations in appropriate locations can relieve EV drivers’ range anxiety. To determine the locations of public charging stations, we propose two optimization models for two different charging modes - fast and slow charging, which aim at minimizing the total cost while satisfying certain coverage goal. Instead of using discrete points, we use geometric objects to represent charging demands. Importantly, to resolve the partial coverage problem (PCP) for networks, we extend the polygon overlay method to split the demands on the road network. After applying the models to Greater Toronto and Hamilton Area (GTHA) and to Downtown Toronto, we show that the proposed models are practical and effective in determining the locations of charging stations. Moreover, they can eliminate PCP and provide much more accurate results than the complementary partial coverage method (CP).     

Aggregation effects on the network design problem

This article examines the effects of various network extraction schemes on the network design problem. Given an original network, many criteria can be used to identify subnetworks on which the network design problem is solved. For the purposes of this article, these subnetworks are obtained using an extraction algorithm which preserves the magnitude of the user equilibrium flows on the links of these subnetworks. The results of the implementation of the network design problem on the original and the extracted subnetworks are presented and compared. We conclude that very good solutions to the network design problem can be obtained from the use of highly aggregate networks.     

Pareto-improving transportation network design and ownership regimes

Private provision of public roads signifies co-existence of free, public-tolled and private-tolled roads. This paper investigates the Pareto-improving transportation network design problem under various ownership regimes by allowing joint choice of road pricing and capacity enhancement on free links. The problem of interest is formulated as a bi-objective mathematical programming model that considers the travel cost of road users in each origin-destination pair and the investment return of the whole network. The non-dominated Pareto-improving solutions of toll and/or capacity enhancement schemes are sought for achieving a win-win situation. A sufficient condition is provided for the existence of the non-dominated Pareto-improving schemes and then the properties of those schemes are analyzed. It is found that, under some mild assumptions, the optimal capacity enhancement is uniquely determined by the link flow under any non-dominated Pareto-improving scheme. As a result, the joint road pricing and capacity enhancement problem reduces to a bi-objective second-best road pricing problem. A revenue distribution mechanism with return rate guarantee is proposed to implement the non-dominated Pareto-improving schemes.     

Robust models for transportation service network design

In this paper robust models are presented for the transportation service network design problem, using the ferry service network design problem as an example application. The base assumption is that only the mean and an upper bound on the passenger demand are known. In one robust model, this information is supplemented by a lower bound on the demand, whereas in a second robust model, the assumption is made that the variance of the demand is known, in addition to the mean and upper bound. The relationship between the two models is investigated and characterized analytically. A case study using the ferry service in Hong Kong is provided to illustrate the models.     

Segment-based alteration for container liner shipping network design

Container liner shipping companies only partially alter their shipping networks to cope with the changing demand, rather than entirely redesign and change the network. In view of the practice, this paper proposes an optimal container liner shipping network alteration problem based on an interesting idea of segment, which is a sequence of legs from a head port to a tail port that are visited by the same type of ship more than once in the existing shipping network. In segment-based network alteration, the segments are intact and each port is visited by the same type of ship and from the same previous ports. As a result, the designed network needs minimum modification before implementation. A mixed-integer linear programming model with a polynomial number of variables is developed for the proposed segmented-based liner shipping network alternation problem. The developed model is applied to an Asia–Europe–Oceania liner shipping network with a total of 46 ports and 11 ship routes. Results demonstrate that the problem could be solved efficiently and the optimized network reduces the total cost of the initial network considerably.     

A reliability‐based network design problem

This paper presents a reliability‐based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity‐reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability‐based network design problem is formulated as a bi‐level program in which the lower level sub‐program is the probit‐based stochastic user equilibrium problem and the upper level sub‐program is the maximization of the new capacity reliability index. The lower level sub‐program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic‐flow pattern, and Monte Carlo stochastic loading. The upper level sub‐program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework.     

A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

Application of Ant System to network design problem

Network design problem (NDP) is the problem of choosing from among a set of alternative projects which optimizes an objective (e.g., minimizes total travel time), while keeping consumption of resources (e.g., budget) within their limits. This problem is difficult to solve, because of its combinatorial nature and nonconvexity of the objective function. Many algorithms are presented to solve the problem more efficiently, while trading-off accuracy with computational speed. This increase in speed stems from certain approximations in the formulation of the problem, decomposition, or heuristics. This study adapts a meta – heuristic approach to solve NDP, namely Ant System (AS). The algorithm is first designed, and then calibrated to solve NDP for the Sioux Falls test network. The behavior of the algorithm is then investigated. The result seems encouraging.     

Multi-objective optimization of a road diet network design

The present study focuses on the development of a model for the optimal design of a road diet plan within a transportation network, and is based on rigorous mathematical models. In most metropolitan areas, there is insufficient road space to dedicate a portion exclusively for cyclists without negatively affecting existing motorists. Thus, it is crucial to find an efficient way to implement a road diet plan that both maximizes the utility for cyclists and minimizes the negative effect on motorists. A network design problem (NDP), which is usually used to find the best option for providing extra road capacity, is adapted here to derive the best solution for limiting road capacity. The resultant NDP for a road diet (NDPRD) takes a bi-level form. The upper-level problem of the NDPRD is established as one of multi-objective optimization. The lower-level problem accommodates user equilibrium (UE) trip assignment with fixed and variable mode-shares. For the fixed mode-share model, the upper-level problem minimizes the total travel time of both cyclists and motorists. For the variable mode-share model, the upper-level problem includes minimization of both the automobile travel share and the average travel time per unit distance for motorists who keep using automobiles after the implementation of a road diet. A multi-objective genetic algorithm (MOGA) is mobilized to solve the proposed problem. The results of a case study, based on a test network, guarantee a robust approximate Pareto optimal front. The possibility that the proposed methodology could be adopted in the design of a road diet plan in a real transportation network is confirmed.