Transit Network Design Problem Research Articles

Electric Transit Network Design by an Improved Artificial Fish-Swarm Algorithm

AbstractThis study solves the electric transit network design problem (ETNDP) by simultaneously optimizing the layout of bus routes, the service frequency, and the location of charging depots. To e...

A cuckoo search based approach to design sustainable transit network

ABSTRACT Transit Network Design and Frequency Setting Problem (TNDFSP) is considered as a multi-objective optimization problem in which the routes of the transit network are determined while the operational constraints are taken into consideration. In this study, an optimization approach based on cuckoo search (CS) algorithm was proposed to solve this problem. Apart from the development of the optimization algorithm, the model incorporated sustainable design objectives and minimized the weighted sum of operator, user and external costs. Operator cost included the number of buses required to operate in the network and the facilities required to operate electric buses. The user costs consisted of waiting and in-vehicle travel time along with the number of transfers. Moreover, the pollutants emitted by conventional buses were considered as the external (environmental) cost. The results were compared on the basis of Mandl’s network. . Overall, the CS-based approach performed significantly in finding the optimal routes for the public transportation network.

An Improved NSGA-II Algorithm for Transit Network Design and Frequency Setting Problem

The transit network design and frequency setting problem is related to the generation of transit routes with corresponding frequency schedule. Considering not only the influence of transfers but also the delay caused by congestion on passengers’ travel time, a multi-objective transit network design model is developed. The model aims to minimize the travel time of passengers and minimize the number of vehicles used in the network. To solve the model belongs to a NP-Hard problem and is intractable due to the high complexity and strict constraints. In order to obtain the better network schemes, a multi-population genetic algorithm is proposed based on NSGA-II framework. With the algorithm, network generation, mode choice, demand assignment, and frequency setting are all integrated to be solved. The effectiveness of the algorithm which includes the high global convergence and the applicability for the problem is verified by comparison with previous works and calculation of a real-size case. The model and algorithm can be used to provide candidates for the sustainable policy formulation of urban transit network scheme.

Analysis of Transit Network Design Using GIS and Honeybee Algorithm in the City of Sanandaj, Iran

Public transit planning is a user-oriented problem, respectful of financial issues and involves different stakeholders such as the general public, the transportation provider and the local government. One of the main components of public transit planning is the transit network design (TND) problem. This research is an attempt to perform transit network design and analysis in the city of Sanandaj, Iran using the capabilities of GIS and Honeybee algorithm. Objectives of this study are formulating a multi-objective model of the TND problem, developing a GIS-based procedure for solving the TND problem and examination of the solutions using artificial metaheuristic methods such as honeybee algorithm. The transit network design approach in this research, aims to reduce the walking distance, the total travel distance and the total number of stops needed for a suitable transit service in Sanandaj, Iran. One of the contributions of this research is developing a transit network design with utilizing a spectrum of GIS software modelling functionalities and using the abilities of the artificial intelligence in modelling and assessment of the transit network.

Transit Network Design Using GIS and Ant Colony Optimization in Sanandaj

The public transit system in Sanandaj has been under review and modification for the last several years. The goal is to reduce the traffic congestion and the share of private car usage in the city and increase the very low share of the public transit. The bus routes in Sanandaj are not connected. There is no connected transit network with the ability to transfer between the routes in locations outside of the downtown terminal. The routes mostly connect the downtown core directly to the peripheries without providing travel options for passengers between peripheries. Although there has been some improvement in the transit system, lack of service in many populated districts of Sanandaj and town nearby makes the transit system unpopular and unreliable. This research is an attempt to provide solutions for the transit network design (TND) problem in Sanandaj using the capabilities of GIS and artificial intelligence methods. GIS offers several tools that enable the decision-makers to investigate the spatial correlations between different features. One of the contributions of this research is developing a transit network design with utilizing a spectrum of GIS software modeling functionalities. The visual ability of GIS is used to generate TNDs. Many studies focus on artificial intelligence as the main method to generate the TNDs, but the focus of this research is to combine GIS and artificial intelligence capabilities in order to generate a multi-objective GIS-based procedure to construct different bus network designs and explore and evaluate them to find the suitable transit network alternative.

An infeasible start heuristic for the transit route network design problem

ABSTRACT This paper develops an efficient heuristic for the transit network design problem, formulated as an integer programming problem. The model includes a preliminary step of route set generation, followed by an iterative procedure that simultaneously selects the best routes and corresponding headways. The iterative procedure is performed by an infeasible start algorithm that first assigns all candidate routes with the maximal frequency, and then iteratively eliminates routes and decreases frequencies of the less attractive ones. Routes are evaluated through a frequency-based transit assignment model that considers online information. The proposed model is applied to the Winnipeg transit network. The transit network found by the suggested model comprised fewer, faster and more frequent lines that serve high volume of passengers, compared to the given transit network. The running time of the algorithm is very short compared to existing methods, and its simplicity enables high level and detailed calibration.

A pareto artificial fish swarm algorithm for solving a multi-objective electric transit network design problem

This study presents a multi-objective optimization model for the urban electric transit network design problem by simultaneously determining the set of transit routes, the service frequency and the location of charging depots with the objectives of minimizing the costs for passengers and operators. The constraints about the bus route, charging depot, vehicle operation and charging schedule are considered to ensure the rational design and operational feasibility of the electric transit network. The solution approach is based on a Pareto artificial fish swarm algorithm (PAFSA) in combination with the crossover and mutation operators. The transit network in an urban region of Beijing is studied in a case study, revealing that the proposed optimization model solved by the PAFSA is able to provide the Pareto optimal solutions to design a relatively large-scaled transit network for the best fits between the passengers and operators.

Solving Transit Network Design Problem Using Many-Objective Evolutionary Approach

In many cities around the world, private vehicles are increasingly causing severe traffic congestion, pollution, and accidents. Public transports have been widely recognized as an effective way to improve urban life. To dissuade citizens from using private vehicles, it is necessary to design a practical, efficient, and economical public bus network. The transit network design problem (TNDP) determines the transit network (i.e., public bus network) for a city. It involves different stakeholders with diverse interests and values. To capture their conflicting expectations, numerous optimization objectives arise naturally. This paper introduces the TNDP as a many-objective optimization problem that generates a diverse set of alternative solutions. We apply several state-of-the-art many-objective evolutionary algorithms for the newly formulated TNDP. To efficiently explore the high-dimensional objective space of the TNDP, we develop problem-specific genetic operators for the evolutionary algorithm. We rigorously tested our approach on several benchmark datasets. The simulation results exhibit the effectiveness of the approach in addressing the challenges of a modern city. Based on the obtained results, we found $\theta $ -DEA to be the most robust among our employed algorithms. In addition, we observed the usefulness of the crossover operator, which randomly combines two solutions into one, and a simple mutation scheme, which is not biased to any objective function, to handle the many-objective nature of the TNDP.

Considering emissions in the transit network design and frequency setting problem with a heterogeneous fleet

Urban transportation contributes significantly to CO2 emissions. Public transport systems are a good strategy to reduce these, but the emissions generated by public transport vehicles should not be neglected during the design of the service. The Transit Network Design and Frequency Setting Problem (TNDFSP) has usually been addressed considering only the passengers’ and the operator's point of view. However, we show it is worthwhile to consider also the emissions already during this planning phase.This paper proposes a memetic algorithm to address the bi-objective TNDFSP where both the total travel time and the CO2 emissions are minimized. The analysis considers a heterogeneous fleet, meaning that buses of different sizes and technologies can be assigned under a budget constraint. The results on benchmark instances show that the proposed memetic algorithm performs as well as state-of-the-art algorithms where CO2 emissions are not considered. In addition, several experiments are carried out to observe the effect of incorporating emissions and heterogeneous fleet into the model. The heterogeneous fleet allows reducing travel times and emissions at the same time, compared to solutions without a heterogeneous fleet. Moreover, the explicit minimization of CO2 emissions within a bi-objective framework allows illustrating the trade-off between both objectives. Reductions of about 30% in the emissions can be achieved by increasing the travel time only 1%, while the costs for the operator remain the same. This clearly demonstrates the benefits of considering both the CO2 emissions and a heterogeneous fleet during the design stage of public transport systems.

Transit network design using a genetic algorithm with integrated road network and disaggregated O–D demand data

Evolutionary algorithms have been used extensively over the past 2 decades to provide solutions to the Transit Network Design Problem and the Transit Network and Frequencies Setting Problem. Genetic algorithms in particular have been used to solve the multi-objective problem of minimizing transit users’ and operational costs. By finding better routes geometry and frequencies, evolutionary algorithms proposed more efficient networks in a timely manner. However, to the knowledge of the authors, no experimentation included precise and complete pedestrian network data for access, egress and transfer routing. Moreover, the accuracy and representativeness of the transit demand data (Origin Destination matrices) are usually generated from fictitious data or survey data with very low coverage and/or representativity. In this paper, experiments conducted with three medium-sized cities in Quebec demonstrate that performing genetic algorithm optimizations using precise local road network data and representative public transit demand data can generate plausible scenarios that are between 10 and 20% more efficient than existing networks, using the same parameters and similar fleet sizes.

Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework

The metro systems of some megacities are facing serious oversaturation problem due to the heavy passenger flow during high peak hours. We consider the bus transit network design problem based on an existing metro network that can balance the modal split between metro and bus transit systems. The challenges facing this problem lie in that passengers have a different preference between metro and bus services, and the bus travel time and passenger demand may exhibit significant variations. This paper develops a two-step model framework to determine a bus transit network and departure frequency with consideration of travel time and passenger demand uncertainties. Firstly, we develop a column generation method to identify the candidate set of bus transit lines and passenger paths. Then a stochastic linear programming model is developed to optimize the bus line frequency and passenger path flow under demand and bus travel time uncertainty. To solve this model, a primal-dual online algorithm based on the online convex optimization theory is built to obtain the optimal solution with a theoretical performance guarantee. Finally, we implement the developed framework into an illustrative network and a real-world Beijing Second Ring public transit network to demonstrate its applicability and promising effects. The computational results show that the method can provide significant benefits for public transit systems.

Transit network design with pollution minimization

A critical step in the design of urban transport networks is the determination of the routes and the frequencies of buses. This situation entails a highly combinatorial optimization problem with a complex computational solution, even for small instances. Several studies have addressed such a situation, minimizing travel times as the main objective. However, the growing trend toward the development of sustainable transport operations requires that the design of the network also considers the emissions of toxic gases that result from combustion, which leads to a new variant of this type of problem, called the pollution transit network design problem. In this paper, the problem is formulated as a biobjective mathematical programming model. Complex problem instances are proposed for this problem, and by using a multi-objective genetic algorithm, we approach the unimodal and bimodal version of the problem by taking into account the elastic demand between buses and cars. By using the proposed mathematical programming model and the genetic algorithm for small and large problem instances, respectively, we show that the generated pollutant emissions are drastically reduced without increasing travel times or costs.

A heuristic aided Stochastic Beam Search algorithm for solving the transit network design problem

Abstract Designing efficient routes for a transit network is one of the main problems faced by city planners of the world. Due to the largeness and complexity of modern day road networks it is impossible to make a good route design manually. So, at present computer algorithms are used to design the routes. Designing routes for transit network is a multi-criteria decision making problem which has to search a large solution space to find an optimal solution. This paper presents a novel heuristic that can quickly generate good solutions. Also we propose a Stochastic Beam Search algorithm with a heuristic inspired successor operator. We conduct extensive experiments on some benchmark datasets and perform statistical tests on the results. We show that our algorithm can successfully explore the search space. Also we compare our results with previous studies and show that our algorithms produce superior results. In particular, for large datasets, the solutions generated by our heuristic in less than a second turn out to be better than solutions generated in two hours by the state of the art algorithm.

A multi-objective meta-heuristic approach for transit network design and frequency setting problem in a bus transit system

This paper studies a multi-objective transit network design and frequency setting (TNDFS) problem with the aim of determining a set of routes and frequency on each route for public buses. The TNDFS problem is solved in two stages. First, the transit network design problem is solved to generate a set of routes using an initial route set generation (IRSG) procedure combined with genetic algorithm. Second, the frequency setting problem is formulated as a multi-objective model to assign the frequency on each route with the objectives of minimizing the passenger time and the operating cost simultaneously. This problem is solved using the multi-objective particle swarm optimization with multiple search strategies (MMOPSO) to generate a Pareto-Front between the passenger time and the operating cost. An extensive computational experiment is performed on the benchmark Mandl’s Swiss network (Mandl, 1980) considering different scenarios and instances. The results obtained using the proposed approach to solve the transit network design problem are compared with that of the state-of-the-art methodologies available in the literature (Arbex & Cunha, 2015; Kechagiopoulos & Beligiannis, 2014; Nikolić & Teodorović, 2013), which outperforms in terms of trip directness and average travel time of passengers. For the frequency setting problem, the solutions obtained using MMOPSO are justified over the NSGA-II.

Transit network design with meta-heuristic algorithms and agent based simulation

Abstract In this work, a transit network design problem is presented. The problem is identified as a typical large-scale complex system. Subsequently, it is decomposed into its sub-components. The first two sub-components, which encompass the network design and frequency setting problems, are then tackled by means of an innovative solution framework that combines a genetic algorithm with agent-based travel demand modelling. An analysis of results obtained from applying the proposed method to different testing scenarios shows that it is capable of designing transit networks that address the individual and collective perspectives of different stakeholders. Hence it can be used as a viable decision support tool for policy makers in the transportation network sector.

Can travel time variability be ignored when solving the transit network design problem?

Can travel time variability be ignored when solving the transit network design problem?

Hybrid Differential Evolution‐Particle Swarm Optimization Algorithm for Multiobjective Urban Transit Network Design Problem with Homogeneous Buses

This paper considers an urban transit network design problem (UTNDP) that deals with construction of an efficient set of transit routes and associated service frequencies on an existing road network. The UTNDP is an NP‐hard problem, characterized by a huge search space, multiobjective nature, and multiple constraints in which the evaluation of candidate route sets can be both time consuming and challenging. This paper proposes a hybrid differential evolution with particle swarm optimization (DE‐PSO) algorithm to solve the UTNDP, aiming to simultaneously optimize route configuration and service frequency with specific objectives in minimizing both the passengers’ and operators’ costs. Computational experiments are conducted based on the well‐known benchmark data of Mandl’s Swiss network and a large dataset of the public transport system of Rivera City, Northern Uruguay. The computational results of the proposed hybrid algorithm improve over the benchmark obtained in most of the previous studies. From the perspective of multiobjective optimization, the proposed hybrid algorithm is able to produce a diverse set of nondominated solutions, given the passengers’ and operators’ costs are conflicting objectives.

Complete hierarchical multi-objective genetic algorithm for transit network design problem

Transit Network Design Problem is a multi-disciplinary problem that is considered one of the most intractable problems for real size networks. In the late 90s, Meta-heuristics started to prove more reliability to the problem. Genetic Algorithm (GA) is one of the popular Meta-heuristics which is usually implemented because it is simply adapted to the problem. In this study, GA is presented as a complete constructive multi-objective algorithm that creates its own routes from scratch then assembles the routes into efficient transit networks. Finally, it handles the multi-criteria nature of the problem until producing the optimal (near optimal) Pareto front solutions. A new frequency setting algorithm is also developed based on simulation results at the bus stop level which takes the bi-level decision making of both users and operators implicitly. Experimental studies on two real size networks are conducted to validate the methodology performance and robustness.

On strategic multistage operational two-stage stochastic 0–1 optimization for the Rapid Transit Network Design problem

The Rapid Transit Network Design planning problem along a time horizon is treated by considering uncertainty in passenger demand, strategic costs and network disruption. The problem has strategic decisions about the timing to construct stations and edges, and operational decisions on the available network at the periods. The uncertainty in the strategic side is represented in a multistage scenario tree, while the uncertainty in the operational side is represented in two-stage scenario trees which are rooted with strategic nodes. The 0–1 deterministic equivalent model can have very large dimensions. So-called fix-and-relax and lazy matheuristic algorithms, which are based on special features of the problem, are proposed, jointly with dynamic scenario aggregation/de-aggregation schemes. A broad computational experience is presented by considering a network case study taken from the literature, where the problem was only treated as a deterministic 0–1 model. 40 nodes in the strategic multistage tree are considered for passenger demand and investment cost and 8 uncertainties are considered for network disruption in each strategic node, in total 320 uncertain situations are jointly considered. For assessing the validity of the proposal, a computational comparison is performed between the plain use of a state-of-the-art optimization solver and the proposals made in this work. The model is so-large (2.6M constraints and 1.6M binary variables) that the solver alone cannot provide a solution in an affordable time. However, a mixture of the both matheuristics provides a solution with a good optimality gap requiring an affordable elapsed time.

Modeling horizontal and vertical equity in the public transport design problem: A case study

In the transportation literature, equity has been and is still used with a variety of meanings and purposes. Traditionally, equity has been considered in strategic transport planning but very few works have been addressing it in a quantitative way, detailing how to explicitly consider it at a transportation design level (tactical and/or operational) focusing on the consequent social role of transportation.This paper deals with how to quantitatively incorporate spatial and social equity principles in the Transit Network Design Problem. With respect to our previous preliminary study, this paper goes a step further in the definition of the solution to the problem, proposing a starting candidate route set generation procedure as a preliminary step to solve before the main optimization. The objective function considers at the same time the cost of users, operators and unsatisfied demand, and a comprehensive horizontal and vertical equity indicator is also specified among the constraints of the problem. An extensive sensitivity analysis investigates how the costs of the system vary with respect to the achieved level of equity. Then, an application to a real case of study is presented to validate the proposed methodology and highlight its usefulness and performances.