Transportation Network Design Problem Research Articles

Approximate dynamic programming for liner shipping network design

AbstractThe global containerised trade heavily relies on liner shipping services, facilitating the worldwide movement of large cargo volumes along fixed routes and schedules. The profitability of shipping companies hinges on how efficiently they design their shipping network; a complex optimization problem known as the liner shipping network design problem (LSNDP). In recent years, approximate dynamic programming (ADP), also known as reinforcement learning, has emerged as a promising approach for large-scale optimisation. This paper introduces a novel Markov decision process for the LSNDP and investigates the potential of ADP. We show that ADP methods based on value iteration produce optimal solutions to small instances, but their scalability is hindered by high memory demands. An ADP method based on a deep neural network requires less memory and successfully obtains feasible solutions. The quality of solutions, however, declines for larger instances, possibly due to the discrete nature of high-dimensional state and action spaces.

Liner shipping network design problem in modern transportation system of Russia

The liner shipping network design problem is considered in the paper. This problem is particularly relevant in the current global political and economic conditions, where finding optimal solutions for business becomes crucial for survival. State-of-the-art formulations and methods for solving the problem in domestic and international scientific papers are discussed. Four types of liner services such as simple service, “butterfly”, “pendulum” and complex service are described. A simple service that can be reduced to the traveling salesman problem is primarily focused on. Our own formulation of the problem is proposed and an example of liner shipping network description, based on the proposed formulation, is provided. In the example, presented in the paper, a container line, based on a single domestic seaport (Vladivostok) and four seaports in China, is demonstrated. It should be noticed, that the problem includes several optimization sub-problems (such as multi-commodity flow problem), solving which is important for finding best solutions for the designed shipping line, but is outside the bounds of this research. The liner services as a sequence of vessel calls to ports are described; and some results of the foregoing generation process are discussed. The optimal solution is selected from the set of generated solutions. It represents a particular case that simultaneously has the lowest costs for implementing the container line and the highest number of serviced container flows. It is noted that this solution is optimal only within the generated solution space and may not be optimal for the considered example of the problem.

Quantum computing for transport network design problems

Transport network design problem (TNDP) is a well-studied problem for planning and operations of transportation systems. They are widely used to determine links for capacity enhancement, link closures to schedule maintenance, identify new road or transit links and more generally network enhancements under resource constraints. As changes in network capacities result in a redistribution of demand on the network, resulting in changes in the congestion patterns, TNDP is generally modelled as a bi-level problem, which is known to be NP-hard. Meta-heuristic methods, such as Tabu Search Method are relied upon to solve these problems, which have been demonstrated to achieve near optimality in reasonable time. The advent of quantum computing has afforded an opportunity to solve these problems faster. We formulate the TNDP problem as a bi-level problem, with the upper level formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem that is solved using quantum annealing on a D-Wave quantum computer. We compare the results with Tabu Search. We find that quantum annealing provides significant computational benefit. The proposed solution has implications for networks across different contexts including communications, traffic, industrial operations, electricity, water, broader supply chains and epidemiology.

A Battery Electric Vehicle Transportation Network Design Model with Bounded Rational Travelers

With governments worldwide emphasizing environmental protection and the global focus on carbon reduction, the battery electric vehicle (BEV) industry has developed rapidly. An urban transportation network with BEVs as the main form of transportation will soon become mainstream. Motivated by the abovementioned background, a BEV transportation network design problem is investigated, and a network design model is established. The model aims to minimize the system travel time of BEV transportation networks and optimize the government’s lane expansion scheme (the location and number of lanes) under a limited budget. To consider the travel characteristics of BEV drivers, the charging time, range anxiety, and bounded rationality factors are simultaneously incorporated into the model. A heuristic algorithm is designed based on the active set algorithm to obtain the local optimal solution to the actual-scale problem. Moreover, a cutting-plane method is used to convert the original problem into a different form, and a column generation technique is embedded in the abovementioned algorithm to avoid the enumeration of paths. Sensitivity analyses of different levels of rationality of BEV drivers and government investment scales are performed. The experimental results demonstrate that the model and algorithm can effectively solve the problem and provide decision support for the government in formulating transportation infrastructure construction policies.

Cyclists' exposure to traffic-generated air pollution in multi-modal transportation network design problem.

Moving toward sustainable transportation is one of the essential issues in cities. Bicycles, as active transportation, are considered an important part of sustainable transportation. However, cyclists engage in more physical activity and air intake, making the quality of air that they inhale important in the programs that aim to improve the share of this mode. This paper develops a multi-modal transportation network design problem (MMNDP) to select links and routes for cycling, cars, and buses to decrease the exposure of cyclists to traffic-generated air pollution. The objective functions of the model include demand coverage, travel time, and exposure. The study also examined the effect of having exclusive lanes for bicycles and buses on the network. In the present study, the non-dominated storing genetic algorithm (NSGA-II) solves the upper-level and a method of successive average (MSA) unravels the lower level of the model. A numerical example and four scenarios evaluate the trade-off between different objective functions of the proposed model. The results reveal that considering exposure to air pollution in our model results in a slight increase in travel time (4%) while the exposure to traffic-generated air pollution for cyclists was reduced significantly (47%). Exclusive lanes also result in exposure reduction in the network (60%). In addition, the demand coverage objective function performs well in increasing the total demand in the network by 47%. However, more demand coverage leads to a rise in travel time by 28% and exposure by 58%. The model also showed an acceptable result in terms of exposure to traffic-generated air pollution compared to the model in the literature.

Uncertain Programming Model for the Cross-Border Multimodal Container Transport System Based on Inland Ports

The importance of inland ports in promoting current cross-border trade is increasingly recognized. In this work, we aim to design the entire network for the cross-border multimodal container transport system based on inland ports. Unlike previous studies, we consider strong uncertainty in cross-border transportation demand to be caused by a variety of realistic factors such as the global economic situation, trade policies among countries, and global epidemics, etc. To handle the demand uncertainty, we develop an uncertain programming model for the considered cross-border multimodal container transportation network design problem to minimize the expectation of the total costs, including carbon emissions, by imposing two types of chance constraints for capacity limitations. Under mild assumptions, we further convert the proposed uncertain model into its equivalent deterministic one, which can be solved by off-the-shelf solvers such as CPLEX, Gurobi, and Lingo. Finally, we illustrate the applicability of the proposed model by taking the Huaihai Economic Zone-Europe multimodal container transport system as a real-world case study. The computational results provide valuable suggestions and policy guidance regarding four issues: the inland port locations, the transportation route choices, the strategies for reducing the total cost, and the schemes for improving network performance against uncertain demand.

Incorporating travel time means and standard deviations into transportation network design problem: a hybrid method based on column generation and Lagrangian relaxation

ABSTRACT Travel times in real-world transportation networks are affected by many disruptions. When we conduct the network design optimization, the traffic condition and its resulting travel time variability should be taken into account. However, most of the previous network design optimizations adopted the lengths or expected travel times of links. Based on travel time means and standard deviations, we develop an arc-based model that is a nonlinear and concave integer program. By the Dantzig-Wolfe reformulation, we transform it into an equivalent column-based model that is an integer linear program with a large number of variables. Based on the column-based model, we develop a hybrid method based on column generation and Lagrangian relaxation. The restricted master problem can be settled by the linear programming solvers. The pricing subproblems incorporate independent reliable shortest path problems and a knapsack problem. In numerical experiments, the proposed method can generate feasible solutions with good integrality gaps.

Liner alliance shipping network design model with shippers' choice inertia and empty container relocation

<abstract><p>Liner companies have responded to escalating trade conflicts and the impact of the COVID-19 pandemic by forming alliances and implementing streamlined approaches to manage empty containers, which has strengthened the resilience of their supply chains. Meanwhile, shippers have grown more sensitive during these turbulent times. Motivated by the market situation, we investigate a liner alliance shipping network design problem considering the choice inertia of shippers and empty container relocation. To address this problem, we propose a bilevel programming model. The upper model aims to maximize the alliance's profit by optimizing the alliance's shipping network and fleet design scheme. The lower model focuses on optimizing the slot allocation scheme and the empty container relocation scheme. To ensure the sustainable operation of the alliance, we develop an inverse optimization model to allocate profits among alliance members. Furthermore, we design a differential evolution metaheuristic algorithm to solve the model. To validate the effectiveness of the proposed model and algorithm, numerical experiments are conducted using actual shipping data from the Asia-Western Europe shipping route. The results confirm the validity of the proposed model and algorithm, which can serve as a crucial decision-making reference for the daily operations of a liner shipping alliance.</p></abstract>

Optimization for bi-objective express transportation network design under multiple topological structures

With the rapid development of the courier industry, customers are placing higher demands on the cost and delivery time of courier services. Therefore, this paper focuses on the bi-objective express transportation network design problem (BO-ETNDP) to minimize the operation cost and maximum arrival time. A multi-structure parallel design methodology (MS-PDM) is proposed to solve the BO-ETNDP. In this methodology, all topological structures commonly used in designing transportation networks are sorted out. For each topological structure, a novel bi-objective nonlinear mixed-integer optimization model for BO-ETNDP is developed considering the impact of the hub’s sorting efficiency on the operation cost and arrival time. To solve these models, a preference-based multi-objective algorithm (PB-MOA) is devised, which embeds the branch-and-cut algorithm and Pareto dominance theory in the framework of this ranking algorithm. In the case study, the applicability of the proposed methodology is verified in a real-world leading express company. The results show that our methodology can effectively avoid the limitation of solving the BO-ETNDP with a specific structure. Besides, the suitable topology for designing express transportation networks in different scenarios are explored through the sensitivity analysis.

An Urban Bus Network Generation Algorithm Based on Particle Swarm Optimization and Force Field Properties

Due to continuous urban sprawl, large-scale bus network design has become a major challenge in urban transport planning. The continuous increase in urban population and scale makes the factors considered in the urban route network design increasingly complex. Contemporary public transportation network design problems are based more on efficiency goals such as the accessibility and comfort of the transportation network, which increases the difficulty of analyzing the problem. Bus network design is not only an NP-hard (nondeterministic polynomial) problem but also a multivariable and multiobjective problem. This paper focuses on the bivariate and multiobjective bus network design problem of route generation and station selection. This paper proposes an algorithm called the Pseudo Force Field. By combining the idea of Particle Swarm Optimization (PSO) and the properties of the force field, a feasible route generation scheme is provided for the design of the bus network. The algorithm does not need to determine the end station and has a high degree of completion of the demand. This solves the problem of the selection of terminal stations in large-scale road network design. On this basis, the article combines Genetic Algorithm (GA) and Pareto frontier to provide a new route optimization algorithm and proves the effectiveness of the algorithm. The model has achieved theoretical results in the design of the bus route network in the megacity of Shenzhen, China.

Simulation-based optimization of large-scale dedicated bus lanes allocation: Using efficient machine learning models as surrogates

Dedicated Bus Lanes (DBLs) have been implemented in many cities to boost buses’ reliability and to alleviate traffic congestions. However, how to correctly allocate DBLs across a large-scale real-world network is challenging. Simulation-Based Optimization (SBO) methods were utilized in this work to resolve this optimal allocation problem. Traditional discrete SBO methods are intractable when handling high-dimensional, costly, simulation-based Transportation Network Design Problems (TNDPs) using a limited computational budget. Thus, several efficient Machine Learning (ML)-based surrogate models and a Jackknife uncertainty estimator were introduced to existing SBO framework in this work. A number of comparative experiments between proposed methods and frequently-used Gaussian Process (GP)-SBO methods were conducted. A mesoscopic simulation and Dynamic Traffic Assignment (DTA) tool was adopted to evaluate the network performance.The results of numerical studies show that the optimization efficiency of proposed method is significantly higher than that of commonly used GP-based method when dealing with high dimensional problems. A real-world DBLs allocation case study in Guiyang, Guizhou Province, China again proves that efficient ML-based SBO method is capable to take much less CPU runtime to obtain a better solution than traditional method. The optimal DBLs allocation scheme found by one of the efficient ML-based methods raises the network performance by 5.05 %. A total of 1,376 h travel time is saved, and the average travel time per traveler drops by 0.75 min. In conclusion, efficient ML-based SBO method proposed in this study is more promising to handle large-scale, discrete, costly simulation-based DBLs allocation problems within a limited computational budget than common GP-based SBO methods.

Designing sustainable intermodal freight transportation networks using a controlled rail tariff discounting policy – The Iranian case

• A sustainable Intermodal Freight Transportation Network is developed. • The government determines a controlled rail tariff discount for rail companies and compensates the money that they lose due to offering the rail tariff discount by the money that will be collected from fuel saving in road freight transportation system. • The rail tariff discount is customized to the network’s OD flows and rail connections. • Multiple users’ route choice behaviors is modeled by applying a stated preference method. • A real case is studied and some insights are presented. Moving freight by intermodal services instead of road services not only saves a large amount of fuel but also improves sustainability. This paper presents a sustainable Intermodal Freight Transportation Network Design Problem (IFTNDP) in which the effectiveness of a new short-term policy, called controlled rail tariff discounting policy, is evaluated. In the IFTNDP, the government locates intermodal hubs and cooperates with rail companies to offer discounted rail tariffs on the rail connections of intermodal routes. Rail companies are allowed to customize the amount of rail tariff discounting for the network’s OD flows and rail connections. In addition, the government compensates the losses that rail companies incur due to offering the rail tariff discounts by the amount that will be collected from fuel savings in the freight transportation system. Hence, the government can boost the utility of intermodal transportation without investing funds to compensate the losses of rail companies. A stated preference model based on a questionnaire is adapted to identify users’ route choice behaviour. Then, the users’ route choice behavior is incorporated into the IFTNDP by a set of constraints, depending on the road and intermodal travelling times and costs. The model is applied to a real freight network and insights made by undertaking sensitivity analyses. The results demonstrate that the controlled rail tariff discounting policy not only increases the contribution of freight intermodal transportation in moving total freight but also enhances government’s profits from fuel savings after compensating rail companies’ losses.

Container ocean shipping network design considering carbon tax and choice inertia of cargo owners

The quality of the container ocean shipping network design directly affects the revenue of liner companies. In this paper, a container ocean shipping network design problem (COND) is investigated. Considering that the governments of many countries have proposed carbon-neutral initiatives, coupled with the constant fluctuations in the shipping market, the carbon tax and cargo owners’ choice inertia factors are taken into consideration simultaneously. To model the COND, a bi-level programming model is developed to jointly optimize the liner type, calling sequence, calling frequency, and sailing speed. The upper model aims to choose the network design scheme that maximizes the liner company’s revenue. The lower model optimizes the freight scheme of the liner company to evaluate the network design scheme selected by the upper model. To solve the abovementioned model, a genetic algorithm is designed, and a real-world trade shipping route between Asia and Western Europe is introduced to perform numerical experiments. Sensitivity analyses are conducted for different carbon tax rates and transportation demands. The experimental results show that the abovementioned model and algorithm can effectively address the COND and provide certain useful managerial insights for the liner company’s daily operation.

Designing reduced congestion road networks via an elitist adaptive chemical reaction optimization

We propose a new approach for solving a variant of the transportation Network Design Problem (NDP) where network congestion is reduced via traffic pattern redesign. The investigated NDP selects a set of roads to be converted from two-way traffic to one-way traffic. This allows increased traffic flow in the selected roads at the cost of restricting flow in the opposing direction roads. An optimal set of converted roads can result in significant congestion reduction for the network without the high construction costs associated with network capacity expansion. The new approach builds on the recently developed Chemical Reaction Optimization (CRO) metaheuristic and leverages Markov chain traffic assignment to predict traffic flow changes in response to network modifications. We propose an elitist and adaptive version of the CRO metaheuristic allowing it to more efficiently search for optimal solutions. We deploy the proposed approach to the cities of Abu Dhabi and Sioux Falls and report on our results. We also compare the Elitist Adaptive CRO (EACRO) results to those of Genetic Algorithm (GA) to demonstrate its performance. Compared to GA, the proposed approach reduces network congestions faster using fewer objective function evaluations. It also produces lower network congestion designs using long optimization runs. However, we find the algorithm to be sensitive to parameter calibration and dependent on the use of elitism for good performance. We explore the internal dynamics of the proposed algorithm and investigate its search effectiveness to understand its superior performance when compared to GA.

Ateş Böceği Algoritması Kullanılarak Toplu Taşıma Frekans Optimizasyonu ve Parametrelerinin Değerlendirilmesi

ABSTRACT: Over the last few decades, rapidly growing cities in terms of population and land use have led to many transportation-based problems such as longer travel times, traffic congestion, traffic crashes, and air and noise pollution. Increasing the modal share of transit systems appears to be one of the most effective methods to solve transportation-based problems. However, transit systems, particularly in countries having limited resources, should be used efficiently to achieve sustainable urban mobility. Even only adjusting frequencies of transit lines, with no infrastructure investment cost requirements, can provide a more efficient transit system. In this paper, a transit frequency setting model based on the Firefly Algorithm (FA), which is a relatively new metaheuristic, for the transportation network design problems is presented to minimize total user cost under a fleet size constraint. The proposed model is performed on a 10-route Mandl’s Test Network using different combinations of parameters to demonstrate the effect of parameter values on the solution quality. After that, the best solution of 30 solutions obtained by the calibrated parameter values is compared to the existing frequency set of the 10-route transit network. The results show that the FA can obtain better frequency sets by selecting the proper values for the parameters.

A branch-and-price algorithm for solving the single-hub feeder network design problem

In liner shipping, containers are generally transshipped in major hub ports in each region, between larger inter-region vessels and smaller feeder vessels. In this paper, we study the problem of designing the feeder vessel network, transporting containers between a regional hub and the surrounding feeder ports. The problem, as modelled, has many similarities with the split delivery vehicle routing problem, but with additional characteristics such as simultaneous pickups and deliveries and weekly departures. The problem also includes fleet sizing with a heterogeneous fleet and allows demand rejection at a penalty cost. We present a branch-and-price framework to solve the problem, where the subproblem is solved by enumerating vessel routes and subsequently assigning commodities by solving a min-cost flow problem for each commodity. The algorithm is tested on instances with up to 12 ports, which are all solved to optimality. Since the problem is similar to the liner shipping network design problem but without transshipments, we further study selected instances from the LINER-LIB instance suite. The Baltic instance is solved to proven optimality and we find the best known solution to the West Africa instance, significantly improving on what can be found in the literature.

Public Transportation Network Design and Frequency Setting: Pareto Optimality through Alternating-Objective Genetic Algorithms

The transportation network design and frequency setting problem concerns the optimization of transportation systems comprising fleets of vehicles serving a set amount of passengers on a predetermined network (e.g., public transport systems). It has been a persistent focus of the transportation planning community while, its NP-hard nature continues to present obstacles in designing efficient, all-encompassing solutions. In this paper, we present a new approach based on an alternating-objective genetic algorithm that aims to find Pareto optimality between user and operator costs. Extensive computational experiments are performed on Mandl’s benchmark test and prove that the results generated by our algorithm are 5–6% improved in comparison to previously published results for Pareto optimality objectives both in regard to user and operator costs. At the same time, the methods presented are computationally inexpensive and easily run on office equipment, thus minimizing the need for expensive server infrastructure and costs. Additionally, we identify a wide variance in the way that similar computational results are reported and, propose a novel way of reporting benchmark results that facilitates comparisons between methods and enables a taxonomy of heuristic approaches to be created. Thus, this paper aims to provide an efficient, easily applicable method for finding Pareto optimality in transportation networks while highlighting specific limitations of existing research both in regards to the methods used and the way they are communicated.

Hub network design for hazardous-materials transportation under uncertainty

This paper considers a hazardous materials (hazmat) transportation network design problem based on hub location topology under uncertainty. The control variables include decisions regarding location of hubs and hazmat response teams, along with the routing schemes. The model aims to minimize the total risk in the network. The measure of risk incorporates average response time to hazmat incidents as well as waiting time at hubs. To tackle the uncertainty of the problem, an efficient interactive approach using mean-absolute deviation and possibilistic programming is developed. Two heuristic algorithms based on lower bound procedure and rolling horizon scheme are presented to solve the model in large scale instances. The advantages of the presented methodologies are demonstrated through numerical experiments based on transportation networks from Sioux Falls, SD, and Western New York. We investigate different design schemes and discuss optimal decisions under different configurations.

A Continuous Transportation Network Design Problem with the Consideration of Road Congestion Charging

This paper proposes a biobjective continuous transportation network design problem concerning road congestion charging with the consideration of speed limit. The efficiency of the traffic network and the reduction of pollution in the network environment are improved by designing a reasonable road capacity enhancement and speed limit strategy. A biobjective bilevel programming model is developed to formulate the proposed network design problem. The first target of the upper problem is the optimization of road charging efficiency, and the other target is the total cost of vehicle emissions; these objectives are required to devise the optimal road capacity enhancement scheme, speed limiting schemes for different time periods, and the road pricing scheme. The lower-level problem involving travellers’ route choice behaviours uses stochastic user equilibrium (SUE) theory. Based on the nondominated sorting genetic algorithm, which is applied to solve the bilevel programming model, a numerical example is developed to illustrate the effectiveness of the proposed model and algorithm. The results show that the implementation of congestion charging measures on the congested road sections would help to alleviate road congestion in the transportation network, effectively save transportation infrastructure investment and limited urban land resources, increase fiscal revenue, and open up new sources of funds for urban infrastructure construction.

A public transport network design using a hidden Markov model and an optimization algorithm

Transportation Network Design Problem (TNDP) includes making the right choices possible when deciding a collection of design criteria to develop a current transportation network in response to rising traffic demand. Traffic congestion, higher maintenance and fuel prices, delays, accidents, and air emissions stem from the general rise in flow volume. Because of the NP-hard nature of this problem, a hidden Markov model and an Equilibrium Optimizer (EO) are employed in this paper to solve it. Each particle (solution) behaves as a search agent in EO, with its position. To reach the equilibrium condition, the search agents change their focus at random regarding the best-so-far approaches, including equilibrium candidates. A well-defined "generation rate" concept has been shown to elevate EO's capacity in avoiding local minima. This article provides a new method to lower the feasible travel time and the public travel cost using the hidden Markov model and EO algorithm. The suggested method's performance was compared to the performance of other algorithms on a test network. The related numerical outcomes show that it is more effective.