Transportation Network Design Problem Research Articles

Improving Initial Generations in PSO Algorithm for Transportation Network Design Problem

Transportation Network Design Problem (TNDP) aims to select the best project sets among a number of new projects. Recently, metaheuristic methods are applied to solve TNDP in the sense of finding better solutions sooner. PSO as a metaheuristic method is based on stochastic optimization and is a parallel revolutionary computation technique. The PSO system initializes with a number of random solutions and seeks for optimal solution by improving generations. This paper studies the behavior of PSO on account of improving initial generation and fitness value domain to find better solutions in comparison with previous attempts.

Liner hub-and-spoke shipping network design

This paper proposes a liner hub-and-spoke shipping network design problem by introducing the concept of a main port, as well as some container shipping constraints such as multi-type container shipment and transit time constraints, which are seldom considered in the previous studies. It develops a mixed-integer programming model with nonconvex multi-linear terms for the proposed problem. An efficient genetic algorithm embedded with a multi-stage decomposition approach is developed to solve the model. Numerical experiments are carried out to assess the effectiveness of the proposed model and the efficiency of the proposed algorithm.

Bi-Level Program of Transportation Network Design Problem Accounting for Equity and Exact Solution Methodology

Bi-Level Program of Transportation Network Design Problem Accounting for Equity and Exact Solution Methodology

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.

A matheuristic for the liner shipping network design problem

We present an integer programming based heuristic, a matheuristic, for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport, while minimizing the cost of operating the network. Liner shipping companies publish a set of routes with a time schedule, and it is an industry standard to have a weekly departure at each port call on a route. A weekly frequency is achieved by deploying several vessels to a single route, respecting the available fleet of container vessels. The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic. The improvement heuristic uses an integer program to select a set of improving port insertions and removals on each service. Computational results are reported for the benchmark suite LINER-LIB 2012 following the industry standard of weekly departures on every schedule. The heuristic shows overall good performance and is able to find high quality solutions within competitive execution times. The matheuristic can also be applied as a decision support tool to improve an existing network by optimizing on a designated subset of the routes. A case study is presented for this approach with very promising results.

Comparative Analysis of Transportation Network Design Problem under Stochastic Capacity

The method to accurately simulate users travel behavior in the network design problem (NDP) is one of the most crucial problems. Most researches in the network equilibrium based approach to model NDP ignore the unreliability aspect of travel time. The uncertain events result in the spatial and temporal variability of network travel times, which directly contributes to the crucial decision of NDP. Specifically, the mean travel time (MTT), the travel time budget (TTB), and the – reliable mean-excess travel time (METT) are employed in the transportation network design problem under uncertain environment due to stochastic link capacity. Numerical results are presented to examine how these models affects decisions under the condition of travel time variability. The comparative analyses show that the performance of DRUE and METTUE is better than DUE which is employed in network design problem under variation degrees because of considering travel time variability.

Robust optimization for the hazardous materials transportation network design problem

In this paper, we reconsider the hazardous materials transportation network design problem with uncertain edge risk (HTNDPUR) which is proved as strong NP-hard. The natural ways to handle NP-hard problems are approximation solutions or FPT algorithms. We prove that the HTNDPUR does not admit any approximation, neither any FPT algorithm, unless P = NP. Furthermore, we utilize the minimax regret criterion to model the HTNDPUR as a bi-level integer programming formulation under edge risk uncertainty, where an interval of possible risk values is associated with each arc. We present a robust heuristic approach that always finds a robust and stable hazmat transportation network. At the end, we test our method on a network of Guangdong province in China to illustrate the efficiency of the algorithm. Our experimental results illustrate that the robust interval risk scenario network performs better than the deterministic scenario network.

Performance of a Genetic Algorithm for Solving the Multi-Objective, Multimodal Transportation Network Design Problem

The optimization of infrastructure planning in a multimodal network is defined as a multi-objective network design problem, with accessibility, use of urban space by parking, operating deficit and climate impact as objectives. Decision variables are the location of park and ride facilities, train stations and the frequency of public transport lines. For a case study the Pareto set is estimated by the Non-dominated Sorting Genetic Algorithm (NSGA-II). Such a Pareto set is one specific outcome of the optimization process, for a specific value of the parameters generation size, number of generations and mutation rate and for a specific outcome of the Monte Carlo simulation within NSGA-II. Similar issues exist for many other metaheuristics. However, when applied in practice, a policy maker desires a result that is robust for these unknown aspects of the method. In this paper Pareto sets from various runs of the NSGA-II algorithm are analyzed and compared. To compare the values of the decision variables in the Pareto sets, new methods are necessary, so these are defined and applied. The results show that the differences concerning decision variables are considerably larger than the differences concerning objectives. This indicates that the randomness of the algorithm may be a problem when determining the decisions to be made. Furthermore, it is concluded that variations caused by different parameters are comparable with the variations caused by randomness within the algorithm.

Differential Evolution Algorithm Based Solution Approaches for Solving Transportation Network Design Problems

Differential Evolution algorithm has effectively been used to solve engineering optimization problems recently. The Differential Evolution algorithm, which uses similar principles with Genetic Algorithms, is more robust on obtaining optimal solution than many other heuristic algorithms with its simpler structure. In this study, Differential Evolution algorithm is applied to the transportation network design problems and its effectiveness on the solution is investigated. In this context, Differential Evolution based models are developed using bi-level programming approach for the solution of the transportation network design problem and determination of the on-street parking places in urban road networks. In these models, optimal investment and parking strategies are investigated on the upper level. On the lower level, deterministic traffic assignment problem, which represents drivers' responses, is solved using Frank-Wolfe algorithm and VISUM traffic modeling software. In order to determine the effectiveness of the proposed models, numerical applications are carried out on Sioux-Falls test network. Results showed that the Differential Evolution algorithm may effectively been used for the solution of transportation network design problems.

Transportation Network Design considering Morning and Evening Peak-Hour Demands

Previous studies of transportation network design problem (NDP) always consider one peak-hour origin-destination (O-D) demand distribution. However, the NDP based on one peak-hour O-D demand matrix might be unable to model the real traffic patterns due to diverse traffic characteristics in the morning and evening peaks and impacts of network structure and link sensitivity. This paper proposes an NDP model simultaneously considering both morning and evening peak-hour demands. The NDP problem is formulated as a bilevel programming model, where the upper level is to minimize the weighted sum of total travel time for network users travelling in both morning and evening commute peaks, and the lower level is to characterize user equilibrium choice behaviors of the travelers in two peaks. The proposed NDP model is transformed into an equivalent mixed integer linear programming (MILP), which can be efficiently solved by optimization solvers. Numerical examples are finally performed to demonstrate the effectiveness of the developed model. It is shown that the proposed NDP model has more promising design effect of improving network efficiency than the traditional NDP model considering one peak-hour demand and avoids the misleading selection of improved links.

Time-Dependent Discrete Transportation Network Design

The transportation network construction takes place over a quite long time span and need enough budget. The budget is from the allocation of funds in phases and the construction cost change in the process of the construction. The general static transportation network design problems ignores the problems above. So the optimal solution obtained by the static model is best in short time, and it is may be unfeasible in the actual situation. Based on the actual situation and the shortage of the static model, the time-dependent transport network design is proposed in this study. The plan horizon is divided into N intervals and a bi-level model is built to describe the problem. The objective of the upper-level is to minimize the total cost of the whole stages. the lower-level model is a user equilibrium model. Then the branch and bound (B-B) algorithm is designed to solve the model. It is obvious that the solution of the time-dependent simulation model is more feasible than the solution of the static sequential design.

Robust Optimization Model for a Network Design Problem Under OD Demand Uncertainty

In many applications, the network design problem faces uncertainty in OD demand, as it can be difficult to estimate current and future values of OD demand. In this paper, we present a network design model under OD demand uncertainty in order to quantify the effect of the uncertainty by the robust optimization. An optimization algorithm based on a cutting constraint algorithm solves the mixed integer linear programming. A computational experiment shows that total travel time is connected with the uncertainty level, the infeasibility tolerance and the reliability level in transportation network design problems.

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).

The Robust Model of Continuous Transportation Network Design Problem with Demand and Cost Uncertainties

In this paper, the continuous transportation network design problem with demand and cost uncertainties is studied while the generated trip between each origin-destination pair is deterministic. Propose a bi-level uncertain model with robust optimizations. In the upper-level problem, the costs of expansion are uncertain by adding random variables to the cost function coefficients. Every random variable belongs to [0,1]. In the lower-level problem, the demand between each origin-destination pair is uncertain and belongs to a bounded interval and an ellipsoid. Then apply a genetic algorithm combined with the Frank-Wolfe algorithm to solve the model. Numerical examples suggest that the robust model with uncertain data has the advantage of operability and stability over the deterministic model.

Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design

Maritime cabotage is a legislation published by a particular coastal country, which is used to conduct the cargo transportation between its two domestic ports. This paper proposes a two-phase mathematical programming model to formulate the liner hub-and-spoke shipping network design problem subject to the maritime cabotage legislations, i.e., the hub location and feeder allocation problem for phase I and the ship route design with ship fleet deployment problem for phase II. The problem in phase I is formulated as a mixed-integer linear programming model. By developing a hub port expanding technique, the problem in phase II is formulated as a vehicle routing problem with pickup and delivery. A Lagrangian relaxation based solution method is proposed to solve it. Numerical implementations based on the Asia–Europe–Oceania shipping services are carried out to account for the impact analysis of the maritime cabotage legislations on liner hub-and-spoke shipping network design problem.

Robust Transportation Network Design Modeling with Regret Value

Based on long-term transportation network design decisions and potential parameter variations, it is important that demand uncertainty is considered in transportation modeling. In this paper, we present a novel robustness measure that combines the two objectives by minimizing the expected travel time while bounding the relative regret in each scenario facing uncertain origin-destination demand (OD demand). The concept of α-robust solution is introduced into the transportation network design problem. We propose a robust transportation network design model with regret value constraints, then design an algorithm based on the genetic algorithm to solve the problem and obtain the optimal solutions for different regret values. Finally, numerical results based on the Nguyen-Dupuis network validate the effectiveness of the algorithm. While detailed analysis on trade-offs, between the expected travel time and the maximum regret value, shows that large reductions in maximum regret do not necessarily result in a great increase in expected travel time. Meanwhile, we compared the robust model presented with the stochastic model and numerical examples demonstrate that the robust planning network is more reliable and less risky than the stochastic model if demand uncertainty is considered in modeling.

Bi-Level Programming Models Applied in Urban Transportation Network Design Problems

In this paper, we conduct a comprehensive survey on the past developments and recent advances of bilevel programming models, algorithms and practical applications in urban transportation network design problems. Moreover, based on this survey, some open problems and future research directions are proposed.

다수단 가변수요 통행배정문제를 위한 부분선형화 알고리즘의 성능비교

Investment scenarios in the transportation network design problem usually contain installation or expansion of multi-mode transportation links. When one applies the mode choice analysis and traffic assignment sequentially for each investment scenario, it is possible that the travel impedance used in the mode choice analysis is different from the user equilibrium cost of the traffic assignment step. Therefore, to estimate the travel impedance and mode choice accurately, one needs to develop a combined model for the mode choice and traffic assignment. In this paper, we derive the inverse demand and the excess demand functions for the multi-mode multinomial logit mode choice function and develop a combined model for the multi-mode variable demand traffic assignment problem. Using data from the regional O/D and network data provided by the KTDB, we compared the performance of the partial linearization algorithm with the Frank-Wolfe algorithm applied to the excess demand model and with the sequential heuristic procedures.

A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing

Robust transportation network design problems generally rely on systems engineering methods that share common research gaps. First, problem sizes are constrained due to the use of multi-objective solution algorithms that are notoriously inefficient due to computationally expensive function evaluations. Second, link disruptions at a network level are difficult to model realistically. In this paper, a stochastic search metaheuristic based on radial basis functions is proposed for constrained multiobjective problems. It is proven to converge, and compared with conventional metaheuristics for four representative test problems. A scenario simulation method based on multivariate Bernoulli random variables that accounts for correlations between link failures is proposed to sample scenarios for a mean-variance toll pricing problem. Four tests are conducted on the classical Sioux Falls network to gain some insights into the algorithm, the simulation model, and to the robust toll pricing problem. The first test empirically measures the efficiency of the simulation algorithm and approximate Pareto set by obtaining a standard error in the e-indicator measure for a given number of scenarios and iterations. The second test compares the dominance of the proposed heuristic’s solutions with a conventional multiobjective genetic algorithm by comparing the average e-indicator. The third test quantifies the gap due to falsely assuming that link failures are independent of each other when they are not. The last test quantifies the value of having the flexibility to adapt a Pareto set of toll pricing solutions to changing probability regimes such as peak and off-peak hurricane or snow seasons.

The effect of roadway capacity expansion on facility sitting

Generally, the transportation planning problem involves with facility sitting, roadway selection, distribution route planning and some related problems, which are optimized based on given network topology. Recently, some of researches noticed that by changing the network topology, which corresponding to adding a decision whether new roadway construction between node- pairs in the given transportation network, is often more cost-effective than only sitting new facilities in given networks. Motivated by aforementioned topology changing result, this paper not only consider about new roadway construction, but also merge the roadway capacity expansion decision into transportation network design problem. The models generated from an integrated model for transportation network design and uncapacitated facility location problem. Then we merge the roadway capacity expansion part and facility capacity decision part into the original model. Mixed integrated programming and network transform mechanism for such models are proposed. Lastly, we measure the effect of roadway capacity expansion on facility sitting. The numerical testing with random generated data shows the feasible and effective of models. In conclusion part, the application in real case of proposed models and algorithms are identified.