Transportation Network Design Problem Research Articles

Developing bi-level equilibrium models for the global container transportation network from the perspectives of multiple stakeholders

Given the importance of containerisation to creating successful global supply chain operations, this paper proposes an equilibrium model that can not only minimise the total container transportation cost for a shipper, but also maximise the total profit accrued from container transportation services offered by a carrier. The proposed model combines game theory with a Genetic Algorithm (GA) to promote a compromise between the conflicting interests of the carrier and the shipper, while optimally balancing the shipper's desire to contain cost against the carrier's desire to increase profit. To verify the usefulness of the proposed model, we applied it to the container transportation network design problem from the perspectives of multiple stakeholders including Chinese container port authorities.

Stochastic multi-objective models for network design problem

Transportation network design problem ( NDP) is inherently multi-objective in nature, because it involves a number of stakeholders with different needs. In addition, the decision-making process sometimes has to be made under uncertainty where certain inputs are not known exactly. In this paper, we develop three stochastic multi-objective models for designing transportation network under demand uncertainty. These three stochastic multi-objective NDP models are formulated as the expected value multi-objective programming ( EVMOP) model, chance constrained multi-objective programming ( CCMOP) model, and dependent chance multi-objective programming ( DCMOP) model in a bi-level programming framework using different criteria to hedge against demand uncertainty. To solve these stochastic multi-objective NDP models, we develop a solution approach that explicitly optimizes all objectives under demand uncertainty by simultaneously generating a family of optimal solutions known as the Pareto optimal solution set. Numerical examples are also presented to illustrate the concept of the three stochastic multi-objective NDP models as well as the effectiveness of the solution approach.

Bilevel programming model and solution method for mixed transportation network design problem

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.

Mixed Transportation Network Design Based on Immune Clone Annealing Algorithm

This paper focuses on the mixed transportation network design problem. A bi-level programming model, constrained by investment budget, is developed to minimize the total impedance of transportation network. The immune clone annealing algorithm, which is designed by combining annealing tactic of simulated annealing algorithm and immune clone algorithm, is introduced to solve the proposed bi-level model. Compared with simulated annealing algorithm, the feasibility and effectiveness of the model and the algorithm is demonstrated through a numerical experiment. The sensitivity analysis on different investment budget constraints is provided, as well as the relation between investment cost and the total impedance of network, investment budget constraint, and decision on network design.

Reversible lane-based traffic network optimization with an advanced traveller information system

In the case of two-way traffic, there are two opposite-direction flows on every road and serious unsymmetrical flows exist in rush-hour periods. One of the primary methods used for handling this kind of traffic flow is the use of reversible lanes. Which and how many lanes should be adjusted are optimization problems. They can be treated as a network design problem, i.e. the optimal decision on the resource distribution of a street and highway system in response to a growing travel demand. This article studies a new form of transportation network design problem by performing the strategy of reversible lanes. In order to describe this problem, a bi-level programming model is given in which the upper level model is to make the total system cost and flow entropy minimum, while the lower level is a stochastic user equilibrium assignment with an advanced traveller information system. Finally, the numerical example shows that, by adopting the reversible lane and advanced traveller information system, the total system cost will be greatly reduced.

A quantum-inspired genetic algorithm for dynamic continuous network design problem

The Network Design Problem (NDP), known to be NP-complete, arises in many application contexts. Transportation NDP involves optimizing the network performance under a budget constraint. Due to its non-convex and discontinuous solution space, a majority of the research efforts have been focused on tackling this problem using metaheuristics. Quantum computing is an active research area in which numerous advances have been made since the early 1990s. Quantum algorithms, such as Shor's factorization algorithm and Grover's database search algorithm, have opened up the possibility of solving NP-hard/NP-complete problems in polynomial time with quantum computers. Quantum-inspired genetic algorithms (QGA), as one of the novel meta-heuristics, seek to use insights gained through quantum computing to improve upon the performance of traditional genetic algorithms. By using the qubit as the basic unit of information in QGA, complex search space can be probabilistically characterized by superposition of states. With a suitable QGA updating mechanism, the qubit chromosome gradually converges to a single state as each qubit in the chromosome reaches the stable state of either 0 or 1. Therefore, without an exhaustive search of the qubit states combination, the solution spaces can be effectively explored and a better quality solution can be obtained with the same level of population, generation, and overall computational effort. In this research, we present a floating-point encoded quantum-inspired genetic algorithm to solve the dynamic transportation network design problem. The proposed algorithm is empirically applied to the Sioux-Falls and Monticello networks to test its effectiveness and applicability. Through numerical experiments, the QGA outperforms the conventional genetic algorithm, even with a smaller population size. Technical, computational and practical issues involved in developing and calibrating quantum-inspired genetic algorithm are discussed.

Freight Transportation Network Design Problem for Maximizing throughput under Uncertainty

A mathematical programming formulation is developed to determine the throughput of a freight transportation network. The impact of demand and capacity uncertainty on the throughput is systematically studied. Mathematical proofs are provided to show that accounting for capacity uncertainty by using a single-point expected value can lead to systematic overestimation of network throughput. This result is also valid for other measures, such as system capacity. Two sampling-based methodologies–independent random number and common random number–are provided to determine network design decisions in the presence of demand uncertainty. The sampling-based solution methods provide an approximate estimate of optimal solution and provide probabilistic bounds on the optimality gap. The presented methodologies are generic and can be applied even if different functional forms (nonlinear, nonconvex) are used to model various aspects of the freight transportation network. The numerical tests demonstrate that not accounting for capacity uncertainty can result in overestimation of system throughput of up to 40%. A common random number-based sampling strategy was found to significantly outperform the independent random number strategy for all the scenarios tested.

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.

Demand responsive urban public transport system design: Methodology and application

In this paper, we present a methodology for solving the Public Transport Network Design Problem (PTNDP) and describe its application in the context of the Design Study developed in order to propose a new structure for the transit system of the city of Santiago, Chile. Firstly, we briefly define the PTNDP as a multilevel programming problem and discuss the solution method implemented. Then, the application of this methodology to the Santiago transit system is presented, and the main results obtained are analyzed. The new restructured system, based on a hierarchy of specialized services that complement and coordinate their operations and using an integrated fare scheme, is compared with an optimized version (optimal frequencies) of the current one, a set of direct services, mainly based on the operation of independent itineraries, without fare integration. The most important conclusions are the following: (a) the private operating costs and the social costs of the restructured system, using higher standard buses, are considerably lower than the costs of the current system; (b) these cost reductions allow government authorities to introduce an important number of modernizing measures without subsidies and fare increases.

'Adaptive Link Adjustment' Applied to the Fixed Charge Transportation Problem

The fixed charge transportation problem (FCTP) is a classic challenge for combinatorial optimization; it is based on the well-known transportation problem (TP), and is one of the prime examples of an NP-complete variant of the TP, of general importance in a wide range of transportation network design problems. Many techniques have been applied to this problem, and the most effective so far (in terms of near-optimal results in reasonable time on large instances) are evolutionary algorithm based approaches. In particular, an EA proposed by Eckert and Gottlieb has produced the best performance so far on a set of specific benchmark instances. We introduce a new scheme, which has more general applicability, but which we test here on the FCTP. The proposed scheme applies an adaptive mutation process immediately following the evaluation of a phenotype. It thereby adapts automatically to learned information encoded in the chromosome. The underlying encoding approach is to encode an ordering of elements for interpretation by a constructive algorithm (such as with the Link and Node Biased encoding for spanning trees, and the Random Keys encoding which has been applied to both scheduling and graph problems), however the main adaptive process rewards links in such a way that genes effectively encode a measure of the number of times their associated link has appeared in selected solutions. Tests are done which compare our approach with Eckert and Gottlieb's results on benchmark FCTP instances, and other approaches.

A holonic approach based integration methodology for transportation and warehousing functions of the supply network

The supply chain (SC) is often defined as a network that is composed of different functions, including suppliers, manufacturing plants, warehouses/distribution centers, retailers and customers. A supply network (SN) is a sequence of different and multiple numbers of functions and individual functional units that must satisfy all capacities and demand requirements imposed by customers with minimum cost to the network. The most important functions of a SN are warehousing and transportation functions. This paper addresses the warehousing and transportation network design problem that involves determining the best strategy for distributing the sub-products from the suppliers to the warehouse and from the warehouse to the manufacturers. Considering some similarities between holonic systems and SN systems, a holonic approach based modeling methodology is proposed in this study. A multiple supplier, single warehouse and multiple manufacturer system are considered to be an integrated warehousing and transportation network. Consequently, a linear programming model is presented to maximize the profit of both of the overall SN and the individual functional units of the SN functions.

Two-way road network design problem with variable lanes

This paper studies a new form of transportation network design problem. In urban transportation network, unreasonable phenomenon can occur in certain traffic period (e.g. on/off duty period), which demonstrates that the flows of opposite directions on a two-way road are seriously asymmetric; one traffic link of a two-way road congest heavily but the other is hardly used. In order to reduce transportation congestion and make full use of the existing road resources, we propose a lane reallocating approach in peak period, and establish a discrete bi-level programming model for the decision-making. Then, based on particle swarm optimization (PSO) technique, a heuristic solution algorithm for the bi-level model is designed. Finally, the lane reallocating approach is demonstrated through a simple transportation network.

Solving the hazmat transport network design problem

In this paper, we consider the problem of network design for hazardous material transportation where the government designates a network, and the carriers choose the routes on the network. We model the problem as a bilevel network flow formulation and analyze the bilevel design problem by comparing it to three other decision scenarios. The bilevel model is difficult to solve and may be ill-posed. We propose a heuristic solution method that always finds a stable solution. The heuristic exploits the network flow structure at both levels to overcome the difficulty and instability of the bilevel integer programming model. Testing on real data shows that the linearization of the bilevel model fails to find stable solutions and that the heuristic finds lower risk networks in less time. Further testing on random instances shows that the heuristically designed networks achieve significant risk reduction over single-level models. The risk is very close to the least risk possible. However, this reduction in risk comes with a significant increase in cost. We extend the bilevel model to account for the cost/risk trade-off by including cost in the first-level objective. The biobjective–bilevel model is a rich decision-support tool that allows for the generation of many good solutions to the design problem.

The Discrete Network Design Problem Over Time

Over time there will be inevitable changes in the travel demand patterns in a transport network. To capture these changing demands and design a gradually upgraded network it is necessary to introduce the time dimension into the transport Network Design Problem (NDP). Previous efforts have extended the continuous network design problem to cater for such considerations. However the continuous problem does not always indicate improvements that are practical. Therefore in this paper we develop a model of the time-dependent discrete network design problem. The importance of the model is illustrated by two numerical studies, which demonstrate the importance of introducing the time dimension to the NDP and the importance of introducing discrete decision variables to the NDP over time. An example on NDP under two cost-recovery principles is also provided to illustrate the application of the model.

Real-Time Mass Passenger Transport Network Optimization Problems

The aim of the real-time mass transport vehicle routing problem (MTVRP) is to find a solution to route n vehicles in real time to pick up and deliver m passengers. This problem is described in the context of flexible large-scale mass transportation options that use new technologies for communication among passengers and vehicles. This study does not focus on the technological aspects required to operate this kind of system but instead treats the theoretical approaches to provide a consistent mathematical formulation of the problem and its solution. This analytical effort is relevant to future transportation options involving large-scale real-time routing of shared-ride fleet transit vehicles. However, the global optimization of a complex system involving routing and scheduling multiple vehicles and passengers as well as design issues has not been specifically studied in the past. This research proposes a methodology to solve it by means of a three-level hierarchical optimization approach. Within the optimization process, a mass transport network design problem (MTNDP) is solved. The MTVRP is introduced and a scheme to solve it is presented. Then the associated algorithm to perform the MTNDP optimization is described in detail. A real-world application is solved for the MTNDP, showing promising results with regard to the applicability of the methodology for large-scale transit problems.

A Capacity Scaling Procedure for the Multi-Commodity Capacitated Transportation Network Design Problem

A Capacity Scaling Procedure for the Multi-Commodity Capacitated Transportation Network Design Problem

The container shipping network design problem with empty container repositioning

This paper addresses the design of container liner shipping service networks by explicitly taking into account empty container repositioning. Two key and interrelated issues, those of deploying ships and containers are usually treated separately by most existing studies on shipping network design. In this paper, both issues are considered simultaneously. The problem is formulated as a two-stage problem. A genetic algorithm-based heuristic is developed for the problem. Through a number of numerical experiments that were conducted it was shown that the problem with the consideration of empty container repositioning provides a more insightful solution than the one without.

Bilevel programming for the continuous transport network design problem

A Continuous Network Design Problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. A bilevel programming technique can be used to formulate this equilibrium network design problem. At the upper level problem, the system performance index is defined as the sum of total travel times and investment costs of link capacity expansions. At the lower level problem, the user equilibrium flow is determined by Wardrop’s first principle and can be formulated as an equivalent minimization problem. In this paper we exploit a descent approach via the implementation of gradient-based methods to solve CNDP generally where the Karush–Kuhn–Tucker points can be obtained. Four variants of gradient-based methods are presented and numerical comparisons are widely made with the previous on three kinds of test networks. The proposed methods have achieved substantially better results in terms of the robustness to the initials and the computational efficiency in solving equilibrium assignment problems than did others especially when the congested road networks are considered.

A Study on Public Transport Evaluation Method Using Multi-modal Traffic Assignment Applied Probit-Based SUE

In this study, a probit-based public transport assignment model is developed.Three transport modes, i. e. railway system, bus and auto, are considered simultaneously in the model.Because there are interactions between the transport modes, e. g., the number of autos in a network heavily influences travel time of bus system, it is natural to consider these modes jointly. Public transport network design problem is also dealt with in this study.In the network design problem, the frequencies of public transport systems are optimized to minimize total disutility in the network.

Bilevel programming for the continuous transport network design problem

A Continuous Network Design Problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. A bilevel programming technique can be used to formulate this equilibrium network design problem. At the upper level problem, the system performance index is defined as the sum of total travel times and investment costs of link capacity expansions. At the lower level problem, the user equilibrium flow is determined by Wardrop’s first principle and can be formulated as an equivalent minimization problem. In this paper we exploit a descent approach via the implementation of gradient-based methods to solve CNDP generally where the Karush–Kuhn–Tucker points can be obtained. Four variants of gradient-based methods are presented and numerical comparisons are widely made with the previous on three kinds of test networks. The proposed methods have achieved substantially better results in terms of the robustness to the initials and the computational efficiency in solving equilibrium assignment problems than did others especially when the congested road networks are considered.