An Algorithm for the Mixed Transportation Network Design Problem.

Xinyu Liu,Qun Chen,Yong Deng

doi:10.1371/journal.pone.0162618

Xinyu Liu, Qun Chen + Show 1 more

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https://doi.org/10.1371/journal.pone.0162618

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Journal: PloS one	Publication Date: Sep 14, 2016
Citations: 8	License type: CC BY 4.0

Affiliation: Central South University, Foshan University

Abstract

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.

Highlights

Definition of network design problem (NDP)The NDP is concerned with modifying a transportation network configuration by adding new links or improving the existing ones to maximize certain social welfare objectives
This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC)
A group of variables is fixed to optimize another group of variables alternately; the problem is transformed into solving a series of continuous network design problem (CNDP) and discrete network design problem (DNDP) repeatedly until the problem converges to the optimal solution

Summary

Introduction

The NDP is concerned with modifying a transportation network configuration by adding new links or improving the existing ones to maximize certain social welfare objectives (e.g., total travel time over the network). The NDPs can be roughly classified into three categories: the discrete network design problem (DNDP), which addresses the selection of the optimal locations (expressed by 0–1 integer decision variables) of new links to be added; the continuous network design problem (CNDP), which determines the optimal capacity enhancement (expressed by continuous decision variable) for a subset of existing links; and the mixed network design problem (MNDP), which combines CNDP and DNDP in a single network. The body of DNDP literature is somewhat smaller than that of CNDP, probably because of the complexity resulting from the presence of discrete variables Exact methods such as branch and bound can be found mostly in DNDP.

Motivation of this study

Conclusion and Discussion