Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach

► Mixed network design problem (MNDP) can be formulated as a mixed-integer linear programming problem (MILP) with the link-based formulation which helps avoiding the path enumeration. ► The global optimality of the approximated MNDP can then be guaranteed following the property of the MILP. ► The pr...

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Bibliographic Details
Published in:Transportation research. Part B: methodological 2011-06, Vol.45 (5), p.808-827
Main Authors: Luathep, Paramet, Sumalee, Agachai, Lam, William H.K., Li, Zhi-Chun, Lo, Hong K.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
Discrete network design
Exact sciences and technology
Global optimization
Ground, air and sea transportation, marine construction
Linear programming
Links
Mathematical models
Mixed network design
Mixed-integer linear programming
Network design problem
Network design problem Discrete network design Mixed network design Mixed-integer linear programming Global optimization
Networks
Optimization
Road transportation and traffic
Transportation networks
Transportation planning, management and economics
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Summary:► Mixed network design problem (MNDP) can be formulated as a mixed-integer linear programming problem (MILP) with the link-based formulation which helps avoiding the path enumeration. ► The global optimality of the approximated MNDP can then be guaranteed following the property of the MILP. ► The proposed algorithm performed well with the tests with small and medium sized networks compared to other existing solution algorithms in the literature. This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) 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 expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature.
ISSN:0191-2615
1879-2367
DOI:10.1016/j.trb.2011.02.002