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Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach
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DOI：10.1016/j.trb.2011.02.002.png)
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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 CUE) 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-low 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. (C) 2011 Elsevier Ltd. All rights reserved.
Keywords:
Network design problem
Discrete network design
Mixed network design
Mixed-integer linear programming
Global optimization
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