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Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach |
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| Authors: | Paramet Luathep Agachai Sumalee William H.K. LamZhi-Chun Li Hong K. Lo |
| Affiliation: | a Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China b Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Hatyai, Songkhla, Thailand c School of Management, Huazhong University of Science and Technology, Wuhan 430074, China d Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China |
| Abstract: | 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. |
| Keywords: | Network design problem Discrete network design Mixed network design Mixed-integer linear programming Global optimization |
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