TY - JOUR
T1 - Global optimization method for mixed transportation network design problem
T2 - A mixed-integer linear programming approach
AU - Luathep, Paramet
AU - Sumalee, Agachai
AU - Lam, William H.K.
AU - Li, Zhi Chun
AU - Lo, Hong K.
PY - 2011/6
Y1 - 2011/6
N2 - 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.
AB - 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.
KW - Discrete network design
KW - Global optimization
KW - Mixed network design
KW - Mixed-integer linear programming
KW - Network design problem
UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000291077100005
UR - https://openalex.org/W1975333294
UR - https://www.scopus.com/pages/publications/79954997494
U2 - 10.1016/j.trb.2011.02.002
DO - 10.1016/j.trb.2011.02.002
M3 - Journal Article
SN - 0191-2615
VL - 45
SP - 808
EP - 827
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
IS - 5
ER -