Global optimization methods for urban road network design problems

Abstract

Adequate infrastructure is required to alleviate the traffic congestion with the sustained growth in demand of passenger and freight transportation. The main study area in this thesis is the related transportation network design problem (NDP), which involves the optimal decision on the expansion of the existing links and/or on the addition of new links within a given budget aiming to achieve the best network performance. Since this class of problem can also be generalized to handle other transport management problem, like road pricing and signal control, or even be applied on other transportation modes, like public transport and shipping, hence, NDP deserves more attention and further studies on its modeling and solution algorithm development issues. In the literature, NDP problem is often formulated as bi-level programming, which is nonconvex and nonlinear in nature. The solution of nonlinear and nonconvex problem is well recognized to be extremely hard. In the literature, many researchers focused on developing various algorithmic methods for solving NDP, ranging from classic solution algorithms to widely used meta-heuristic methods. However, though a lot of efforts have been made, challenges still exist mainly in two aspects. First, solution accuracy should be enhanced. Due to nonconvex property of the NDP problems, most algorithms developed in previous studies can only find local optimal solution, rather than global optimization solution. Although these solution algorithms are efficient and fast to obtain a “good” solution, the solution quality is compromised, being a local optimal, rather than the globally best. Other than the local optimization method, a class of stochastic global optimization method, including Genetic Algorithm (GA) and simulated annealing (SA), is applied to solve NDP. However, due to the inherent characteristic of stochastic optimization method, global solution cannot be guaranteed. Second, computational efficiency in terms of calculation time should be improved. NDP problems with real-size network or a large size of candidate projects remain far from being tractable. The thesis contributes to the NDP problems in two main aspects: firstly, to develop more realistic mathematical programming model for urban transportation network design problems; secondly, to propose efficient global optimization solution algorithms for network design problems and ensure the true optimal transportation planning. Firstly, a continuous network design problem (CNDP) that aims to optimize the network performance via road capacity expansion is considered in the thesis. Road users are assumed to follow the traffic assignment principle of stochastic user equilibrium, specifically, the logit route choice model, which is a more general model and includes deterministic user equilibrium flow pattern as an extreme case. To obtain the exact global optimal solution of the problem, a global optimal solution algorithm is proposed based on a tight linear programming relaxation. The developed model, which is bi-level and…