Abstract
Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.
Highlights
Traffic congestion is a major challenge in many cities
The nonlinear and mixed-integer parts are formulated as primal and dual problems derived from the original mixed-integer nonlinear programming (MINLP) minimization problem: (i) the primal problem is constituted as solving the original problem with a feasible solution for the binary variables; it renders an upper bound to the original problem. (ii) given the solution results of the primal problem, the dual problem is designed as a mixed-integer linear programming (MILP) to render a new solution for the binary variables
We developed a hybrid exact-heuristic method to address the Discrete Network Design Problem (DNDP) tailored to large-size networks in which, given a limited budget, the best subset of candidate road projects is sought
Summary
Traffic congestion is a major challenge in many cities. In addition to demand management, in many cases investment into the expansion of the road network is inevitable. To crunch the complexity of the problem, a two-stage relaxation method is developed (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the UE-TAP in the lower level as a constraint Optimal investment into the roads construction projects mixed-integer nonlinear programming (MINLP) problem which is solved using an Outer Approximation (OA) algorithm (ii) To arrive at a tractable mixed integer linear programming (MILP) problem, we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, during which, a new binary solution is sought to be evaluated (i.e. solving its corresponding UE-TAP). The intractable multi-commodity MILP is decomposed to a tractable single-commodity MILP and a tractable nonlinear UE-TAP This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for large-size networks. Appendix A provides a basic discussion on the Outer Approximation method
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