Lagrangian Relaxation Heuristic for Selecting Interdependent Transportation Projects under Cost Uncertainty

Abstract

The capital budgeting process for a transportation system is usually complicated by the interdependencies of projects and the uncertainty of project costs. The existence of project interdependence in transportation systems makes it difficult to evaluate the project effects with analytical methods. Furthermore, when the construction costs of candidate projects are uncertain, the budget constraints that bind project selection become chance constraints, and this may render most existing approaches inapplicable. This paper formulates the project selection problem as a nonlinear integer optimization problem whose objective function is implicit but can be evaluated with network simulation. The Lagrangian method is applied to relax the complex project constraints that are nonlinear under cost uncertainty. An efficient genetic algorithm is developed to solve the Lagrangian subproblems. This paper applies an equilibrium traffic assignment model to evaluate the project impacts and the objective values of the Lagrangian subproblems. Experiments are designed to test the performance of the developed approach on a fairly generic highway system. The experiment results show that the developed approach can effectively solve the problem of selecting interdependent projects under cost uncertainty.