Abstract
This paper addresses a problem of determining links to be expanded in an urban road network so that traffic congestion there is minimized. We propose a new lower bound of a branch and bound method for a nonlinear mixed integer programming model. This new lower bound is calculated through a feasible direction method and a Lagrangean relaxation. We prove that this Lagrangean relaxation problem can be solved easily by a transformation of the objective function, and this lower bound is stronger than LeBlanc's lower bound. We also present a procedure to find a good Lagrangean multiplier which is incorporated into our branch and bound algorithm and heuristic algorithm. Simple numerical examples are given to illustrate our lower bound and branch and bound algorithm.
