Modified differential evolution algorithm for the continuous network design problem

The Continuous Network Design Problem (CNDP) is recognized to be one of the most difficult problems in transportation field since the bilevel formulation of the CNDP is nonconvex. On the other hand, the computation time is crucial importance for solving the CNDP because the algorithms implemented on real sized networks require solving traffic assignment model many times, which is the most time consuming part of the solution process. Although the methods developed so far are capable of solving the CNDP, an efficient algorithm, which is able to solve the CNDP with less number of User Equilibrium (UE) assignments, is still needed. Therefore, this paper deals with solving the CNDP using MOdified Differential Evolution (MODE) algorithm with a new local search and mutation operators. For this purpose, a bilevel model is proposed, in which the upper level problem deals with minimizing the sum of total travel time and investment cost of link capacity expansions, while at the lower level problem, UE link Bows are determined by Wardrop's first principle. A numerical example is presented to compare the proposed MODE algorithm with some existing methods. Results showed that the proposed algorithm may effectively be used in order to reduce the number of UE assignments in solving the CNDP. (C) 2013 The Authors. Published by Elsevier Ltd.