Artificial bee colony algorithm for continuous network design problem with link capacity expansions

In general, Continuous Network Design Problem (CNDP) is concerned with the optimal capacity expansion of existing links in a given network. The measure of network performance can be described as the sum of total travel times and the investment cost, converted to travel time, for capacity expansions of links. Due to the nonconvex characteristics of CNDP, the problem is formulated as a bi-level programming problem. Although proposed algorithms in literature are capable of solving CNDP for a given road network, an efficient algorithm, which is capable of finding the global or near global optima of the upper level decision variables of CNDP, is still needed. Therefore, this paper deals with the finding of optimal link capacity expansions in a given road network using the Artificial Bee Colony (ABC) algorithm. More precisely, a bi-level method has been proposed, in which the lower level problem is formulated as a user equilibrium traffic assignment model, solved by the ABC. To show the effectiveness of the ABC algorithm, the example road network is used for different size of travel demand. Results produced by the ABC algorithm are compared with the results obtained by Simulated Annealing (SA) and Genetic Algorithm (GA) taken from literature. According to the results, the ABC algorithm can be used effectively to solve CNDP with link capacity expansions within much less number of traffic assignments than SA and GA.