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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 718015, 11 pages
Research Article

Determining Optimal Link Capacity Expansions in Road Networks Using Cuckoo Search Algorithm with Lévy Flights

Department of Civil Engineering, Faculty of Engineering, Pamukkale University, 20070 Denizli, Turkey

Received 28 June 2013; Accepted 31 July 2013

Academic Editor: Xin-She Yang

Copyright © 2013 Ozgur Baskan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


During the last two decades, Continuous Network Design Problem (CNDP) has received much more attention because of increasing trend of traffic congestion in road networks. In the CNDP, the problem is to find optimal link capacity expansions by minimizing the sum of total travel time and investment cost of capacity expansions in a road network. Considering both increasing traffic congestion and limited budgets of local authorities, the CNDP deserves to receive more attention in order to use available budget economically and to mitigate traffic congestion. The CNDP can generally be formulated as bilevel programming model in which the upper level deals with finding optimal link capacity expansions, whereas at the lower level, User Equilibrium (UE) link flows are determined by Wardrop’s first principle. In this paper, cuckoo search (CS) algorithm with Lévy flights is introduced for finding optimal link capacity expansions because of its recent successful applications in solving such complex problems. CS is applied to the 16-link and Sioux Falls networks and compared with available methods in the literature. Results show the potential of CS for finding optimal or near optimal link capacity expansions in a given road network.