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.

The Continuous Network Design Problem (CNDP) deals with determining the set of link capacity expansions and the corresponding equilibrium link flows which minimizes the system performance index defined as the sum of total travel times and investment costs of link capacity expansions. In general, the CNDP is characterized by a bilevel programming model, in which the upper level problem is generally to minimize the total system cost under limited expenditure, while at the lower level problem, the User Equilibrium (UE) link flows are determined by Wardrop’s first principle. It is well known that bilevel model is nonconvex and algorithms for finding global or near global optimum solutions are preferable to be used in solving it. Furthermore, the computation time is tremendous for solving the CNDP because the algorithms implemented on real sized networks require solving traffic assignment model many times. Therefore, an efficient algorithm, which is capable of finding the global or near global optimum solution of the CNDP with less number of traffic assignments, is still needed. In this study, the Harmony Search (HS) algorithm is used to solve the upper level objective function and numerical calculations are performed on eighteen link and Sioux Falls networks. The lower level problem is formulated as user equilibrium traffic assignment model and Frank-Wolfe method is used to solve it. It has been observed that the HS algorithm is more effective than many other compared algorithms on both example networks to solve the CNDP in terms of the objective function value and UE traffic assignment number.

In this study, a bi-level formulation is presented for solving the Equilibrium Network Design Problem (ENDP). The optimisation of the signal timing has been carried out at the upper-level using the Harmony Search Algorithm (HSA), whilst the traffic assignment has been carried out through the Path Flow Estimator (PFE) at the lower level. The results of HSA have been first compared with those obtained using the Genetic Algorithm, and the Hill Climbing on a two-junction network for a fixed set of link flows. Secondly, the HSA with PFE has been applied to the medium-sized network to show the applicability of the proposed algorithm in solving the ENDP. Additionally, in order to test the sensitivity of perceived travel time error, we have used the HSA with PFE with various level of perceived travel time. The results showed that the proposed method is quite simple and efficient in solving the ENDP.