Study on continuous network design problem using simulated annealing and genetic algorithm

摘要

In general, a continuous network design problem (CNDP) is formulated as a bi-level program. The objective function at the upper level is defined as the total travel time on the network, plus total investment costs of link capacity expansions. The lower level problem is formulated as a certain traffic assignment model. It is well known that such bi-level program is non-convex and non-differentiable and algorithms for finding global optimal solutions are preferable to be used in solving it. Simulated annealing (SA) and genetic algorithm (GA) are two global methods and can then be used to determine the optimal solution of CNDP. Since application of SA and GA on continuous network design on real transportation network requires solving traffic assignment model many times at each iteration of the algorithm, computation time needed is tremendous. It is important to compare the efficacy of the two methods and choose the more efficient one as reference method in practice. In this paper, the continuous network design problem has been studied using SA and GA on a simulated network. The lower level program is formulated as user equilibrium traffic assignment model and Frank–Wolf method is used to solve it. It is found that when demand is large, SA is more efficient than GA in solving CNDP, and much more computational effort is needed for GA to achieve the same optimal solution as SA. However, when demand is light, GA can reach a more optimal solution at the expense of more computation time. It is also found that increasing the iteration number at each temperature in SA does not necessarily improve solution. The finding in this example is different from [Karoonsoontawong, A., & Waller, S. T. (2006). Dynamic continuous network design problem – Linear bilevel programming and metaheuristic approaches. Network Modeling 2006 Transportation Research Record (1964) (pp. 104–117)]. The reason might be the bi-level model in this example is nonlinear while the bi-level model in their study is linear.