Metamodel-Based Optimization Method for Traffic Network Signal Design under Stochastic Demand

Traffic network design problems (NDPs) play an important role in urban planning. Since there exist uncertainties in the real urban traffic network, neglecting the uncertainty factors may lead to unreasonable decisions. This paper considers the transportation network signal design problem under stochastic origin-destination (OD) demand. In general, solving this stochastic problem requires a large amount of computational budget to calculate the equilibrium flow corresponding to a certain demand distribution, which limits its real applications. To reduce the computational time in calculating the equilibrium flow under stochastic demand, this paper proposes a metamodel-based optimization method. First, a combined metamodel that integrates a physical modeling part and a model bias generic part is developed. The metamodel is used to approximate the time-consuming average equilibrium flow solution process, hence to improve the computational efficiency. To further improve the convergence and the solution optimality performance of the metamodel-based optimization, the gradient information of traffic flow with respect to the signal plan is incorporated in the optimization model. A gradient-based metamodel algorithm is then proposed. In the numerical example, a six-node test network is used to examine the proposed metamodel-based optimization method. The proposed combined metamodel is compared with the benchmark method to investigate the importance of incorporating a model bias generic part and the traffic flow gradient information in the combined metamodel. Although there is a reduction in solution optimality since the metamodel is an approximation of the original model, the metamodel methods greatly improve the computational efficiency (the computational time is reduced by 4.84 to 13.47 times in the cases of different initial points). By incorporating the model bias, the combined metamodel can better approximate the original optimal solution. Moreover, incorporating the gradient information of the traffic flow in the optimization search algorithm can further improve the solution performance. Numerical results show that the gradient-based metamodel method can effectively improve the computation efficiency while slightly reducing the solution optimality (with an increase of 0.09% in the expected total travel cost).