A Simulation-Based Model for Continuous Network Design Problem Using Bayesian Optimization

Abstract

This paper investigates the continuous network design problem (CNDP) and proposes a simulation-based bi-level model and solution framework based on Bayesian optimization. In the bi-level model, the upper level minimizes the total system cost, and the lower level assigns traffic under an approximated dynamic equilibrium condition corresponding to the given network design strategy. A simulation tool integrated micro- and macro- traffic dynamics, namely SUMO, is employed to solve the lower-level problem. The embedded high-fidelity, non-linear understanding of traffic in the simulator oftentimes gains additional complexity due to the lack of tractable mathematical representation. Thus, a Bayesian machine learning technique is utilized to build the link between simulation and optimization. The proposed solution framework takes both the advantages of fine-grained simulations and the efficiency of surrogate-based optimization techniques. Moreover, lane width expansion is innovatively proposed as the decision variable of CNDP to bridge the gap between theory and practice. The relationship between link free-flow speed (FFS) and lane width is also explored based on real data and established to accurately calibrate the simulation input. For demonstrative purposes, numerical experiments on the optimal lane width expansion design were conducted in the inner city of Suzhou, China. The results show that with proper parameter settings, the proposed method is capable to find the global optimal solution within a very tight computational budget, which makes the simulation-based framework an encouraging option for policymakers to enhance transportation network performance.