Bi-objective simulation optimization for online feedback control of variable speed limits considering uncertain traffic demands and compliance behaviours

Variable speed limits (VSL) stands out as a well-established and effective strategy to alleviate traffic congestion and enhance traffic safety on motorways. It allows variable message signs (VMSs) to dynamically determine the speed limits according to real-time traffic states. This paper introduces an innovative online feedback control approach designed to regulate speed limit values on VMSs, addressing multiple bottlenecks while considering their spatiotemporal constraints. Moreover, we offline optimize the gain coefficients of this feedback control approach in the simulation-based optimization (SBO) framework. Specifically, with average and variance of space-mean speeds as bi-objectives, a stochastic SBO model considering uncertain traffic demands and compliance behaviours is established and solved by a bi-objective surrogate-based promising area search (BOSPAS) algorithm. Real-field experiments conducted in Edmonton, Canada, demonstrate the well-performing bi-objectives of the proposed approach, especially in handling uncertain compliance behaviours and traffic demands. Compared with the uncontrolled scenario, the feedback control schemes with the offline optimized gain coefficients improve the average and variance of space-mean speeds by up to 16.2% and 20.8%, respectively. Meanwhile, by the comparison of detailed performances, it is found that the optimized control schemes perform better than the uncontrolled scheme from the overall and local aspects. In conclusion, this study puts forward a general framework that applies an online feedback control approach with gain coefficients optimized offline by an SBO method to deal with real-time decision-making problems under uncertainties.