Robust nonlinear decision mapping approach for online bus speed control under uncertainty

Abstract The degradation of bus system attractiveness is primarily caused by low‐level service quality and reliability. As an essential technology for bus operation management, online bus speed control has proven to be a flexible and effective solution to mitigate bus bunching and enhance the service level of bus operation systems. In this study, we propose a robust nonlinear decision mapping (RNDM) approach that uses real‐time key bus system states to control bus speeds and accounts for uncertainties associated with passenger demands at stations and traffic speeds of interstation links. We develop this approach through a design process that involves learning the input–output mapping relation of a nonlinear programming simulation‐based optimization (NLPSO) method using regression tree with AdaBoost. Critical parameters of the fitted regression tree with AdaBoost are then optimized offline using a distributionally robust simulation‐based optimization (DRSO) model that is solved by a simulation‐based optimization (SO) algorithm. The resulting RNDM method effectively handles two types of uncertainties, expressed by two ambiguity sets of probability distributions, and ensures good bus operation performance even under worst‐case uncertainty levels. Numerical experiments reveal that the RNDM, NLPSO, and integer programming SO (IPSO) methods successfully mitigate bus bunching and improve service efficiency and robustness, compared to the no‐control scenario. Furthermore, the RNDM method outperforms NLPSO and IPSO in terms of comprehensive performance under uncertainties and demonstrates practical operability. In conclusion, this study presents an innovative general framework that uses a nonlinear decision mapping optimized offline by an SO approach to address online simulation‐based optimal decision‐making problems under uncertainties, which can be applied to solve similar problems.