Bi-objective robust nonlinear decision approach for en-route bus speed control considering implementation errors and traffic uncertainties

This study proposes a bi-objective robust nonlinear decision mapping (Bi-RNDM) approach for en-route bus speed control, aiming to enhance bus service level and reliability. Through a two-stage procedure, the proposed approach addresses the challenges due to traffic flow uncertainties and implementation errors from bus drivers. In the first stage, a bi-objective nonlinear programming model (Bi-NLPM) is built and solved to collect labeled data, which are then used to pre-train the mapping relationship between bus system states and optimal bus control speeds using support vector machines (SVM). This results in a bi-objective pre-trained nonlinear decision mapping (Bi-PNDM) consisting of an SVM-based classifier and an SVM-based regressor. In the second stage, a bi-objective robust critical parameter simulation-based optimization (BRCPSO) model is built within the min–max expectation framework, and it is solved using a modified bi-objective robust simulation-based optimization (MBORSO) algorithm to optimize the critical parameters of Bi-PNDM. The resulting Bi-RNDM improves the operation performance by reducing the deviation in service headway as well as the deviation from service schedule, considering the existence of traffic uncertainties and implementation errors from bus drivers. Numerical experiments are conducted based on the case study of the bus line 406 in Changsha, China, to demonstrate the efficiency of the MBORSO algorithm and the superior bus service level and robustness of the Bi-RNDM method. Results show that the proposed Bi-RNDM method can effectively balance the two competitive objectives, and the produced speed control is implementable for only about 20% of the operation period, suggesting high practicality. The proposed framework is not only applicable in the bus speed control problems, as it promises for addressing other complex multi-objective online optimal decision-making problems that are under various uncertainties and resolvable through data-driven nonlinear decision mapping.