Multi-modal travel route planning considering environmental preference under uncertainties: A distributionally robust optimization approach

MaaS (Mobility as a Service) is the main trend in future transportation development. From the user perspective, it is primarily manifested as a shift in travel behavior, transitioning from reliance on single modes, such as private cars, to a mixed mode of various transportation options. In order to facilitate providing door-to-door services for travelers, this paper proposes a user-centric route planning approach under a new multi-modal framework, which it considers five travel modes, including bus, metro, car-hailing, as well as bike-sharing and walking that effectively addresses the last mile problem. Given the diverse travel objectives among travelers, this paper integrates travel time, cost, comfort, and green travel awareness into the objective function. Moreover, a multi-modal network travel route optimization model is established to generate route planning that aligns with traveler’s preferences. To address the challenges of multiple time uncertainties and incomplete distribution information resulting from problems such as road congestion and uneven distribution of bike-sharing and car-hailing during a trip, this paper proposes a distributionally robust optimization model to describe the uncertainties in two dimensions of the objective function. A generalized interval-valued trapezoidal possibility distribution is used to describe the time for finding a bike-sharing or for waiting a car-hailing service. The robust objective function and constraints are equivalently formulated as a deterministic model. The distributionally robust optimization model for uncertain travel times of buses and car-hailing services is demonstrated to be semi-infinite but can be safely and equivalently approximated under the Gaussian perturbations ambiguity set. Through comparative analyses with the traditional robust optimization method using experimental cases, the proposed distributionally robust optimization model exhibits superior performance. In addition, sensitivity analyzes are conducted on the relevant factors that influence travelers’ reduction in carbon emissions after the implementation of carbon incentive measures. The results demonstrate the effectiveness of the incentives introduced, which provides valuable information for the government to improve various incentive measures aimed at promoting low-carbon travel among travelers.