Stochastic ridesharing equilibrium problem with compensation optimization

In the urban traffic system with ridesharing programs, we develop a generalized stochastic user equilibrium model to formulate travelers’ mode and route choice behavior. To suit more general scenarios, the proposed model takes into consideration travelers’ heterogeneity in terms of car ownership and value of time, and travelers’ limited perceived information based on the stochastic user equilibrium principle instead of Wardrop's user equilibrium principle. The proposed model is formulated as variational inequalities and an equivalent nonlinear mixed complementarity problem due to the inseparable and asymmetric travel cost functions. Furthermore, we address the decision-making problem of ridesharing compensation from the perspective of traffic managers and policy-makers who want to minimize the total travel cost and vehicular air pollution emissions simultaneously. A bi-objective optimization model and two single-objective optimization models are proposed to formulate this decision-making problem, in which travelers’ mode and route choice behavior has been respected. As a mathematical problem with complementarity constraints, the bi-objective optimization model is solved by an improved Non-Dominated Sorting Genetic Algorithm II to generate a set of Pareto-optimal solutions for policy-makers and allow them to choose desired solutions. Finally, several numerical experiments based on two different scales of networks are conducted to demonstrate the properties of the problem and the performance of the proposed model and algorithm. The results show that rational pricing of ridesharing compensation can indeed mitigate urban traffic congestion and pollution emissions simultaneously. Moreover, by integrating travelers’ choice behavior based on the stochastic user equilibrium principle instead of the user equilibrium principle in the ridesharing compensation optimization model, this study derives a series of more effective decision-making strategies for ridesharing compensation.