A Bi-Level Optimization Approach to Network Flow Management Incorporating Travelers’ Herd Effect

Herd effect is a widespread phenomenon in real-world situations. This study explores how the herd effect can be used to manage network flow effectively. We examined its impact on travelers’ route choices and propose a mixed network flow evolution process that incorporates the herd effect, considering two types of travelers: those who receive route subsidy information and those who do not. Based on this evolution process, we developed a bi-level optimization model to determine the optimal subsidized routes, the subsidy amounts per kilometer, and the proportion of travelers receiving subsidy information. A hybrid algorithm with two iterative procedures was proposed to solve the model, in which the adaptive genetic algorithm (AGA) was employed to solve the upper-level nonlinear mixed-integer programming problem, and the partial linearization method was used to solve the lower-level network flow evolution process. Numerical results indicate that the presence of herd effect can effectively reduce both the total travel time of the network and the overall subsidy costs. The findings of this study have significant implications for the utilization of the herd effect in designing navigation software and developing congestion pricing strategies.