The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems.

Dynamic user optimal simultaneous route and departure time choice(DUO-SRDTC) problems are usually formulated as variational inequality (VI) problems whose solution algorithms generally require continuous and monotone route travel cost functions to guarantee convergence. However, the monotonicity of the route travel cost functions can not be ensured even if the route travel time functions are monotone. In contrast to traditional formulations, this paper formulates a DUO-SRDT C problem (that can have fixed or elastic demand) as a system of nonlinear equations. The system of nonlinear equations is a function of generalized origin-destination (OD) travel costs rather than route flows and includes a dynamic user optimal (DUO) route choice subproblem with perfectly elastic demand and a quadratic programming (QP) subproblem under certain assumptions. This study also proposes a solution method based on the backtracking inexact Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, the extra gradient algorithm, and the Frank-Wolf e algorithm The BFGS method, the extra gradient algorithm, and the Frank-Wolf e algorithm are used to solve the system of nonlinear equations, the DUO route choice subproblem, and the QP subproblem, respectively. The proposed formulation and solution method can avoid the requirement of monotonicity of the route travel cost functions to obtain a convergent solution and provide a new approach with which to solve DUO-SRDTC problems. Finally, numeric examples are used to demonstrate the performance of the proposed solution method. [ABSTRACT FROM AUTHOR]