Convexification Approaches for Regional Route Guidance and Demand Management with Generalized Mfds

The joint demand management with route guidance problem is formulated as a nonlinear and non-convex Model Predictive Control problem. To tackle this challenging problem, we propose two different solution approaches: (i) a successive convexification approach that constructs convex bounding sets for all nonlinear terms, and (ii) a linear approximation approach that solves the problem using approximations of the generalized with triangular macroscopic fundamental diagrams. The proposed approaches offer a different tradeoff between execution speed and solution quality, as the linear approximation approach runs faster while the successive convexification approach yields better quality solutions. Lower bounds on the optimal solution are also obtained through the successive convexification approach. Macroscopic simulation results illustrate the efficiency of the successive convexification and linear approximation approaches yielding an optimality gap of less than 5.5% and 10% in all considered cases, respectively. Furthermore, both approaches outperform a state-of-practice nonlinear solver in terms of solution quality and execution time. Finally, substantial gains are also obtained regarding travel time and traffic flow efficiency in a realistic microsimulation environment