Braess Paradox in Optimal Multiperiod Resource-Constrained Restoration Scheduling Problem

Abstract

This study examines the Braess paradox in the context of the multiple-period restoration scheduling problem. A bilevel programming model is devised, where the upper-level problem is to determine the optimal sequence of recovery activities considering the limited resource constraint, while the low-level problem is the traffic assignment model that captures passengers’ responses to the changes in the transportation network capacity. Then, a novel genetic algorithm (GA) is developed to solve the proposed restoration scheduling problem. Our case study first shows that the optimal restoration schedule does not concur with the results obtained based on the link importance measurement, and the former can achieve a 4% total travel time reduction compared with the latter. Then, various numerical experiments are conducted to illustrate the occurrence and properties of the Braess paradox, which is that the network performance in some restoration periods can be better than that before the disruption or after a disrupted link is recovered. Moreover, it is revealed that with sufficient resources for multiple links to be repaired simultaneously, it is unnecessary to do so in the optimal rehabilitation schedule due to the existence of the Braess paradox. Finally, in terms of algorithmic performance, our proposed-GA outperforms the particle swarm optimisation algorithm and can reduce the computation time by up to 14%.