On Progressive Network Recovery from Massive Failures under Uncertainty

Network recovery after large-scale failures has tremendous cost implications. While numerous approaches have been proposed to restore critical services after large-scale failures, they mostly assume having full knowledge of failure location, which cannot be achieved in real failure scenarios. Making restoration decisions under uncertainty is often further complicated in a large-scale failure. This paper addresses progressive network recovery under the uncertain knowledge of damages. We formulate the problem as a mixed integer linear programming and show that it is NP-hard. We propose an iterative stochastic recovery algorithm (ISR) to recover the network in a progressive manner to satisfy the critical services. At each optimization step, we make a decision to repair a part of the network and gather more information iteratively, until critical services are completely restored. We propose three different approaches: 1) an iterative shortest path algorithm; 2) an approximate branch and bound (ISR-BB); and 3) an iterative multicommodity LP relaxation (ISR-MULT). Further, we compared our approach with the state-of-the-art centrality-based damage assessment and recovery (CeDAR) and iterative split and prune (ISP) algorithms. Our results show that ISR-BB and ISR-MULT outperform the state-of-the-art ISP and CeDAR algorithms while we can configure our choice of tradeoff between the execution time, the number of repairs (cost), and the demand loss. We show that our recovery algorithm, on average, can reduce the total number of repairs by a factor of about 3 with respect to ISP, while satisfying all critical demands.