Optimizing designs and operations of a single network or multiple interdependent infrastructures under stochastic arc disruption

In this paper, we consider an infrastructure as a network with supply, transshipment, and demand nodes. A subset of potential arcs can be constructed between node pairs for conveying service flows. The paper studies two optimization models under stochastic arc disruption. Model 1 focuses on a single network with small-scale failures, and repairs arcs for quick service restoration. Model 2 considers multiple interdependent infrastructures under large-scale disruptions, and mitigates cascading failures by selectively disconnecting failed components. We formulate both models as scenario-based stochastic mixed-integer programs, in which the first-stage problem builds arcs, and the second-stage problem optimizes recourse operations for restoring service or mitigating losses. The goal is to minimize the total cost of infrastructure design and recovery operations. We develop cutting-plane algorithms and several heuristic approaches for solving the two models. Model 1 is tested on an IEEE 118-bus system. Model 2 is tested on systems consisting of the 118-bus system, a 20-node network, and/or a 50-node network, with randomly generated interdependency sets in three different topological forms (i.e., chain, tree, and cycle). The computational results demonstrate that (i) decomposition and cutting-plane algorithms effectively solve Model 1, and (ii) heuristic approaches dramatically decrease the CPU time for Model 2, but yield worse bounds when cardinalities of interdependency sets increase. Future research includes developing special algorithms for optimizing Model 2 for complex multiple infrastructures with special topological forms of system interdependency.