Formulating the Restoration of Distribution Networks as a Multiple Traveling Salesman Problem

Abstract

Severe weather events can cause extensive damage to electrical distribution networks, requiring a multi-day restoration effort. Optimizing the dispatch of repair crews minimizes the severe socio-economic consequences of such events. Considering both repair times and travel times, we use graphical manipulations to transform this multiple crew scheduling problem into a type of traveling salesman problem(TSP). Specifically, we demonstrate that the restoration problem bears major resemblance to an instance of a cost constrained reward maximizing mTSP (multiple TSP) on node and edge weighted (doubly weighted) graphs (a variant we dub the CCRM-mTSP-DW), where the objective is to maximize the aggregate reward earned during the upcoming restoration window, provided no crew violates its time budget and electrical continuity constraints are met. Despite the rich history of research on the TSP and its variants, this CCRM-mTSP-DW variant has not been studied before, although its closest cousin happens to be the "Selective TSP" (S-TSP). This reinterpretation of the restoration problem not only opens up the possibility of drawing on existing solution methods developed for the TSP and its variants, it also adds a new chapter in the annals of research on "TSP-like'' problems. In this paper, we propose a "TSP-like'' mixed integer linear programming (MILP) model for solving the restoration problem and validate it on the IEEE PES 123-node test feeder network.