Formulations for designing robust networks. An application to wind power collection

TL;DR

This paper develops formulations and algorithms for designing survivable capacitated networks, ensuring robustness against edge failures, with applications to wind power collection systems.

Contribution

It introduces three novel formulations—cut-set, flow, and bi-level—for survivable network design, and compares their computational efficiency.

Findings

The bi-level formulation effectively models attacker-defender scenarios.

Algorithms demonstrate varying efficiencies across formulations.

The approaches improve robustness in wind power network design.

Abstract

We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E $\subset$ E, covering T and r, such that the network induced by E is k-survivable: after the removal of any k edges, there still exists a feasible flow from r to T. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set, a flow and a bi-level formulation where the second-level is a min-max problem (with an attacker and a defender). We propose algorithms for each problem formulation and compare their efficiency.