A hybrid ga for the edge-biconnectivity augmentation problem

Abstract

In the design of communication networks, robustness against failures in single links or nodes is an important issue. This paper proposes a new approach for the A/’P-complete edge-biconnectivity augmentation (E2AUG) problem, in which a given graph Go(V, Eo) needs to be augmented by the cheapest possible set of edges A UG so that a single edge deletion does not disconnect Go. The new approach is based on a preliminary reduction of the problem and a genetic algorithm (GA) using a binary vector to represent a set of augmenting edges and therefore a candidate solution. Two strategies are proposed to deal with infeasible solutions that do not lead to edge-biconnectivity. In the first, more traditional variant, infeasible solutions are detected and simply discarded. The second method is a hybrid approach that uses an effective heuristic to repair infeasible solutions by adding usually cheap edges to A UG until the graph augmented with AUG becomes edge-biconnected. The two G A-variants are empirically compared to each other and to another iterative heuristic for the E2AUG problem using instances involving up to 1270 edges.