Solution of minimum spanning forest problems with reliability constraints

TL;DR

This paper introduces a new optimization problem for designing reliable networks with minimum cost, and proposes a mixed integer programming model and a metaheuristic to solve it efficiently.

Contribution

It formulates the reliability constrained k-rooted minimum spanning forest problem and develops a novel metaheuristic approach for its solution.

Findings

Metaheuristic finds high-quality solutions quickly.

The approach is effective for network design applications.

Computational tests validate the method's efficiency.

Abstract

We propose the reliability constrained k-rooted minimum spanning forest, a relevant optimization problem whose aim is to find a k-rooted minimum cost forest that connects given customers to a number of supply vertices, in such a way that a minimum required reliability on each path between a customer and a supply vertex is satisfied and the cost is a minimum. The reliability of an edge is the probability that no failure occurs on that edge, whereas the reliability of a path is the product of the reliabilities of the edges in such path. The problem has relevant applications in the design of networks, in fields such as telecommunications, electricity and transports. For its solution, we propose a mixed integer linear programming model, and an adaptive large neighborhood search metaheuristic which invokes several shaking and local search operators. Extensive computational tests prove that the metaheuristic can provide good quality solutions in very short computing times.