A Genetic Algorithm for the Bi-Level Topological Design of Local Area Networks.

José-Fernando Camacho-Vallejo,Francisco López-Ramos,Ricardo Pedraza Rodríguez,Julio Mar-Ortiz,Lourens J Waldorp

doi:10.1371/journal.pone.0128067

Abstract

Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment. Usually these networks consist of several LAN segments connected by bridges. The topological LAN design bi-level problem consists on assigning users to clusters and the union of clusters by bridges in order to obtain a minimum response time network with minimum connection cost. Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree. In this paper, we propose a genetic algorithm for solving the bi-level topological design of a Local Access Network. Our solution method considers the Stackelberg equilibrium to solve the bi-level problem. The Stackelberg-Genetic algorithm procedure deals with the fact that the follower’s problem cannot be optimally solved in a straightforward manner. The computational results obtained from two different sets of instances show that the performance of the developed algorithm is efficient and that it is more suitable for solving the bi-level problem than a previous Nash-Genetic approach.

Highlights

The design of computer and telecommunication networks is a hard constrained combinatorial optimization problem that has received considerable attention from practitioners and researchers during the recent years
The telecommunication network design problem consists of deciding the number, types, and locations of the network active elements, as well as the links and their capacities
In the existing literature we can identify two kinds of problems related to the telecommunication networks design: hub location [1] and topological design [2]

Summary

Introduction

The design of computer and telecommunication networks is a hard constrained combinatorial optimization problem that has received considerable attention from practitioners and researchers during the recent years. The computational time consumed for solving the lower level needs to be minimized When it is possible, the lower level is optimally solved; in the cases when the lower level problem is NP-hard or a strong combinatorial problem, it is assumed that since the follower rationally reacts to a leader’s decision, an acceptable solution (good quality in a low computational cost) will be made. By considering this approach an acceptable Stackelberg equilibrium is reached. The partial average message delay caused by the edge e(p,q)

E is defined as

Findings

Conclusions and Further Research