# A MULTI-POPULATION GENETIC ALGORITHM FOR TREE-SHAPED NETWORK DESIGN PROBLEMS

### Dalila B. M. M. Fontes, José Fernando Gonçalves

#### 2009

#### Abstract

In this work we propose a multi-population genetic algorithm for tree-shaped network design problems using random keys. Recent literature on finding optimal spanning trees suggests the use of genetic algorithms. Furthermore, random keys encoding has been proved efficient at dealing with problems where the relative order of tasks is important. Here we propose to use random keys for encoding trees. The topology of these trees is restricted, since no path from the root vertex to any other vertex may have more than a pre-defined number of arcs. In addition, the problems under consideration also exhibit the characteristic of flows. Therefore, we want to find a minimum cost tree satisfying all demand vertices and the pre-defined number of arcs. The contributions of this paper are twofold: on one hand we address a new problem, which is an extension of the well known NP-hard hop-constrained MST problem since we also consider determining arc flows such that vertices requirements are met at minimum cost and the cost functions considered include a fixed cost component and a nonlinear flow routing component; on the other hand, we propose a new genetic algorithm to efficiently find solutions to this problem.

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#### Paper Citation

#### in Harvard Style

B. M. M. Fontes D. and Fernando Gonçalves J. (2009). **A MULTI-POPULATION GENETIC ALGORITHM FOR TREE-SHAPED NETWORK DESIGN PROBLEMS** . In *Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)* ISBN 978-989-674-014-6, pages 177-182. DOI: 10.5220/0002281101770182

#### in Bibtex Style

@conference{icec09,

author={Dalila B. M. M. Fontes and José Fernando Gonçalves},

title={A MULTI-POPULATION GENETIC ALGORITHM FOR TREE-SHAPED NETWORK DESIGN PROBLEMS},

booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)},

year={2009},

pages={177-182},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002281101770182},

isbn={978-989-674-014-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)

TI - A MULTI-POPULATION GENETIC ALGORITHM FOR TREE-SHAPED NETWORK DESIGN PROBLEMS

SN - 978-989-674-014-6

AU - B. M. M. Fontes D.

AU - Fernando Gonçalves J.

PY - 2009

SP - 177

EP - 182

DO - 10.5220/0002281101770182