Nonlinear network optimization: an embedding vector space approach

  • Authors:

  • Eduardo G. Carrano;Ricardo H. C. Takahashi;Carlos M. Fonseca;Oriane M. Neto

  • Affiliations:

  • Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, Brazil;Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil;Department of Electronic Engineering and Informatics, Faculty of Science and Technology, Universidade do Algarve, Faro, Portugal and Center for Management Studies, Instituto Superior Técnico, ...;Department of Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

  • Venue:
  • IEEE Transactions on Evolutionary Computation
  • Year:
  • 2010

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Abstract

This paper proposes a normed-space vector representation of networks which allows defining evolutionary operators for network optimization that resemble continuousspace operators. These operators are employed here to build a genetic algorithm which becomes generic for the optimization of tree networks, without the requirement of any special encoding scheme. Such a genetic algorithm has been compared with several encoding-based genetic algorithms, on 25 and 50-node instances of the optimal communication spanning tree and of the quadratic minimum spanning tree, and has been shown to outperform all other algorithms in a stochastic dominance analysis. The proposed approach has also been applied to an electric power distribution network design (a multibranch problem), outperforming the results presented in a former reference (which have been obtained with an Ant Colony algorithm). The results of some landscape dispersion analysis suggest that the proposed normed-space network vector representation is analogous to some continuous-variable space dilation operations, which define favorable space coordinates for optimization.