Table of Contents
Journal of Artificial Evolution and Applications
Volume 2008, Article ID 143624, 14 pages
Research Article

Geometric Particle Swarm Optimization

1Centre for Informatics and Systems of the University of Coimbra, Polo II - University of Coimbra, Coimbra 3030-290, Portugal
2Department of Computing and Electronic Systems, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK
3Dalle Molle Institute for Artificial Intelligence (IDSIA), Galleria 2, Manno-Lugano 6928, Switzerland

Received 21 July 2007; Accepted 4 December 2007

Academic Editor: T. Blackwell

Copyright © 2008 Alberto Moraglio et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Using a geometric framework for the interpretation of crossover of recent introduction, we show an intimate connection between particle swarm optimisation (PSO) and evolutionary algorithms. This connection enables us to generalise PSO to virtually any solution representation in a natural and straightforward way. The new Geometric PSO (GPSO) applies naturally to both continuous and combinatorial spaces. We demonstrate this for the cases of Euclidean, Manhattan and Hamming spaces and report extensive experimental results. We also demonstrate the applicability of GPSO to more challenging combinatorial spaces. The Sudoku puzzle is a perfect candidate to test new algorithmic ideas because it is entertaining and instructive as well as being a nontrivial constrained combinatorial problem. We apply GPSO to solve the Sudoku puzzle.