On the Efficient Construction of Rectangular Grids from Given Data Points

  • Jan Poland
  • Kosmas Knödler
  • Andreas Zell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2037)


Many combinatorial optimization problems provide their data in an input space with a given dimension. Genetic algorithms for those problems can benefit by using this natural dimension for the encoding of the individuals rather than a traditional one-dimensional bit string. This is true in particular if each data point of the problem corresponds to a bit or a group of bits of the chromosome.We develop different methods for constructing a rectangular grid of near-optimal dimension for given data points, providing a natural encoding of the individuals. Our algorithms are tested with some large TSP instances.


Genetic Algorithm Grid Size Travel Salesman Problem Travel Salesman Problem Rectangular Grid 
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  1. 1.
    T.N. Bui and B.R. Moon. A new genetic approach for the traveling salesman problem. In International Conference on Evolutionary Computation, pages 7–12, 1994.Google Scholar
  2. 2.
    J. Grefenstette, R. Gopal, B. Rosmaita, and D. Van Gucht. Genetic algorithms for the travelling salesman problem. In Proceedings of the first International Conference on Genetic Algorithms and Application, pages 160–168, 1985.Google Scholar
  3. 3.
    A. Homaifar, S. Guan, and G.E. Liepins. A new approach on the traveling salesman problem by genetic algorithms. In 5th International Conference on Genetic Algorithms, pages 460–466, 1993.Google Scholar
  4. 4.
    T.N. Bui and B.R. Moon. On multidimensional encoding/crossover. In 6th International Conference on Genetic Algorithms, pages 49–56, 1995.Google Scholar
  5. 5.
    B.R. Moon and C.K. Kim. A two-dimensional embedding of graphs for genetic algorithms. In 7th International Conference on Genetic Algorithms, pages 204–211, 1997.Google Scholar
  6. 6.
    T. Kohonen. Self-Organization and Associative Memory. Springer-Verlag, 3rd edition, 1989.Google Scholar
  7. 7.
    A. Zell. Simulation neuronaler Netze. Addison-Wesley, Bonn, 1994.zbMATHGoogle Scholar
  8. 8.
    J Vesanto, J. Himberg, E. Alhoniemi, and J. Parhankangas. SOM Toolbox for Matlab 5. Technical Report A57, Helsinki University of Technology,, April 2000.
  9. 9.
    J. Poland and K. Knödler et al. A genetic algorithm with variable alphabet coding for a new NP-complete problem from application. Preprint, 2000.Google Scholar
  10. 10.
    K. Knödler, J. Poland, A. Mitterer, and A. Zell. Optimizing data measurements at test beds using multi-step genetic algorithms. Preprint, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jan Poland
  • Kosmas Knödler
  • Andreas Zell
    • 1
  1. 1.Universität TöbingenTübingenGermany

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