On the Efficient Construction of Rectangular Grids from Given Data Points
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.
KeywordsGenetic Algorithm Grid Size Travel Salesman Problem Travel Salesman Problem Rectangular Grid
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- 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.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.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.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.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.T. Kohonen. Self-Organization and Associative Memory. Springer-Verlag, 3rd edition, 1989.Google Scholar
- 8.J Vesanto, J. Himberg, E. Alhoniemi, and J. Parhankangas. SOM Toolbox for Matlab 5. Technical Report A57, Helsinki University of Technology, http://www.cis.hut.fi/projects/somtoolbox/, April 2000.
- 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.K. Knödler, J. Poland, A. Mitterer, and A. Zell. Optimizing data measurements at test beds using multi-step genetic algorithms. Preprint, 2000.Google Scholar