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Using Quasi Random Sequences in Genetic Algorithms

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Abstract

The selection of initial points in a population-based heuristic optimization method is important since it affects the search for several iterations and often has an influence on the final solution. If no a priori information about the optimization problem is available, the initial population is often selected randomly using pseudo random numbers. Many times, however, it is more important that the points are as evenly distributed as possible than that they imitate random points. Therefore, we have studied the use of quasi random sequences in the initialization of a genetic algorithm. Sample points in a quasi random sequence are designed to have very good distribution properties. The modified genetic algorithms using quasi random sequences in the initial population have been tested by solving a large number of continuous benchmark problems from the literature. The numerical results of three genetic algorithm implementations using different quasi random sequences have been compared to those of a traditional implementation of using pseudo random numbers. The results are promising.

Key words

  • random numbers
  • global continuous optimization
  • genetic algorithms

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References

  • Ali, M. M., Törn, A., and Viitanen, S. (2002). A direct search variant of the simulated annealing algorithm for optimization involving continuous variables. Computers & Operations Research, 29 (1): 87–102.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Andre, J., Siarry, P., and Dognon, T. (2001). An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization. Advances in Engineering Software, 32 (1): 49–60.

    CrossRef  Google Scholar 

  • Androulakis, I. P., Maranas, C. D., and Floudas, C. A. (1995). aBB: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization, 7: 335–363.

    Google Scholar 

  • Battiti, R. and Tecchiolli, G. (1996). The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization Annals of Operations Research, 63: 153–188.

    CrossRef  MATH  Google Scholar 

  • Bratley, P. and Fox, B. L. (1988). Algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Transactions on Mathematical Software, 14 (1): 88–100.

    CrossRef  MATH  Google Scholar 

  • Bratley, P., Fox, B. L., and Niederreiter, H. (1992). Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation, 2 (3): 195–213.

    CrossRef  MATH  Google Scholar 

  • Chelouah, R. and Siarry, P. (2000). Tabu search applied to global optimization. European Journal of Operational Research, 123 (2): 256–270.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Deb, K. (2001). Multi-Objective Optimization using Evolutionary Algorihtms. John Wiley & Sons.

    Google Scholar 

  • Decker, A. and Aarts, E. (1991). Global optimization and simulated annealing. Mathematical Programming, 50: 367–393.

    CrossRef  MathSciNet  Google Scholar 

  • Dykes, S. and Rosen, B. (1994). Parallel very fast simulated reannealing by temperature block partitioning. In Proceedings of the 1994 IEEE International Conference on Systems, Man, and Cybernetics,volume 2, pages 1914–1919. IEEE Press.

    Google Scholar 

  • Gentle, J. E. (1998). Random number generation and Monte Carlo methods. Springer-Verlag. Glover, F (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8 (1): 156–166.

    Google Scholar 

  • Glover, F. (1999). Scatter search and path relinking. In Corne, D., Dorigo, M., and Glover, F., editors, New Ideas in Optimization,pages 297–316. McGraw Hill.

    Google Scholar 

  • Glover, F., Laguna, M., and Marti, R. (2000). Scatter search. Manuscript via private communication.

    Google Scholar 

  • Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.

    Google Scholar 

  • Kuipers, L. and Niederreiter, H (1974). Uniform Distribution of Sequences. John Wiley & Sons.

    Google Scholar 

  • Madsen, K. (2002). Test problems for global optimization http://www.imm.dtu.dk/km/GlobOpt/testex/.

  • Mascagni, M. and Karaivanova, A. (2000). What are quasirandom numbers and are they good for anything besides integration? In Proceedings of Advances in Reactor Physics and Mathematics and Computation into the Next Millenium (PHYSOR2000).

    Google Scholar 

  • Matlab toolbox (2002). Genetic and evolutionary algorithm toolbox for use with matlab. http://www.geatbx.com/.

    Google Scholar 

  • Michalewicz, Z. (1994). Genetic algorithms + data structures = evolution program. Springer-Verlag.

    Google Scholar 

  • Miettinen, K., Mäkelä, M. M., and Toivanen, J. (2000). Comparison of four penalty function-based methods in handling constraints with genetic algorithms. Technical Report B 17/2000, University of Jyväskylä, Department of Mathematical Information Technology.

    Google Scholar 

  • Morokoff, W. J. and Caflisch, R. E. (1994). Quasi-random sequences and their discrepancies. SIAM Journal on Scientific Computing, 15 (6): 1251–1279.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Niederreiter, H. (1983). Quasi-Monte Carlo methods for global optimization. In Grossmann, W., Pflug, G., Vincze, I, and Wertz, W., editors, Proceedings of the 4th Pannonian Symposium on Mathematical Statistics, pages 251–267.

    Google Scholar 

  • Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM.

    Google Scholar 

  • Özdamar, L. and Demirhan, M. (2000). Experiments with new stochastic global optimization search techniques. Computers & Operations Research, 27: 841–865.

    CrossRef  MATH  Google Scholar 

  • Press, W. H. and Teukolsky, S. A. (1989). Quasi- (that is, sub-) random numbers. Computers in Physics, 3 (6): 76–79.

    Google Scholar 

  • Roli, A (2002). Test problems in R2. http://iridia.ulb.ac.be/aroli/ICEO/Functions/Functions.html.

  • Sobol’, I. M. (1979). On the systematic search in a hypercube. SIAM Journal on Numerical Analysis, 16 (5): 790–793.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Sobol’, I. M. (1998). On quasi-Monte Carlo integrations. Mathematics and Computers in Simulation, 47 (2–5): 103–112.

    CrossRef  MathSciNet  Google Scholar 

  • Sobol’, I. M. and Bakin, S. G. (1994). On the crude multidimensional search. Journal of Computational and Applied Mathematics, 56 (3): 283–293.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Törn, A., Ali, M. M., and Viitanen, S. (1999). Stochastic global optimization: Problem classes and solution techniques. Journal of Global Optimization, 14 (4): 437–447.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Törn, A. and 2ilinskas, A. (1989). Global Optimization. Springer-Verlag.

    Google Scholar 

  • Trafalis, B. and Kasap, S. (2002). A novel metaheuristics approach for continuous global optimization. Journal of Global Optimization, 23 (2): 171–190.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Tuffin, B. (1996). On the use of low discrepancy sequences in Monte Carlo methods. Technical Report 1060, I.R.I.S.A., Rennes, France.

    Google Scholar 

  • Wikramaratna, R. S. (1989). ACORN — a new method for generating sequences of uniformly distributed pseudo-random numbers. Journal of Computational Physics, 83 (1): 16–31.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Maaranen, H., Miettinen, K., Mäkelä, M.M. (2003). Using Quasi Random Sequences in Genetic Algorithms. In: Rudnicki, M., Wiak, S. (eds) Optimization and Inverse Problems in Electromagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2494-4_4

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  • DOI: https://doi.org/10.1007/978-94-017-2494-4_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6375-5

  • Online ISBN: 978-94-017-2494-4

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