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Genetic operators for two-dimentional shape optimization

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1063))

Abstract

This paper presents a Genetic Algorithm approach to two-dimensional shape optimization. Shapes are represented as arrays of boolean pixels (material/void), or bit-arrays. The inadequacy of the (one-dimensional) bitstring representation is emphasized, both a priori and experimentally. This leads to the design of crossover operators adapted to the two-dimensional representation. Similarly, some non standard mutation operators are introduced and studied. A strategy involving evolutionary choice among these different operators is finally proposed. All experiments are performed on a simple test-problem of Optimum Design, as the computational cost of real-world problems forbids extensive experimental tests.

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References

  1. G. Allaire and R. V. Kohn. Optimal design for minimum weight and compliance in plane stress using extremal microstructures. European Journal of Mechanics, A/Solids, 12(6): 839–878, 1993.

    Google Scholar 

  2. J. Antonisse. A new interpretation of schema notation that overturns the binary encoding constraint. In J. D. Schaffer, editor, Proceedings of the 3 rd International Conference on Genetic Algorithms, pages 86–91. Morgan Kaufmann, June 1989.

    Google Scholar 

  3. M. Bendsoe and N. Kikushi. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71:197–224, 1988.

    Google Scholar 

  4. D. L. Calloway. Using a genetic algorithm to design binary phase-only filters for pattern recognition. In R. K. Belew and L. B. Booker, editors, Proceedings of the 4 th International Conference on Genetic Algorithms. Morgan Kaufmann, 1991.

    Google Scholar 

  5. R. A. Caruna and J. D. Schaffer. Representation and hidden bias: Gray vs binary coding for genetic algorithms. In Proceedings of ICML-88, International Conference on Machine Learning. Morgan Kaufmann, 1988.

    Google Scholar 

  6. C. D. Chapman, K. Saitou, and M. J. Jakiela. Genetic algorithms as an approach to configuration and topology design. Journal of Mechanical Design, 116:1005–1012, 1994.

    Google Scholar 

  7. C. Ghaddar, Y. Maday, and A. T. Patera. Analysis of a part design procedure. Submitted to Nümerishe Mathematik, 1995.

    Google Scholar 

  8. D. E. Goldberg. Genetic algorithms in search, optimization and machine learning. Addison Wesley, 1989.

    Google Scholar 

  9. J. J. Grefenstette. Incorporating problem specific knowledge in genetic algorithms. In Davis L., editor, Genetic Algorithms and Simulated Annealing, pages 42–60. Morgan Kaufmann, 1987.

    Google Scholar 

  10. J. J. Grefenstette. Virtual genetic algorithms: First results. Technical Report AIC-95-013, Navy Center for Applied Research in Artificial Intelligence, February 1995.

    Google Scholar 

  11. J. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, 1975.

    Google Scholar 

  12. E. Jensen. Topological Structural Design using Genetic Algorithms. PhD thesis, Purdue University, November 1992.

    Google Scholar 

  13. C. Z. Janikow and Z. Michalewicz. An experimental comparison of binary and floating point representations in genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of 4th International Conference on Genetic Algorithms, pages 31–36. Morgan Kaufmann, July 1991.

    Google Scholar 

  14. C. Kane. Algorithmes génétiques et Optimisation topologique. PhD thesis, Université de Paris VI, 1995. Soutenance prévue en 1996.

    Google Scholar 

  15. C. Kane, F. Jouve, and M. Schoenauer. Structural topology optimization in linear and nonlinear elasticity using genetic algorithms. In Proceedings of the ASME 21st Design Automation Conference. ASME, Sept. 1995.

    Google Scholar 

  16. Z. Michalewicz and C. Z. Janikow. Handling constraints in genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the 4 th International Conference on Genetic Algorithms, pages 151–157, 1991.

    Google Scholar 

  17. N. J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5:183–20, 1991.

    Google Scholar 

  18. N. J. Radcliffe and P. D. Surry. Fitness variance of formae and performance prediction. In D. Whitley and M. Vose, editors, Foundations of Genetic Algorithms 3, pages 51–72. Morgan Kaufmann, 1994.

    Google Scholar 

  19. H.-P. Schwefel. Numerical Optimization of Computer Models. John Wiley & Sons, New-York, 1981.

    Google Scholar 

  20. W. M. Spears. Adapting crossover in a genetic algorithm. In R. K. Belew and L. B. Booker, editors, Proceedings of the 4 th International Conference on Genetic Algorithms. Morgan Kaufmann, 1991.

    Google Scholar 

  21. W. M. Spears. Adapting crossover in evolutionary algorithms. In J. R. McDonnell, R. G. Reynolds, and D. B. Fogel, editors, Proceedings of the 4 th Annual Conference on Evolutionary Programming, pages 367–384. MIT Press, March 1995.

    Google Scholar 

  22. M. Sebag and M. Schoenauer. Controling crossover through inductive learning. In Y. Davidor, H.-P. Schwefel, and R. Manner, editors, Proceedings of the 3 rd Conference on Parallel Problems Solving from Nature, pages 209–218. Springer-Verlag, LNCS 866, October 1994.

    Google Scholar 

  23. G. Syswerda. Uniform crossover in genetic algorithms. In J. D. Schaffer, editor, Proceedings of the 3 rd International Conference on Genetic Algorithms, pages 2–9. Morgan Kaufmann, 1989.

    Google Scholar 

  24. D. Whitley, T. Starkweather, and D. Fuquay. Scheduling problems and travelling salesman: The genetic edge recombination operator. In J. D. Schaffer, editor, Proceedings of the 3 rd International Conference on Genetic Algorithms. Morgan Kaufmann, 1989.

    Google Scholar 

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Jean-Marc Alliot Evelyne Lutton Edmund Ronald Marc Schoenauer Dominique Snyers

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© 1996 Springer-Verlag Berlin Heidelberg

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Kane, C., Schoenauer, M. (1996). Genetic operators for two-dimentional shape optimization. In: Alliot, JM., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds) Artificial Evolution. AE 1995. Lecture Notes in Computer Science, vol 1063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61108-8_50

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  • DOI: https://doi.org/10.1007/3-540-61108-8_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61108-0

  • Online ISBN: 978-3-540-49948-0

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