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Rotationally Invariant Crossover Operators in Evolutionary Multi-objective Optimization

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Simulated Evolution and Learning (SEAL 2006)

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Abstract

Multi-objective problems with parameter interactions can present difficulties to many optimization algorithms. We have investigated the behaviour of Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX), Parent-centric Crossover (PCX), and Differential Evolution (DE), as possible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II (Non-dominated Sorting Genetic Algorithm II) on four rotated test problems exhibiting parameter interactions. The rotationally invariant crossover operators demonstrated improved performance in optimizing the problems, over a non-rotationally invariant crossover operator.

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References

  1. Salomon, R.: Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions: A survey of some theoretical and practical aspects of genetic algorithms. Bio. Systems 39(3), 263–278 (1996)

    Article  Google Scholar 

  2. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  3. Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(2), 115–148 (1995)

    MATH  MathSciNet  Google Scholar 

  4. Deb, K., Kumar, A.: Real-coded genetic algorithms with simulated binary crossover: Studies on multi-modal and multi-objective problems. Complex Systems 9(6), 431–454 (1995)

    Google Scholar 

  5. Corne, D., Dorigo, M., Glover, F. (eds.): New Ideas in Optimization. McGraw-Hill, London (1999)

    Google Scholar 

  6. Iorio, A., Li, X.: Incorporating directional information within a differential evolution algorithm for multiobjective optimization. In: Proceedings of the 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), IEEE Press, Los Alamitos (2006)

    Google Scholar 

  7. Iorio, A., Li, X.: Rotated test problems for assessing the performance of multiobjective optimization algorithms. In: Proceedings of the 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), IEEE Press, Los Alamitos (2006)

    Google Scholar 

  8. Price, K.: New Ideas in Optimization, p. 98. McGraw-Hill, New York (1999)

    Google Scholar 

  9. Ballester, P., Carter, J.N.: Real-parameter genetic algorithms for finding multiple optimal solutions in multi-modal optimization. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 707–717. Springer, Heidelberg (2003)

    Google Scholar 

  10. Ono, I., Kita, H., Kobayashi, S.: A Real-coded Genetic Algorithm using the Unimodal Normal Distribution Crossover. Advances in Evolutionary Computing: Theory and Applications, pp. 213–237. Springer, Heidelberg (2003)

    Google Scholar 

  11. Kita, H.: A comparison study of self-adaptation in evolution strategies and real-coded genetic algorithms. Evolutionary Computation 9(2), 223–241 (2001)

    Article  MathSciNet  Google Scholar 

  12. Ono, I., Kobayashi, S., Yoshida, K.: Optimal lens design by real-coded genetic algorithms using UNDX. Computer Methods in Applied Mechanics and Engineering 186, 483–497 (2000)

    Article  MATH  Google Scholar 

  13. Kita, H., Ono, I., Kobayashi, S.: Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms. In: Proc. 1999 Congress on Evolutionary Computation (CEC 1999), pp. 1581–1587 (1999)

    Google Scholar 

  14. Deb, K., Joshi, D., Anand, A.: Real-coded evolutionary algorithms with parent-centric recombination. Indian Institute of Technology, Kanpur, Tech. Rep. KanGAL Report No.2001003 (2001)

    Google Scholar 

  15. Deb, K., Joshi, D., Anand, A.: Real-coded evolutionary algorithms with parent-centric recombination. In: Proceedings of the 2002 Congress on Evolutionary Computation CEC 2002, pp. 61–66. IEEE Press, Los Alamitos (2002)

    Chapter  Google Scholar 

  16. Tsutsui, S., Yamamura, M.: Multi-parent recombination with simplex crossover in real coded genetic algorithms. In: Proceedings of the 1999 Genetic and Evolutionary Computation Conference (GECCO 1999), pp. 657–664 (1999)

    Google Scholar 

  17. Chang, C.S., Xu, D.Y.: Differential evolution of fuzzy automatic train operation for mass rapid transit system. IEEE Proceedings of Electric Power Applications 147(3), 206–212 (2000)

    Article  Google Scholar 

  18. Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), vol. 2, pp. 971–978 (2001)

    Google Scholar 

  19. Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based multi-objective differential evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), vol. 2, pp. 862–869. IEEE Press, Los Alamitos (2003)

    Google Scholar 

  20. Madavan, N.K.: Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 2, pp. 1145–1150. IEEE Press, Los Alamitos (2002)

    Chapter  Google Scholar 

  21. Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization, p. 88. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  22. Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Iorio, A., Li, X. (2006). Rotationally Invariant Crossover Operators in Evolutionary Multi-objective Optimization. In: Wang, TD., et al. Simulated Evolution and Learning. SEAL 2006. Lecture Notes in Computer Science, vol 4247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11903697_40

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  • DOI: https://doi.org/10.1007/11903697_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47331-2

  • Online ISBN: 978-3-540-47332-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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