Journal of KIISE:Software and Applications (한국정보과학회논문지:소프트웨어및응용)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
권호 표지

Non-Synonymously Redundant Encodings and Normalization in Genetic Algorithms

비유사 중복 인코딩을 사용하는 유전 알고리즘을 위한 정규화 연산

  • 최성순 (서울대학교 컴퓨터공학부) ;
  • 문병로 (서울대학교 컴퓨터공학부)
  • Published : 2007.06.15
Download PDF
⟨ Previous Next ⟩

Abstract

Normalization transforms one parent genotype to be consistent with the other before crossover. In this paper, we explain how normalization alleviates the difficulties caused by non-synonymously redundant encodings in genetic algorithms. We define the encodings with maximally non-synonymous property and prove that the encodings induce uncorrelated search spaces. Extensive experiments for a number of problems show that normalization transforms the uncorrelated search spaces to correlated ones and leads to significant improvement in performance.

정규화는 교차 연산 전에 두 부모해 사이의 일관성을 유지하기 위하여 한 부모해를 다른 부모해에 맞추어 변환하는 연산이다. 본 논문은 비유사 중복 인코딩이 유전 알고리즘의 성능을 떨어뜨리는 이유와 정규화 연산이 비유사 중복 인코딩에 의해 유발되는 문제점들을 어떻게 완화하는지 설명한다. 이를 위해 완전 비유사 중복 인코딩을 정의하고, 완전 비유사 중복 인코딩에 의해 적합도와 거리의 상관성이 없는 탐색 공간이 만들어짐을 증명한다. 또한, 완전 비유사 중복 인코딩을 사용하는 다수의 문제들에 대한 실험을 바탕으로, 정규화를 통해 상관성이 없는 탐색 공간이 상관성이 있는 탐색 공간으로 변화되어 유전알고리즘의 성능이 향상됨을 보인다.

Keywords

References

  1. N. J. Radcliffe. Forma analysis and random respectful recombination. In Fouth International Conference on Genetic Algorithms, pages 222-230, 1991
  2. E. Falkenauer. Genetic Algorithms and Grouping Problems. Wiley, 1998
  3. N. Y. Nikolaev and H. Iba. Regularization approach to inductive genetic programming. IEEE Trans. on Evolutionary Computation, 5(4):359-375, 2001 https://doi.org/10.1109/4235.942530
  4. Y. S. Yeun, W. S. Ruy, Y. S. Yang, and N. J. Kim. Implementing linear models in genetic programming. IEEE Trans. on Evolutionary Computation, 8(6):542-566, 2004 https://doi.org/10.1109/TEVC.2004.836818
  5. M. J. Martin-Bautista and M. A. Vila. A survey of genetic feature selection in mining issues. In Cogress on Evolutionary Computation, pages 1314-1321, 1999 https://doi.org/10.1109/CEC.1999.782599
  6. G. Laszewski. Intelligent structural operators for the k-way graph partitioning problem. In Forth International Conference on Genetic Algorithms, pages 45-52, 1991
  7. T. N. Bui and B. R. Moon. Genetic algorithm and graph partitioning. IEEE Trans. on Computers, 45(7):841-855, 1996 https://doi.org/10.1109/12.508322
  8. S. J. Kang and B. R. Moon. A hybrid genetic algorithm for multiway graph paritioning. In Genetic and Evolutionary Computation Conference, pages 159-166, 2000
  9. S. S. Choi and B. R. Moon. Isomorphism, normalization, and a genetic algorithm for sorting network optimization. In Genetic and Evolutionary Computation Conference, pages 327-334, 2002
  10. C. Igel and P. Stagge. Effects of phenotypic redundancy in structure optimization. IEEE Trans. on Evolutionary Computation, 6(1):74-85, 2002 https://doi.org/10.1109/4235.985693
  11. P. Schuster. Molecular insights into evolution of phenotypes. In J. P. Crutchfield and P. Schuster, editors, Evolutionary Dynamics - Exploring the Interplay of Accident, Selection, Neutrality and Function. Oxford Univ. Press, 2002
  12. M. Gerrits and P. Hogeweg. Redundant coding of an NP-complete problem allows effective genetic algorithm search. In Parallel Problem Solving from Nature, pages 70-74, 1990
  13. B. A. Julstrom. Redundant genetic encodings may not be harmful. In Genetic and Evolutionary Computation Conference, page 791, 1999
  14. M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press, 1983
  15. R. Shipman. Genetic redundancy: Desirable or problematic for evolutionary adaptation. In Fourth International Conference on Artificial Neural Networks and Genetic Algorithms, pages 337-344. Springer-Verlag, 1999
  16. M. A. Shackleton, R. Shipman, and M. Ebner. An investigation of redundant genotype-phenotype mappings and their role in evolutionary search. In Congress on Evolutionary Computation, pages 493-500, 2000 https://doi.org/10.1109/CEC.2000.870337
  17. M. Ebner, M. Shackleton, and R. Shipman. How neutral networks influence evolvability. Complexity, 7(2):19-33, 2002 https://doi.org/10.1002/cplx.10021
  18. J. D. Knowles and R. A. Watson. On the utility of redundant encodings in mutation-based evolutionary search. In Parallel Problem Solving from Nature, pages 88-98, 2002
  19. C. Van Hoyweghen and B. Naudts. Symmetry in the search space. In Congress on Evolutionary Computation, pages 1072-1079, 2000 https://doi.org/10.1109/CEC.2000.870766
  20. C. Van Hoyweghen, D. E. Goldberg, and B. Naudts. Building block superiority, multimodality and synchronization problems. In Genetic and Evolutionary Computation Conference, pages 694-701, 2001
  21. C. Van Hoyweghen, B. Naudts, and D. E. Goldberg. Spin-flip symmetry and synchronization. Evolutionary Computation, 10(4):317-344, 2002 https://doi.org/10.1162/106365602760972749
  22. K. Weicker and N. Weicker. Burden and benefits of redundancy. In Foundations of Genetic Algorithms, volume 6, pages 313-333. Morgan Kaufmann, 2001
  23. F. Rothlauf and D. E. Goldberg. Redundant representations in evolutionary computation. Evolutionary Computation, 11(4):381-415, 2003 https://doi.org/10.1162/106365603322519288
  24. H. Muhlenbein. Parallel genetic algorithms in combinatorial optimization. In Computer Science and Operations Research: New Developments in Their Interfaces, pages 441-453, 1992
  25. R. Dorne and J. K. Hao. A new genetic local search algorithm for graph coloring. In Parallel Problem Solving from Nature, pages 745-754. Springer-Verlag, 1998
  26. J. H. Kim, S. S. Choi, and B. R. Moon. Neural network normalization for genetic search. In Genetic and Evolutionary Computation Conference, pages 398-399, 2004
  27. S. Chen. Is the Common Good ? A New Perspective Developed in Genetic Algorithms. PhD thesis, Robotics Institute, Carnegie Mellon University, 1999
  28. G. Syswerda. Uniform crossover in genetic algorithms. In Third International Conference on Genetic Algorithms, pages 2-9, 1989
  29. S. Chen and S. Smith. Commonality and genetic algorithms. Technical Report CMU-RI-TR-96-27, Robotics Institute, Carnegie Mellon University, 1996
  30. D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, 1989
  31. L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, 1991
  32. R. A. Watson and J. B. Pollack. Recombination without respect: Schema combination and disruption in genetic algorithm crossover. In Genetic and Evolutionary Computation Conference, 2000
  33. S. Forrest and M. Mitchell. Relative building-block fitness and the building-block hypothesis. In Foundations of Genetic Algorithms, volume 2, pages 109-126. Morgan Kaufmann, 1993
  34. J. Horn and D. E. Goldberg. Genetic algorithm difficulty and the modality of fitness landscapes. In Foundations of Genetic Algorithms, volume 3, pages 243-270. Morgan Kaufmann, 1995
  35. S. A. Kauffman. Adaptation on rugged fitness landscapes. In D. Stein, editor, Lectures in the Sciences of Complexity, pages 527-618. Addison Wesley, 1989
  36. E. D. Weinberger. Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics, 63:325-336, 1990 https://doi.org/10.1007/BF00202749
  37. P. F. Stadler. Landscapes and their correlation functions. Journal of Mathematical Chemistry, 20:1-45, 1996 https://doi.org/10.1007/BF01165154
  38. T. Jones and S. Forrest. Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In Sixth International Conference on Genetic Algorithms, pages 184-192. Morgan Kaufmann, 1995
  39. K. D. Boese, A. B. Kahng, and S. Muddu. A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters, 16:101-113, 1994 https://doi.org/10.1016/0167-6377(94)90065-5
  40. P. Merz and B. Freisleben. Fitness landscapes, memetic algorithms and greedy operators for graph bi-partitioning. Evolutionary Computation, 8(1):61-91, 2000 https://doi.org/10.1162/106365600568103
  41. P. Merz and B. Freisleben. Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans. on Evolutionary Computation, 4(4):337-352, 2000 https://doi.org/10.1109/4235.887234
  42. M. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NPCompleteness. Freeman, San Francisco, 1979
  43. J. P. Kim and B. R. Moon. A hybrid genetic search for multi-way graph partitioning based on direct partitioning. In Genetic and Evolutionary Computation Conference, pages 408-415, 2001
  44. R. A. Watson, G. S. Hornby, and J. B. Pollack. Modeling building block interdependency. In Parallel Problem Solving from Nature, pages 97-106. Springer-Verlag, 1998
  45. M. Dietzfelbinger, B. Naudts, C. Van Hoyweghen, and I. Wegener. The analysis of a recombinative hill-climber on H-IFF. IEEE Trans. on Evolutionary Computation, 7(5):417-423, 2003 https://doi.org/10.1109/TEVC.2003.818192
  46. F. Rothlauf. Representations for Genetic and Evolutionary Algorithms. Second Edition. Springer, 2006
  47. P. Merz and B. Freisleben. Genetic local search for the TSP: New results. IEEE Conference on Evolutionary Computation, pages 159-164, 1997 https://doi.org/10.1109/ICEC.1997.592288
  48. Y. Nagata and S. Kobayashi. Edge assembly crossover: A high-power genetic algorithm for the traveling salesman problem. In Seventh International Conference on Genetic Algorithms, pages 450-457. Morgan Kaufmann, 1997
  49. S. Jung and B. R. Moon. Toward minimal restriction of genetic encoding and crossovers for the 2D-Euclidean TSP. IEEE Trans. on Evolutionary Computation, 6(6):557-565, 2002 https://doi.org/10.1109/TEVC.2002.804321
  50. D. I. Seo and B. R. Moon. Voronoi quantized crossover for traveling salesman problem. In Genetic and Evolutionary Computation Conference, pages 544-552, 2002
  51. N. J. Radcliffe and P. D. Surry. Fitness variance of formae and performance prediction. In Foundations of Genetic Algorithms, volume 3, pages 51-72. Morgan Kaufmann, 1995
  52. E. Aarts and J. K. Lenstra, editors. Local Search in Combinatorial Optimization. John Wiley & Sons, 1997
  53. W. D. Hillis. Co-evolving parasites improve simulated evolution as an optimization procedure. In C. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen, editors, Artificial Life II. Addison Wesley, 1992
  54. G. L. Drescher. Evolution of 16-number sorting networks revisited. Unpublished manuscript, 1994
  55. S. S. Choi and B. R. Moon. A graph-based Lamarckian-Baldwinian hybrid for the sorting network problem. IEEE Trans. on Evolutionary Computation, 9(1):105-114, 2005 https://doi.org/10.1109/TEVC.2004.841682