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Non-Synonymously Redundant Encodings and Normalization in Genetic Algorithms  

Choi, Sung-Soon (서울대학교 컴퓨터공학부)
Moon, Byung-Ro (서울대학교 컴퓨터공학부)
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.
Keywords
genetic algorithms; hybrid genetic algorithms; normalization; search space analysis;
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1 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   DOI   ScienceOn
2 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
3 G. L. Drescher. Evolution of 16-number sorting networks revisited. Unpublished manuscript, 1994
4 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
5 E. Aarts and J. K. Lenstra, editors. Local Search in Combinatorial Optimization. John Wiley & Sons, 1997
6 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
7 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   DOI   ScienceOn
8 D. I. Seo and B. R. Moon. Voronoi quantized crossover for traveling salesman problem. In Genetic and Evolutionary Computation Conference, pages 544-552, 2002
9 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
10 P. Merz and B. Freisleben. Genetic local search for the TSP: New results. IEEE Conference on Evolutionary Computation, pages 159-164, 1997   DOI
11 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   DOI   ScienceOn
12 F. Rothlauf. Representations for Genetic and Evolutionary Algorithms. Second Edition. Springer, 2006
13 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
14 P. Merz and B. Freisleben. Fitness landscapes, memetic algorithms and greedy operators for graph bi-partitioning. Evolutionary Computation, 8(1):61-91, 2000   DOI   ScienceOn
15 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   DOI   ScienceOn
16 M. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NPCompleteness. Freeman, San Francisco, 1979
17 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
18 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   DOI   ScienceOn
19 P. F. Stadler. Landscapes and their correlation functions. Journal of Mathematical Chemistry, 20:1-45, 1996   DOI
20 E. D. Weinberger. Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics, 63:325-336, 1990   DOI
21 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
22 S. A. Kauffman. Adaptation on rugged fitness landscapes. In D. Stein, editor, Lectures in the Sciences of Complexity, pages 527-618. Addison Wesley, 1989
23 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
24 S. Chen and S. Smith. Commonality and genetic algorithms. Technical Report CMU-RI-TR-96-27, Robotics Institute, Carnegie Mellon University, 1996
25 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
26 L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, 1991
27 G. Syswerda. Uniform crossover in genetic algorithms. In Third International Conference on Genetic Algorithms, pages 2-9, 1989
28 D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, 1989
29 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
30 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
31 S. Chen. Is the Common Good ? A New Perspective Developed in Genetic Algorithms. PhD thesis, Robotics Institute, Carnegie Mellon University, 1999
32 F. Rothlauf and D. E. Goldberg. Redundant representations in evolutionary computation. Evolutionary Computation, 11(4):381-415, 2003   DOI   ScienceOn
33 H. Muhlenbein. Parallel genetic algorithms in combinatorial optimization. In Computer Science and Operations Research: New Developments in Their Interfaces, pages 441-453, 1992
34 C. Van Hoyweghen, B. Naudts, and D. E. Goldberg. Spin-flip symmetry and synchronization. Evolutionary Computation, 10(4):317-344, 2002   DOI   ScienceOn
35 K. Weicker and N. Weicker. Burden and benefits of redundancy. In Foundations of Genetic Algorithms, volume 6, pages 313-333. Morgan Kaufmann, 2001
36 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   DOI
37 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
38 C. Van Hoyweghen and B. Naudts. Symmetry in the search space. In Congress on Evolutionary Computation, pages 1072-1079, 2000   DOI
39 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
40 M. Ebner, M. Shackleton, and R. Shipman. How neutral networks influence evolvability. Complexity, 7(2):19-33, 2002   DOI   ScienceOn
41 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
42 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
43 M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press, 1983
44 B. A. Julstrom. Redundant genetic encodings may not be harmful. In Genetic and Evolutionary Computation Conference, page 791, 1999
45 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
46 C. Igel and P. Stagge. Effects of phenotypic redundancy in structure optimization. IEEE Trans. on Evolutionary Computation, 6(1):74-85, 2002   DOI   ScienceOn
47 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
48 G. Laszewski. Intelligent structural operators for the k-way graph partitioning problem. In Forth International Conference on Genetic Algorithms, pages 45-52, 1991
49 T. N. Bui and B. R. Moon. Genetic algorithm and graph partitioning. IEEE Trans. on Computers, 45(7):841-855, 1996   DOI   ScienceOn
50 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
51 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   DOI   ScienceOn
52 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   DOI
53 E. Falkenauer. Genetic Algorithms and Grouping Problems. Wiley, 1998
54 N. Y. Nikolaev and H. Iba. Regularization approach to inductive genetic programming. IEEE Trans. on Evolutionary Computation, 5(4):359-375, 2001   DOI   ScienceOn
55 N. J. Radcliffe. Forma analysis and random respectful recombination. In Fouth International Conference on Genetic Algorithms, pages 222-230, 1991