article

Measures of Diversity for Populations and Distances Between Individuals with Highly Reorganizable Genomes

Authors:

Claudio Mattiussi,

Dario FloreanoAuthors Info & Claims

Evolutionary Computation, Volume 12, Issue 4

Pages 495 - 515

https://doi.org/10.1162/1063656043138923

Published: 01 December 2004 Publication History

Abstract

In this paper we address the problem of defining a measure of diversity for a population of individuals whose genome can be subjected to major reorganizations during the evolutionary process. To this end, we introduce a measure of diversity for populations of strings of variable length defined on a finite alphabet, and from this measure we derive a semi-metric distance between pairs of strings. The definitions are based on counting the number of substrings of the strings, considered first separately and then collectively. This approach is related to the concept of linguistic complexity, whose definition we generalize from single strings to populations. Using the substring count approach we also define a new kind of Tanimoto distance between strings. We show how to extend the approach to representations that are not based on strings and, in particular, to the tree-based representations used in the field of genetic programming. We describe how suffix trees can allow these measures and distances to be implemented with a computational cost that is linear in both space and time relative to the length of the strings and the size of the population. The definitions were devised to assess the diversity of populations having genomes of variable length and variable structure during evolutionary computation runs, but applications in quantitative genomics, proteomics, and pattern recognition can be also envisaged.

References

[1]

Crochemore, M., Hancart, C., and Lecroq, T. (2001). Algorithmique du texte. Vuibert, Paris.]]

[2]

Crochemore, M. and Rytter, W. (2002). Jewels of Stringology. World Scientific, Singapore.]]

[3]

de Jong, E., Watson, R., and Pollack, J. (2001). Reducing bloat and promoting diversity using multi-objective methods. In et al., L. S., editor, GECCO 2001, pages 11-18, San Francisco, CA. Morgan Kaufmann.]]

[4]

Graur, D. and Li, W.-H. (2000). Fundamentals of Molecular Evolution. Sinauer Associates, Sunderland, MA, 2nd edition.]]

[5]

Gusfield, G. (1997). Algorithms on Strings, Trees, and Sequences. Cambridge University Press, Sunderland, MA.]]

Digital Library

[6]

Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. Prentice Hall, Upper Saddle River, NY, 2nd edition.]]

Digital Library

[7]

Keijzer, M. (1996). Efficiently representing populations in genetic programming. In Angeline, P. et al., editor, Advances in Genetic Programming, volume 2, pages 259- 278, CAmbridge, MA. MIT Press.]]

Digital Library

[8]

Keller, R. and Banzhaf, W. (1994). Explicit maintenance of genetic diversity on genospaces. Unpublished manuscript. Available online at Citeseer.]]

[9]

Langdon, W. and Poli, R. (2002). Foundations of Genetic Programming. Springer, Berlin.]]

Digital Library

[10]

Leung, Y., Gao, Y., and Xu, Z. (1997). Degree of population diversity - a perspective on premature convergence in genetic algorithms and its markov chain analysis. IEEE Trans. Neural Networks, 8(5):1165-1176.]]

Digital Library

[11]

Levandowsky, M. and Winter, D. (1971). Distance between sets. Nature, 234(5):34-35.]]

[12]

Lipkus, A. (1999). A proof of the triangle inequality for the tanimoto distance. J. of Mathematical Chemistry, 26:263-265.]]

[13]

Mattiussi, C. and Floreano, D. (2004). Evolution of analog networks using local string alignment on highly reorganizable genomes. In et al., R. Z., editor, Proceedings of the 2004 NASA/DoD Conference on Evolvable Hardware, 24-26 June 2004, Seattle, pages 30-37, Los Alamitos, CA. IEEE Computer Society.]]

[14]

McCreight, E. (1976). A space-economical suffix tree construction algorithm. J. ACM, 23(1):262-272.]]

Digital Library

[15]

Monro, G. (1987). The concept of multiset. Zeitschr. f. math. Logik ung Grundlagen d. Math., 33:171-178.]]

[16]

Morrison, W. and de Jong, K. (2002). Measurement of population diversity. In et al., P. C., editor, EA 2001, volume 2310 of LNCS, pages 31-41, Berlin. Springer.]]

Digital Library

[17]

O'Reilly, U.-M. (1997). Using a distance metric on genetic programs to understand genetic operators. In IEEE International Conference on Systems, Man, and Cybernetics, volume 5, pages 4092-4097.]]

[18]

Sankoff, D. and Kruskal, J. (1983). Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Addison-Wesley, Reading, MA.]]

[19]

Shapiro, J. (2002). A 21st century view of evolution. J. Biol. Phys., 28:1-20.]]

[20]

Theodoridis, S. and Koutroumbas, K. (2003). Pattern Recognition. Academic Press, Sand Diego, CA, 2nd edition.]]

Digital Library

[21]

Tomassini, M., Vanneschi, L., Fernández, F., and Galeano, G. (2004). A study of diversity in multipopulation genetic programming. In et al., P. L., editor, EA 2003, Artificial Evolution: 6th International Conference, Marseilles, France, October 27-30, 2003, volume 2936 of LNCS, pages 243-255, Berlin. Springer.]]

[22]

Trifonov, E. (1990). Making sense of the human genome. In Sarma, R. and Sarma, M., editors, Structure and Methods, volume 1, pages 69-77. Adenine Press, New York.]]

[23]

Troyanskaya, O., Arbell, O.and Koren, Y., Landau, G., and Bolshoy, A. (2002). Sequence complexity of prokariotic genomic sequences: A fast algorithm for calculating linguistic complexity. Bioinformatics, 18(5):679-688.]]

[24]

Ukkonen, E. (1995). On-line construction of suffix trees. Algorithmica, 14:249-260.]]

Digital Library

[25]

Wineberg, M. and Oppacher, F. (2000). Enhancing the ga's ability to cope with dynamic environments. In et al., D. W., editor, GECCO 2000, pages 3-10, San Francisco, CA. Morgan Kaufmann.]]

[26]

Wineberg, M. and Oppacher, F. (2003a). Distance between populations. In et al., E. C.-P., editor, GECCO 2003, volume 2724 of LNCS, pages 1481-1492, Berlin. Springer.]]

[27]

Wineberg, M. and Oppacher, F. (2003b). The underlying similarity of diversity measures used in evolutionary computation. In et al., E. C.-P., editor, GECCO 2003, volume 2724 of LNCS, pages 1493-1504, Berlin. Springer.]]

Cited By

Fan LSu ZLiu XWang Y(2024)Decomposition based cross-parallel multiobjective genetic programming for symbolic regressionApplied Soft Computing10.1016/j.asoc.2024.112239167:PAOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112239
Dialameh MHamzeh A(2021)Dynamic feature weighting for multi-label classification problemsProgress in Artificial Intelligence10.1007/s13748-021-00237-310:3(283-295)Online publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1007/s13748-021-00237-3
Zhang HLiu YZhou J(2018)Balanced-evolution genetic algorithm for combinatorial optimization problemsNatural Computing: an international journal10.1007/s11047-018-9670-517:3(611-639)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s11047-018-9670-5
Show More Cited By

Measures of Diversity for Populations and Distances Between Individuals with Highly Reorganizable Genomes
1. Applied computing
  1. Life and medical sciences
2. Computing methodologies

Recommendations

Population Diversity and Fitness Measures Based on Genomic Distances
Ectropy of diversity measures for populations in Euclidean space

Measures to evaluate the diversity of a set of points (population) in Euclidean space play an important role in a variety of areas of science and engineering. Well-known measures are often used without a clear insight into their quality and many of them ...
Review and Study of Genotypic Diversity Measures for Real-Coded Representations

The exploration/exploitation balance is a major concern in the control of evolutionary algorithms (EAs) performance. Exploration is associated with the distribution of individuals on a landscape, and can be estimated by a genotypic diversity measure (...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Evolutionary Computation

Evolutionary Computation Volume 12, Issue 4

December 2004

141 pages

ISSN:1063-6560

EISSN:1530-9304

Issue’s Table of Contents

Publisher

MIT Press

Cambridge, MA, United States

Publication History

Published: 01 December 2004

Published in EVOL Volume 12, Issue 4

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

15
Total Citations
View Citations
89
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Fan LSu ZLiu XWang Y(2024)Decomposition based cross-parallel multiobjective genetic programming for symbolic regressionApplied Soft Computing10.1016/j.asoc.2024.112239167:PAOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112239
Dialameh MHamzeh A(2021)Dynamic feature weighting for multi-label classification problemsProgress in Artificial Intelligence10.1007/s13748-021-00237-310:3(283-295)Online publication date: 1-Sep-2021
https://dl.acm.org/doi/10.1007/s13748-021-00237-3
Zhang HLiu YZhou J(2018)Balanced-evolution genetic algorithm for combinatorial optimization problemsNatural Computing: an international journal10.1007/s11047-018-9670-517:3(611-639)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s11047-018-9670-5
Singhal NSharma MMangal S(2018)Optimal placement of an actuator in a two degrees of freedom system to generate desired vibrationsMicrosystem Technologies10.1007/s00542-018-3711-y24:8(3389-3398)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00542-018-3711-y
Lewis RHolborn P(2017)How to Pack Trapezoids: Exact and Evolutionary AlgorithmsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2016.260900021:3(463-476)Online publication date: 26-May-2017
https://dl.acm.org/doi/10.1109/TEVC.2016.2609000
Wettergren TCosta R(2015)Efficient genetic algorithms for optimising the location of discrete nodes to cover multiple demand pointsInternational Journal of Metaheuristics10.1504/IJMHEUR.2015.0744294:3/4(244-267)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1504/IJMHEUR.2015.074429
Zahadat PSchmickl T(2014)Generation of diversity in a reaction-diffusion-based controllerArtificial Life10.1162/ARTL_a_0013420:3(319-342)Online publication date: 1-Jul-2014
https://dl.acm.org/doi/10.1162/ARTL_a_00134
Črepinšek MLiu SMernik M(2013)Exploration and exploitation in evolutionary algorithmsACM Computing Surveys10.1145/2480741.248075245:3(1-33)Online publication date: 3-Jul-2013
https://dl.acm.org/doi/10.1145/2480741.2480752
Esparcia-Alcázar AMoravec J(2013)Fitness approximation for bot evolution in genetic programmingSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-012-0965-717:8(1479-1487)Online publication date: 1-Aug-2013
https://dl.acm.org/doi/10.1007/s00500-012-0965-7
Lacevic BAmaldi E(2011)Ectropy of diversity measures for populations in Euclidean spaceInformation Sciences: an International Journal10.1016/j.ins.2010.12.004181:11(2316-2339)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1016/j.ins.2010.12.004
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Issue’s Table of Contents