EXPLORING THE COMPLEXITY OF A PROPOSED RECURSIVE MEASURE OF RECOMBINATIONAL DISTANCE
Robert Collier, Mark Wineberg
2010
Abstract
When studying evolutionary systems, either from the natural world or artificially constructed using simulated populations, researchers must be able to quantify the genotypic differences that are observed. With the simple genetic algorithm employing both a unary mutation operator and a binary recombination operator to maintain variation in the population, it is exceedingly difficult to quantify the distance between elements of the chromosome space with an approach that is truly representative of the distance that would need to be traversed by the evolutionary mechanism. Although evaluation function dependence and the binary arity of the recombination operator both contribute to this difficulty, it is possible to redefine the function of recombination in such a way as to facilitate the computation of a more representative measurement of the distance the genetic algorithm would need to traverse to create a specific chromosome from a given population. The recursive approach presented here entails the definition of unary recombination operators and ultimately results in a technique for calculating the recombinational distance between chromosomes with a time complexity that is improved logarithmically over a simplistic approach.
References
- Altenberg, L. 1997. Fitness Distance Correlation Analysis: An Instructive Counterexample. Proceedings of the 7th International Conference on Genetic Algorithms, pp. 57--64.
- Culberson, J. C. 1995. Mutation-Crossover Isomorphisms and the Construction of Discriminating Functions. Evolutionary Computation, 2, pp. 279--311.
- Dybowski, R., Collins, T. D. and Weller, P. R. 1996. Visualization of Binary String Convergence by Sammon Mapping. Proceedings of the 5th Annual Conference on Evolutionary Programming, pp. 377-- 383.
- Gitchoff, P. and Wagner, G. P. 1996. Recombination Induced Hypergraphs. Complexity, 2(1), pp. 37--43.
- Goldberg, D. E. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc.
- Hamming, R. 1950. Error Detecting and Error Correcting Codes. Bell System Technical Journal, 29(2), pp. 147-- 160.
- Jones, T. 1995. Evolutionary Algorithms, Fitness Landscapes, and Search. Thesis Document. The University of New Mexico, Albuquerque, New Mexico, USA.
- Jones, T. 1995. One Operator, One Landscape. Working Paper. Santa Fe Institute.
- Merrell, D. J. 1994. The Adaptive Seascape: The Mechanism of Evolution. pp. 59.
- Mitchell, M. 1996. An Introduction To Genetic Algorithms. Cambridge, MA, USA: MIT Press.
- Sammon, J. W. 1969. A Nonlinear Mapping for Data Structure Analysis. IEEE Transactions on Computers, 18(5), pp. 401--409.
- Spears, W. M. 1998. The Role of Mutation and Recombination in Evolutionary Algorithms. Thesis Document. George Mason University, Fairfax, VA, USA.
- Stadler, P. F. 2002. Fitness Landscapes. Biological Evolution and Statistical Physics, pp. 183--204.
- Van Wijk, J. J. 2005. The Value of Visualization. IEEE Visualization Conference, 0, pp. 11.
- Vose, M. D. 1990. Formalizing Genetic Algorithms. Proceedings of Genetic Algorithms, Neural Nets, and Simulated Annealing Applied to Problems in Signal and Image Processing.
- Wineberg, M. and Oppacher, F. 2003. The Underlying Similarity of Diversity Measures Used in Evolutionary Computation. Proceedings of the 5th Genetic and Evolutionary Computation Conference, pp. 1493-- 1504.
- Wright, S. 1932. The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. Proceedings of the 11th International Congress of Genetics, 8, pp. 209--222.
Paper Citation
in Harvard Style
Collier R. and Wineberg M. (2010). EXPLORING THE COMPLEXITY OF A PROPOSED RECURSIVE MEASURE OF RECOMBINATIONAL DISTANCE . In Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010) ISBN 978-989-8425-31-7, pages 85-94. DOI: 10.5220/0003085800850094
in Bibtex Style
@conference{icec10,
author={Robert Collier and Mark Wineberg},
title={EXPLORING THE COMPLEXITY OF A PROPOSED RECURSIVE MEASURE OF RECOMBINATIONAL DISTANCE},
booktitle={Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)},
year={2010},
pages={85-94},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003085800850094},
isbn={978-989-8425-31-7},
}
in EndNote Style
TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)
TI - EXPLORING THE COMPLEXITY OF A PROPOSED RECURSIVE MEASURE OF RECOMBINATIONAL DISTANCE
SN - 978-989-8425-31-7
AU - Collier R.
AU - Wineberg M.
PY - 2010
SP - 85
EP - 94
DO - 10.5220/0003085800850094