On Elements of Evolution and Genetics in the Application of Genetic Algorithm to Optimization Mathematics

Main Article Content

Eziokwu, C. Emmanuel
Avoaja, A. Diana
Ekemezie, Chinenye Loveth

Abstract

This work is a major review of the existing on evolution and genetics. It was started by discussing the Charles Darwin theory of evolution i.e. by exploring patterns of bones in vertebrates showing typical pentadactyl limbs, vestigial structures, sorology, parasitology etc. with special attention in man and his races. Following was the existence theory of genetics in the development of man. The introduction of chromosomes was used to strengthen this resulting in the development of character. The occasional occurrences of mutation in the chromosomes due to some factors were also discussed together with the idea of sex linkage. Later, at the end, the mathematics of genetic algorithm was applied in the work to see how selection chromosomes could influence artificial intelligence and neural network training mostly seen in the area of optimization mathematics.

Keywords:
Chromosomes, environment, evolution science, genetic behavior, mathematical genetic algorithm, mutation, variation.

Article Details

How to Cite
Emmanuel, E. C., Diana, A. A., & Loveth, E. C. (2020). On Elements of Evolution and Genetics in the Application of Genetic Algorithm to Optimization Mathematics. Asian Research Journal of Current Science, 2(1), 34-59. Retrieved from https://globalpresshub.com/index.php/ARJOCS/article/view/814
Section
Original Research Article

References

Barton NH, Keightley PD. Understanding quantitative genetic variation. Nature Reviews Genetics. 2002;3:11-21.

Barton NH, Turelli M. Natural and sexual selection on many loci. Ge-netics. 1991; 127:229-225.

Bulmer MG. The Mathematical Theory of Quantitative Genetics. Oxford: Clarendon Press; 1980.

Fisher RA. Correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. Edinb. 1918; 52:399-433.

Gimelfarb A. Genotypic variation for a quantitative character maintained under stabilizing selection without mutations: epistasis. Genetics. 1989;123:217-227.

Kimura M. The Neutral Theory of Molecular Evolution. Cambrigde: University Press; 1983.

Lande R. Quantitative genetic analysis of multivariate evolution applied to brain: Body size allometry. Evolution. 1979;34: 402-416

Lande R, Arnold SJ. The measurement of selection on correlated char-acters. Evolution. 1983;37:1210-1226

Lessard S. Fisher’s fundamental theorem of natural selection re-visited. Theor. Pop. Biol. 1997;52:119-136.

Lin CY, Hajela P. Genetic algorithms in optimization problems with discrete and integer design variables. Engineering Optimization. 1992;19:309-327.

Lyubich Yu I. Basic concepts and theorems of evolutionary genetics of free populations. Russ. Math. Surv. 1971; 26:51-123.

Lyubich Yu I. Mathematical structures in poplation genetics. Berlin Heidelberg New York: Springer; 1992.

Michalwicz Z. Genetic algorithms + data structures = Evolution programs, 2nd ed., Springer-Verlag, Berlin; 1994.

Nagylaki T. Rate of evolution of a character without epistasis. Proc. Natl. Acad. Sci. 1989;86:1910-1913.

Nagylaki T. Error bounds for the fundamental and secondary theorems of natural selection. Proc. Natl. Acad. Sci. USA. 1991;88:2402-2406.

Nagylaki T, Crow J. Continuous selective models. Theor. Pop. Biol. 1974;5:257-283.

Nagylaki T, Lou Y. Evolution under multiallelic migration-selection models. Theor. Popul. Biol. 2007;72:21-40.

Okereke EC, Akogoun. Lecture notes on genetics and variation, Federal University of Technology, Yola, Nigeria; 1986.

Otto SP. The Evolutionary Enigma of Sex. Amer. Natur. 2009;174:S1S14.

Reeve JP. Predicting long-term response to selection. Genet. Res. 2000;75:83-94.

Schneider KA. Long-term evolution of polygenic traits under frequency-dependent selection induced by intraspecific competition. Theor. Popul. Biol. 2007;71:342-366.

Schneider KA. Maximization principles for frequency-dependent selec-tion I: the one-locus two-allele case. Theor. Popul. Biol. 2008;74:251-262.

Schneider KA. Maximization principles for frequency-dependent selec-tion II: the one-locus multiallele case. J. Math. Biol., in Press; 2010.

Shashahani S. A new mathematical framework for the study of linkage and selection. Memoirs Amer. Math. Soc. 211. Providence, R.I.: Amer. Math. Soc; 1979.

Singiresu S. Rao. Engineering optimization theory and practice. New Age International Publishers, New Delhi; 2008.

Svirezhev Yu M. Optimality principles in population genetics. In: Studies in Theoretical Genetics, Novisibirsk: Inst. Of Cytology and Genetics. (In Russian). 1972;86-102.

Turelli M, Barton NH. Genetic and statistical analyses of strong selection on polygenic traits: What, me normal? Genetics. 1994;138:913-941.

Turelli M, Barton NH. Polygenic variation maintained by balancing se-lection: pleiotropy, sex-dependent allelic effects and G×E interactions. Genetics. 2004;166: 10531079.

Wright S. Evolution in Mendelian Populations Genetics. 1931;16:97-159.

Wright S. Genetics of Populations. In: Encyclopedia Britannica, 14th ed. 1948;10:111-115.

Zhang XS, Wang J, Hill WG. Influence of dominance, leptokurto-sis and pleiotropy of deleterious mutations on quantitative genetic variation at mutation-selection balance. Genetics. 2004;166:597-610.

Price GR. Selection and covariance. Nature. 1970;227:520-521.