The Walsh Transform and the Theory of the Simple Genetic Algorithm

2017 ◽  
pp. 25-44 ◽  
Author(s):  
Michael D. Vose ◽  
Alden H. Wright
Keyword(s):  
Genetic Algorithm ◽  
Walsh Transform ◽  
Simple Genetic Algorithm

scholarly journals The Simple Genetic Algorithm and the Walsh Transform: Part I, Theory

1998 ◽  
Vol 6 (3) ◽  
pp. 253-273 ◽  
Author(s):  
Michael D. Vose ◽  
Alden H. Wright
Keyword(s):  
Genetic Algorithm ◽  
Fourier Transform ◽  
Walsh Transform ◽  
Binary Representation ◽  
Infinite Population ◽  
Simple Genetic Algorithm ◽  
Mixing Matrix ◽  
Orthogonal Decompositions ◽  
The Fourier Transform ◽  
Theoretical Results

This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.

scholarly journals The Simple Genetic Algorithm and the Walsh Transform: Part II, The Inverse

1998 ◽  
Vol 6 (3) ◽  
pp. 275-289 ◽  
Author(s):  
Michael D. Vose ◽  
Alden H. Wright
Keyword(s):  
Genetic Algorithm ◽  
Fixed Point ◽  
Fixed Points ◽  
Walsh Transform ◽  
Next Generation ◽  
Simple Genetic Algorithm ◽  
The Relationship ◽  
Crossover And Mutation ◽  
Special Case ◽  
Walsh Basis

This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh transform. The mixing scheme (comprised of crossover and mutation) is essentially “triangularized” when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.

scholarly journals A Multiple Mitosis Genetic Algorithm

2019 ◽  
Vol 8 (3) ◽  
pp. 252
Author(s):  
K. Kamil ◽  
K.H Chong ◽  
H. Hashim ◽  
S.A. Shaaya
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Total Population ◽  
Global Optimum ◽  
Natural Process ◽  
Local Optimum ◽  
Simple Genetic Algorithm ◽  
Cell Reproduction ◽  
Solve Optimization Problem ◽  
High Diversity

<p>Genetic algorithm is a well-known metaheuristic method to solve optimization problem mimic the natural process of cell reproduction. Having great advantages on solving optimization problem makes this method popular among researchers to improve the performance of simple Genetic Algorithm and apply it in many areas. However, Genetic Algorithm has its own weakness of less diversity which cause premature convergence where the potential answer trapped in its local optimum.  This paper proposed a method Multiple Mitosis Genetic Algorithm to improve the performance of simple Genetic Algorithm to promote high diversity of high-quality individuals by having 3 different steps which are set multiplying factor before the crossover process, conduct multiple mitosis crossover and introduce mini loop in each generation. Results shows that the percentage of great quality individuals improve until 90 percent of total population to find the global optimum.</p>

scholarly journals Designing a competent simple genetic algorithm for search and optimization

2000 ◽  
Vol 36 (12) ◽  
pp. 3757-3761 ◽  
Author(s):  
Patrick Reed ◽  
Barbara Minsker ◽  
David E. Goldberg
Keyword(s):  
Genetic Algorithm ◽  
Simple Genetic Algorithm

Talking Drum: A Local Area Network Music Installation

1999 ◽  
Vol 9 ◽  
pp. 23-28 ◽  
Author(s):  
Chris Brown
Keyword(s):  
Genetic Algorithm ◽  
Time Delays ◽  
Computer Network ◽  
Local Area Network ◽  
Local Area ◽  
Area Network ◽  
Performance Space ◽  
Simple Genetic Algorithm ◽  
Musical Concepts ◽  
Network Music

Talking Drum is an interactive computer network music installation designed for the diffusion of cyclically repeating rhythms produced by four electronically synchronized instruments separated by distances up to 50 feet (16 m). The reverberant character of the performance space and the distance-related time-delays between stations combine with the speed and rhythms of the music to create a complex, multifocal mix that audiences explore by moving independently through the installation. The software uses Afro-Cuban musical concepts as a model for creating an interactive drum machine. It implements a simple genetic algorithm to mediate the interaction between pre-composed and improvised rhythms.

Sign in / Sign up

Export Citation Format

Share Document