Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
An introduction to genetic algorithms
An introduction to genetic algorithms
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Simple genetic algorithms with linear fitness
Evolutionary Computation
Modeling simple genetic algorithms
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part i, theory
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part ii, the inverse
Evolutionary Computation
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
Coarse graining selection and mutation
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Intrinsic System Model of the Genetic Algorithm with α-Selection
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Theory of the simple genetic algorithm with α-selection, uniform crossover and bitwise mutation
WSEAS TRANSACTIONS on SYSTEMS
ICS'10 Proceedings of the 14th WSEAS international conference on Systems: part of the 14th WSEAS CSCC multiconference - Volume II
| Hi-index | 0.00 |
Genetic algorithms are random heuristic search (RHS) algorithms with a wide range of applications in adaptation and optimisation problems. The most advanced approach for a general theory of genetic algorithms is offered by the dynamical system model which describes the stochastic trajectory of a population under the dynamics of a genetic algorithm with the help of an underlying deterministic heuristic function and its fixed points. However, even for the simple genetic algorithm (SGA) with fitness-proportional selection, crossover and mutation the determination of the population trajectory and the fixed points of the heuristic function is unfeasible for practical problem sizes. In order to simplify the mathematical analysis α-selection is introduced in this paper. Based on this selection scheme it is possible to derive the dynamical system model and the fixed points in closed form. Although the heuristic function is not compatible with the equivalence relation imposed by schemata in the strict sense a simple coarse-grained system model with a single exogenous parameter is derivable for a given schemata family. In addition to the theoretical analysis experimental results are presented which confirm the theoretical predictions.