Transition and convergence properties of genetic algorithms applied to fitness functions perturbed concurrently by additive and multiplicative noise

Authors:
Takéhiko Nakama
Affiliations:
Department of Applied Mathematics and Statistics, The John's Hopkins University, Baltimore, MD
Venue:
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Year:
2009

Citing 10
Cited 1

Matrix analysis

Matrix analysis
Optimal stabilization of families of linear stochastic differntial equations with jump corfficients and multiplicative noise

SIAM Journal on Control and Optimization
The Simple Genetic Algorithm: Foundations and Theory

The Simple Genetic Algorithm: Foundations and Theory
Noisy Local Optimization with Evolution Strategies

Noisy Local Optimization with Evolution Strategies
Genetic algorithms, selection schemes, and the varying effects of noise

Evolutionary Computation
Theoretical analysis of genetic algorithms in noisy environments based on a Markov Model

Proceedings of the 10th annual conference on Genetic and evolutionary computation
On the robustness of population-based versus point-basedoptimization in the presence of noise

IEEE Transactions on Evolutionary Computation
A new model of simulated evolutionary computation-convergenceanalysis and specifications

IEEE Transactions on Evolutionary Computation
Evolutionary optimization in uncertain environments-a survey

IEEE Transactions on Evolutionary Computation
A general noise model and its effects on evolution strategy performance

IEEE Transactions on Evolutionary Computation

A controlled migration genetic algorithm operator for hardware-in-the-loop experimentation

Engineering Applications of Artificial Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate the properties of genetic algorithms (GAs) applied to fitness functions perturbed concurrently by additive noise and multiplicative noise that each take on finitely many values. First we explicitly construct a Markov chain that models GAs in this noisy environment. By analyzing this chain, we establish a condition that is both necessary and sufficient for GAs to eventually find a globally optimal solution with probability 1. Furthermore, we identify a condition that is both necessary and sufficient for GAs to eventually with probability 1 fail to find any globally optimal solution. Interestingly, both of these conditions are completely determined by the fitness function and multiplicative noise, and they are unaffected by the additive noise. Our analysis also shows that the chain converges to stationarity. Based on this property and the transition probabilities of the chain, we derive an upper bound for the number of iterations sufficient to ensure with certain probability that a GA selects a globally optimal solution upon termination.