## Genetic Invariance: A New Approach to Genetic Algorithms

Michael Lewchuk
Masters Thesis
April 1992
Postscrip available here

## Abstract

Genetic algorithms are adaptive search algorithms which generate and
test a population of individuals, where each individual corresponds to
a solution. They then adapt to the information obtained from testing,
seeking superior solutions by selecting and combining solutions of
above average value. As the number of superior individuals in the
population increases, the number of inferior individuals decreases.
This thesis introduces Genetic Invariance, a similar family of generate
and test problem solvers which uses a different selection and
replacement strategy. In the best case, it achieves superior solutions
without eliminating inferior characteristics. Although
characteristics may initially be associated with inferior solutions,
they may prove to be superior when combined with other particular
characteristics. Mathematical analysis of lower bounds of Genetic
Invariance on a simple function is given, and several properties of
Genetic Invariance are explained using this analysis. A comparison and
contrast is done to show how the two selection strategies achieve
optimization in different ways. An analysis of the assumption and
strategies of each system explains likely beneficial and detrimental
effects of each system, while empirical analysis is given which
demonstrates these effects. Together, they show each system's features
and drawbacks.
Keywords: genetic algorithms, gene invariance, one max function analysis