Genetic
algorithms essentially form a class of non-linear search
processes occurring in the study of mathematical optimization
problems and exhibit remarkable analogy with the Darwinian
evolution, in that the key issue in both these processes
is a fitness-dependent mode of selection of strategies
or traits for evolutionary propagation of the target
population. Genetic algorithms are run via the three
fundamental stochastic operators of selection, crossover
and mutation, acting on an initial population, and then
obtain the various generations assuming payoff-proportionate
selection of the agents. Evolutionary game theory too
studies Darwinian evolution by assuming payoff-proportionate
selection of strategies. Replicator equations describe
the dynamics of evolutionary game theory. In this paper,
we obtain a standard genetic algorithm generated numerical
simulation for the replicator dynamics of a single-species
population with a constant ecosystem as the backdrop,
and find that the agents with higher fitness tend to
accumulate with the iterates showing an oscillatory
pattern without settling to any fitness sink.
Genetic
Algorithms (GAs) are increasingly finding frequent use
in myriad spheres of human enquiry as effective tools
in the process of dynamic learning. Evolutionary sciences,
particularly the areas of evolutionary biology and evolutionary
economics, have a large body of scholarly works compiled
over the last decade and a half that have analyzed and
established the emergence of GA programs as robust mathematical
tools for evolutionary learning.In
this paper, we have obtained a simulation of the replicator
dynamics of the Evolutionary Game Theory (EGT), using
the standard GA for a single-species toy ecosystem model,
keeping the ecosystem as a fixed and static backdrop.
We present a brief overview of the standard GA to make
the paper self-contained.
A
standard GA (henceforth GA in this paper) - the genetic
algorithm described in detail by Goldberg - is a stochastic
search process for non-linear optimization problems.
A GA transforms a set of mathematical objects (population
of agents) that are fixed-length binary strings, each
associated with a fitness measure (payoff) to a new
set of strings (offspring) by means of certain stochastic
operators. Usually in the standard GA, the population
size is kept fixed throughout (Goldberg, 1989). |
