Adaptive Genetic Algorithms - Computational Intelligence in Time Series Forecasting - page 319

that indicates the percentage of a generation contributing the offspring for the next
generation. Based on this measure he could control a dynamic population size by
adding or deleting additional population chromosomes in order to balance out the
contribution percentages over the entire current population.
Entirely different approaches to resolving the premature convergence problem
have been proposed by Arabas et al . (1994) and by Kubota and Fukuda (1997),
based on the concepts of age of chromosome and of age structure of population
respectively. In the age of chromosome concept, the number of generations that a
chromosome has survived is taken as an indicator that replaces the plain selection
mechanism. The concept assigns to every created chromosome its lifetime , which
determines the age at which the chromosome will die. The lifetime length is
calculated by taking into account the minimum, average, and the maximum fitness
values within the current population and the minimum and maximum fitness values
in the past generations. The chromosomes with the outstanding fitness values get a
longer lifetime assigned.
The concept of age structure of population maintains the genetic diversity of
the population by deleting the aged individuals. This mimics nature by removing
individuals from the population by reaching the lethal age. Defining the natural life
cycle as the time interval between the birth of parents and the birth of offspring,
there are two conceptual possibilities to be used
x the parents and the children may not simultaneously live as long as the
parents live (AGA algorithm)
x both the parents and the children may coexists for a period of time (ASGA
algorithm), which is the most natural case.
In the aged genetic algorithm concept, each individual is characterized by its
age and its lethal age as parameters. As soon as an individual is born it is assigned
a lethal age and the zero value of its age parameter. Thereafter, its parents die
immediately. The remaining individuals increase their age parameter value by one
in every generation. Starting with an initial generation in which all individuals
have a zero-value age parameter, an age operator manages the aging and dying
process.
The effect of the proposed genetic algorithm with age structure was tested on a
simulated knapsack problem. The simulation results have shown that the new
concept can prevent individuals with a large fitness value from overrunning the
population and maintain a considerable genetic diversity in the population. The
introduced age concept also helps in solving optimization problems with a
relatively small population size. There are, however, some unpleasant effects that
accompany the age concept application (Knappmeier, 2003):
x there is an increased possibility of weak individuals surviving as long as
their lethal time is not expired
x there is an enlarged possibility for strong individuals to die formally earlier,
i.e. before they become bad, when their lethal time has expired.