Adaptive Genetic Algorithms - Computational Intelligence in Time Series Forecasting - page 314

x Reproduction. This parameter determines the rate at which the old solution
will be copied into the new population. When its value is increased the
chance of survival of a solution in the subsequent generation will also be
increased. This subsequently increases the number of “super-fit”
individuals in the next generation, which is not always desirable.
Apart from the above genetic parameters and their probabilities, two additional
parameters can be used for GA adaptation:
x Population size. This GA parameter can be adapted to the problem to be
solved. During the search process, the proper population size is the most
critical factor that strongly influences the convergence speed of the search
process, in the sense that too small a population size speeds up the search
convergence and leads eventually to a premature solution. On the contrary,
a very large population size could stretch the search process ad infinitum
(Baker, 1985).
x Fitness function. As a performance index, this helps in carrying out the
selection process optimally and has to be defined adequately with respect
to the problem to be solved.
9.3 Probabilistic Control of Genetic Algorithms Parameters
In the early 1980s it was a general view that the on-line adjustment of crossover
probability ,or crossover rate , can be favourable for optimal progress in the search
process, because it can help in avoiding the premature end of the search process
through the higher loss of the alleles. Using the entropy measure over the entire
population, Wilson (1986) was able to quantify the benefit of crossover
adjustment. To compensate for this, the value of mutation probability should be
increased. This indicates that, when the GA parameters are adaptively tuned, the
following two tendencies have to be balanced out:
x convergence to the solution optimum, after the region that contains the
solution optimum or nearly the optimum has been traced
x searching for new regions of the solution space in order to find a real global
optimum.
This illustrates that the genetic algorithm operates by a permanent balancing
between the best result that can be achieved and searching for the possibility to
achieve some better results. For monitoring the status of the balance the
exploitation-to-exploration relation (EER) has been introduced to serve as a
diversity measure of the search process. In the above case, the balance between the
values of the crossover probability p ( c ) and the mutation probability p ( m ) should
be kept at an optimal level. In practice, moderate values of crossover probability
(0.5 < p ( c ) < 1.0) and small balancing values of the mutation probability (0.001 <
p ( m ) < 0.05) are commonly used.
Li et al. (1992) proposed an EER-based dynamic GA , capable of balancing
ideally the GA behaviour by adjusting the crossover and mutation probabilities, by