Page 98 - Data Science Algorithms in a Week

82 Fred K. Gruber

Adaptive parameter control in which the mutation rate is modified according to a
measure of how well the search is going, and self-adaptive parameter control in which the
mutation rate is evolved together with the variables that are being optimized.
An example of a dynamic mutation rate is tested in Bäck and Schütz (1996) where
the mutation rate depended on the generation according to

 n  2   1
p   2 t  
t
 T  1 

t
Where is the current generation and T is the maximum number of generations.
In the adaptive methodology, the goodness of the search is evaluated and the
mutation rate, and sometimes the crossover rate, is modified accordingly. One technique
that is found to produce good results in Vasconcelos et al. (2001) measured the “genetic
diversity” of the search according to the ratio of the average fitness to the best fitness or
gdm gdm
. A value of close to 1 implies that all individuals have the same genetic code
(or the same fitness) and the search is converging. To avoid premature convergence, it is
necessary to increase exploration (by increasing the mutation rate) and to reduce the
gdm
exploitation (by reducing the crossover rate). For the contrary, if the falls below a
lower limit the crossover rate is increased and the mutation rate reduced.
In the self-adaptive methodology, several bits are added to each individual that will
represent the mutation rate for that particular individual. This way the mutation rate
evolves with each individual. This technique is investigated by Bäck and Schütz (1996).
Another important variation is elitism in which the best individual is copied to the
next generation without modifications. This way the best solution is never lost (see, for
example, Xiangrong and Fang, 2002).

DATA SET IMPLEMENTATION

All experiments use data from the study conducted by Ryan (1999) that contains
information on 125 subjects. A web site is used for this experiment, where 648 images
are shown sequentially to each subject. The response required from the individuals is
their preference for each image (1: Yes, 0: No). The images are characterized by seven
discrete properties or features, with specific levels:

 Density – Describes the number of circles in an image (3 levels).
 Color family – Describes the hue of the circles (3 levels).