.
Implement a genetic algorithm for minimizing the AIC for the baseball salary regression problem. Model your algorithm on Example 3.5.
a.
Compare the effects of using different mutation rates.
b.
Compare the effects of using different generation sizes.
c.
Instead of the selection mechanism used in Example 3.5, try the following three mechanisms:
i.
Independent selection of one parent with probability proportional to fitness and the other completely at random
ii.
Independent selection of each parent with probability proportional to fitness
iii.
Tournament selection with
P/5 strata, and/or another number of strata that you prefer To implement some of these approaches, you may need to scale the fitness function. For example, consider the scaled fitness functions
π
given by
where
a
and
b
are chosen so that the mean fitness equals the mean objective function value and the maximum fitness is a user-chosen
c
times greater than the mean fitness,
f
is the mean and
s
is the standard deviation of the unscaled objective function values in the current generation,
z
is a number generally chosen between 1 and 3, and
v
is a number slightly larger than 1. Some scalings can sometimes produce negative values for
i
. In such situations, we may apply the transformation
φnew(
ϑ
where
d(t) is the absolute value of the fitness of the worst chromosome in generation
t, in the last
k
generations for some
k, or in all preceding generations. Each of these scaling approaches has the capacity to dampen the variation in
f
, thereby retaining
within-generation diversity and increasing the potential to find the global optimum.
Compare and comment on the results for your chosen methods.
e.
Implement the following crossover approach, termed
uniform crossover
[622]: Each locus in the offspring is filled with an allele independently selected at random from the alleles expressed in that position in the parents.