PYTHON::

Solve the following problem using a genetic algorithm (GA):

Minimize f(X1, X2, X3) = X1

2 + X2

2 + X3

2 for -1.0 <= Xi <= 5.0, i = 1, 2, 3.

The goal is to find values of X1, X2, and X3 (in the given interval) that will cause f(.,.,.) to have

the minimum value. Use real (floating-point) values, not bit-string representations. Use

proportional selection, single-point crossover, and gene-wise mutation (as discussed in class).

Use the following parameter values:

N = 30; pc = 0.8; pm = 0.1; max generations (for use as a stopping condition) = 50.

For a typical single run, report the following:

a. At intervals of 10 generations, the best and the worst fitnesses (the f values) in the current

generation and the corresponding X-vectors; the average fitness of all the members of the

current generation;

b. The best-of-run solution (the vector and its fitness).

Next, collect data on 30 independent runs, and then report:

a. At intervals of 10 generations, the following averages (and the corresponding standard

deviations) over 30 values: the best-of-generation fitness, the average-of-generation

fitness;

b. The average (and the corresponding standard deviation) (over 30 values) of the best-of-

run fitness.

That is, the three quantities in (a) and (b) above are each an average of 30 values.