$1$ Part A: Initial search landscapes

$1\mathrm{.}1$ One$-$max problem

Consider the simple case of evolving a string that contains all $1$s in every lo$-$

cation. Let the length of the strings be $30.$ The initial population should be

randomly created. Use standard mutation and one$-$point crossover. The fitness

of a solution is the number of $1$s in the string.

Plot the average fitness of the population versus the generations passed.

This exercise is to show the operation of a genetic algorithm. We know the

optimal solution in advance. This represents a very easy search landscape and

is included to illustrate the operation of a genetic algorithm.

When plotting the average fitness, you don$$t need to write code to do the plot$-$

ting; feel free to output the values to a text$/$csv file and use excel, gnuplot or

other to plot the results.

$1\mathrm{.}2$ Evolving to a target string

This is the same as before but instead of evolving to a string of $1$s$,$ the population

will evolve to find some target string.

Define a target string $($a sequence of $1$s and $0$s$)$ and adopt the same approach

as before with an appropriate fitness function $($number of matching values$).$ Plot

the average fitness as before.

$1\mathrm{.}3$ Deceptive Landscape

Modify the fitness function from the one$-$max problem, such that the fitness

function is equal to the number of $1$s in the string for all cases except when

there are no

tt $1$s present. In this case, the fitness should be $2\backslash$times $($length of the solution$).$

Plot the average fitness over time.

This problem represents a deceptive problem and should be very hard for

the GA to find the optimal.