Task $1)$ Fitness Functions

Use MATLAB script to program the following fitness functions. These functions are for minimisation

problems and will be used to validate the performance of optimisation algorithms.

For all the above functions, set $D=10.$

Task $2)$ Design a Genetic Algorithm

Write a Matlab code for a Genetic Algorithm. The following operators should be used

Selection operator: Tournament selection

Crossover operator: Whole arithmetic crossover

Mutation operator: Uniform mutation

Other parameter settings:

Set total number of generations Tmax$=100.$

Set population size $N=50.$

Set offspring population size $M=100.$

Set the intermediate population in the mating pool $100.$

Set the total number of iteration $1000.$

Test the Genetic Algorithm against the four fitness functions in Task $1.$ Repeat every

optimisation process for $20$ times and show the average performance $($fitness value$).$

Change the selection operator to Proportional Selection and re$-$run all the previous optimisation

experiments. Compare the result with the initial one and comment on it$.$

Change the crossover operator to Simple$-$point arithmetic crossover and re$-$run all the

optimisation experiments. Compare the result with the initial one and comment on it$.$

Please answer both tasks mainly task $2$ fully, task $2$ requires task $1.$