Brac University

CSE$422$: Artificial Intelligence

Question $1($CO$1)$

Maximum weight $=12$

The above problem is a $0/1$ Knapsack problem. You have to carry the different objects in your bag in a way such that the reward is maximized without exceeding the weight limit$.$ You can carry an object exactly once but you always have to carry the object labeled $$H$.$ Assuming you are asked to use Genetic Algorithm for this problem, answer the following questions

Encode the problem and create an initial population of $4$ different chromosomes

Explain what would be an appropriate fitness function for this problem. Use the fitness function and perform natural selection to choose the $2$ fittest chromosomes.

Using the selected chromosomes perform a single$-$point crossover to get $2$ offspring.

Perform mutation and check the fitness of the final offspring. Explain your work.

Question $2($CO$1)$

Suppose you have an equation f$($x$)=$ x$2-5$x $+6.$ Assume x can be any number between $0$ to $15.$ Now your job is to find an appropriate value of x such that the value of f$($x$)=0$ using Genetic Algorithm

Consider the fact that every chromosome will have $4$ genes, illustrate an appropriate encoding technique to create an initial population of $4$ randomly generated chromosomes.

Using an appropriate fitness function deduce the $2$ fittest chromosomes and perform a single pointer crossover from the middle to create two offspring.

Explain how you can mutate the offspring derived from $($B$)$ and comment on the fitness of the final produced offspring.

Question$3($CO$1)$