Based on the following code;

$$

import random

$$

# Read input file function

def read$\_$input$\_$file$($filename$)$:

$$ with open$($filename$,\text{'}$r$\text{'})$ as file:

$$ data $=[]$

$$ for line in file:

$$ data.append$($list$($map$($int$,$ line.strip$().$split$(\text{'},\text{'}))))$

$$ return data

$$

# Fitness function to evaluate the total score of a task assignment

def fitness$($chromosome$,$ data$)$:

$$ total$\_$score $=0$

$$ for task, person in enumerate$($chromosome$)$:

$$ total$\_$score $+=$ data$[$person$][$task$]$

$$ return total$\_$score

$$

# Selection function using tournament selection

def selection$($population$,$ fitnesses$)$:

$$ selected $=$ random.choices$($population$,$ weights$=$fitnesses, k$=2)$

$$ return selected

$$

# Crossover function $($Order Crossover$)$

def crossover$($parent$1,$ parent$2)$:

$$ size $=$ len$($parent$1)$

$$ start, end $=$ sorted$($random$.$sample$($range$($size$),2))$

$$ child $=[$None$]*$ size

$$

$$ # Inherit the middle section from parent$1$

$$ child$[$start:end$]=$ parent$1[$start:end$]$

$$

$$ # Fill remaining tasks in order from parent$2$

$$ fill$\_$positions $=[$i for i in range$($size$)$ if child$[$i$]$ is None$]$

$$ fill$\_$values $=[$task for task in parent$2$ if task not in child$]$

$$

$$ for i$,$ value in zip$($fill$\_$positions, fill$\_$values$)$:

$$ child$[$i$]=$ value

$$

$$ return child

$$

# Mutation function: Swap two random tasks

def mutate$($chromosome$,$ mutation$\_$rate$=0\mathrm{.}05)$:

$$ if random.random$()<$ mutation$\_$rate:

$$ i$,$ j $=$ random.sample$($range$($len$($chromosome$)),2)$

$$ chromosome$[$i$],$ chromosome$[$j$]=$ chromosome$[$j$],$ chromosome$[$i$]$

$$

# Genetic Algorithm function

def genetic$\_$algorithm$($data$,$ population$\_$size$=100,$ generations$=1000,$ mutation$\_$rate$=0\mathrm{.}05)$:

$$ num$\_$tasks $=$ len$($data$[0])$

$$ num$\_$people $=$ len$($data$)$

$$

$$ # Generate initial population $($random permutations of task assignments$)$

$$ population $=[$random$.$sample$($range$($num$\_$people$),$ num$\_$tasks$)$ for $\_$ in range$($population$\_$size$)]$

$$

$$ best$\_$solution $=$ None

$$ best$\_$fitness $=-$float$(\text{'}$inf$\text{'})$

$$

$$ # Evolve over generations

$$ for gen in range$($generations$)$:

$$ # Calculate fitness for all chromosomes

$$ fitnesses $=[$fitness$($chromo$,$ data$)$ for chromo in population$]$

$$

$$ # Track the best solution

$$ max$\_$fitness $=$ max$($fitnesses$)$

$$ if max$\_$fitness $>$ best$\_$fitness:

$$ best$\_$fitness $=$ max$\_$fitness

$$ best$\_$solution $=$ population$[$fitnesses$.$index$($max$\_$fitness$)]$

$$

$$ # Selection and Crossover

$$ new$\_$population $=[]$

$$ for $\_$ in range$($population$\_$size $//2)$:

$$ parent$1,$ parent$2=$ selection$($population$,$ fitnesses$)$

$$ child$1=$ crossover$($parent$1,$ parent$2)$

$$ child$2=$ crossover$($parent$2,$ parent$1)$

$$ new$\_$population.extend$([$child$1,$ child$2])$

$$

$$ # Mutation

$$ for chromo in new$\_$population:

$$ mutate$($chromo$,$ mutation$\_$rate$)$

$$

$$ population $=$ new$\_$population

$$

$$ # Print progress every $100$ generations

$$ if gen $\%50==0$:

$$ print$($f$"$Generation $\{$gen$\}$: Best Fitness $=\{$best$\_$fitness$\}")$

$$

$$ return best$\_$solution, best$\_$fitness

$$

# Main execution

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

$$ # Load data from file $($assumed to be called 'task$\_$assignment$\_$input.txt$\text{'})$

$$ data $=$ read$\_$input$\_$file$(\text{'}$GAtxt$.$txt$\text{'})$

$$

$$ # Run genetic algorithm

$$ best$\_$solution, best$\_$fitness $=$ genetic$\_$algorithm$($data$)$

$$

$$ # Output the best solution and its fitness score

$$ print$("$Best Task Assignment:", best$\_$solution$)$

$$ print$("$Best Fitness $($Total Score$)$:$",$ best$\_$fitness$)$

$$

;

Do the following;

Write a report detailing the following:

$($a$)$ Describe a chromosome in the initial population and the population size used.

$($b$)$ Define the fitness function you used.

$($c$)$ Describe the selection method used.

$($d$)$ Describe the mutation operator and the mutation rate used.

$($e$)$ Describe the crossover operator and the crossover rate used.

$($f$)$ Describe the termination criterion.