Assignment $1$:

There are $n$ tasks assigned to $n$ workers, and each worker can be assigned only one task.

Each worker can complete any one of the tasks, but the time spent varies. Use the ant colony

algorithm to find the best allocation scheme that minimizes the total time spent.

Sample Input

$3$ workers

Sample Output

Time Spent:$8$

Optimal assignment: worker$1$: task$2$; worker$2$: task$1$; worker$3$: task$3$

Build a mathematical model to describe the problem; $(3$ marks$)$

Formulate state transition probability and pheromone update strategy; $(4$ marks$)$

Write a program to solve the problem. $($Please add the necessary instructions on how to

run the program; any languages are acceptable; The input and output format does not need to

refer to the sample$)$; $(8$ marks$)$