Solution to Exercise 2: Assigning Tasks

The remaining exercises are challenging to solve with PSO. When we think of solutions to these problems, it’s hard to define a velocity for them. Using a genetic algorithm is more natural—and that’s why we’ll do just that.

Exercise 2

In this problem, we have $n$ tasks and $m$ employees. The matrix $W$ tells us how much time each employee needs to do each task. What would a solution for this problem look like?

In this case, a solution is an assignment of each task to some worker. There could be workers with no tasks assigned and workers with multiple tasks assigned. Mathematically, we can think of a solution as a matrix $S$ with size $m \times n,$ where $S_{i,j} = 1$ ...