Particle swarm optimization (PSO) is a population-based optimization algorithm that is inspired by the social behavior of birds. It has been applied to a variety of optimization problems, including finding the global minimum of a function.

Let us imagine you wanted to minimise a function, such as

f(x) = x² + 2x + 1, where x is a real-valued variable. High might you design a PSO to find this? (You are not required to actually solve it, but only give an explanation.)