Other Methods

So far, we’ve learned what population methods are and why they’re important. We can solve an even bigger group of optimization problems with these methods. These are the problems that can’t be solved with exact methods, or the exact solution would consume too many resources. We’ll be able to implement a solution for any optimization problem using population algorithms.

Although we’ve seen two of the most used population algorithms—genetic algorithms and PSO—it’s worth knowing other population methods. The following is a nonexhaustive list of population methods with a brief explanation of the idea behind them.

Differential evolution

They’re very similar to genetic algorithms but create new individuals a bit differently. Specifically, differential evolution (DE) uses the directional information of solution vectors. This makes the algorithm converge faster than genetic algorithms but at the cost of less exploration of the solution space.

In plain English, the way mutation is implemented in DE is different: It uses three or more vectors. For example, the classic version of the algorithm creates a new individual from three existing ones, as follows:

$$s = s_1 + M(s_2 - s_3)$$

Here, $s$, $s_1$, $s_2$, and $s_3$ are solutions, and $M$ is the mutation factor, which determines how much the mutation changes the current population. This looks more like a crossover, but in the DE world, this is called a mutation. By adding and subtracting existing vectors, the algorithm uses the directional information of the entire population, as we stated above.