What is the importance of switching to a differential evolution algorithm?

Question

In the differential evolution algorithm for optimization problems. There are three evolutionary processes that cross mutation and select

I'm just a beginner, but I tried to remove the intersection process and there is no significant difference from the original algorithm.

So what is the importance of the transition in the differential evolution algorithm?

Answer 1

If you are not using a crossover, your algorithm may simply explore the problem space and not use it. In general, an evolutionary algorithm succeeds if it provides a good balance between exploration and exploitation levels.

For example, DE/rand/1/Either-Or is a variant of DE that excludes the crossover operator but uses the efficient mutation operator . According to “Differential Evolution: A Review of the Present State,” in this algorithm, probe vectors that are pure mutants meet with probability pF , and those that are pure recombinants meet with probability 1 − pF . It is shown that this option gives competitive results against the classic DE variants rand / 1 / bin and target-to-best / 1 / bin ( Main link ).

X(i,G) is the i-th target (parent) vector Generation G, U(i,G) is the corresponding test vector, F is the coefficient of the difference vector scale and k = 0.5*(F + 1)[in the original paper] .
The crossover is not used in this scheme, but the mutation is effective enough to compare with the original DE algorithm.