Does a differential evolution algorithm mutate its population during a generation?

Question

I'm implementing a differential evolution algorithm and when it comes to evolving a population, the page I am referencing is vague on how the new population is generated.

https://en.wikipedia.org/wiki/Differential_evolution#Algorithm

The algorithm looks like the population is mutated during evolution.

# x, a, b, c are agents in the population
# subscriptable to find position in specific dimension
# pop is filled with Agent objects
for i, x in enumerate(pop):
  [a, b, c] = random.sample(pop[:i]+pop[i+1:], 3)
  ri = random.randint(0, len(x))
  new_position = []
  for j in range(len(x)):
    if random.uniform(0, 1) < CR or j == ri:
      new_pos.append(a[j] + (F * (b[j] - c[j])))
    else:
      new_pos.append(x[j])
  # Agent() class constructor for agent, takes position as arg
  new_agent = Agent(new_pos)
  if fitness(new_agent) <= fitness(x):
    pop[i] = new_agent # replace x with new_agent

But I wonder if instead it means a new population is made and then populated iteratively:

new_pop = []
for i, x in enumerate(pop):
  [a, b, c] = random.sample(pop[:i]+pop[i+1:], 3)
  ri = random.randint(0, len(x))
  new_position = []
  for j in range(len(x)):
    if random.uniform(0, 1) < CR or j == ri:
      new_pos.append(a[j] + (F * (b[j] - c[j])))
    else:
      new_pos.append(x[j])
  new_agent = Agent(new_pos)
  if fitness(new_agent) <= fitness(x):
    new_pop.append(new_agent)
  else:
    new_pop.append(x)
pop = new_pop

Note new_pop is made, and filled with agents as the for loop continues.

The first allows previously evolved agents to be used again in the same generation; in other words, the population is changed during the evolution. The second doesn't allow updated agents to be re-used, and only at the end is the original population changed.

Which is it?

It may be a good idea to provide the sources of these pseudocodes. — nbro, Apr 15 '21 at 10:21

score 2 · Accepted Answer · answered Apr 17 '21 at 18:33

Quoting the original paper:

For each target vector $x_{i,G}$ ,a mutant vector is generated according to $$ v_{i,G+1} = x_{r_1,G} + F\left(x_{r_2,G} + x_{r_3,G}\right)$$

And later

To decide whether or not it should become a member of generation $G + 1$, the trial vector $v_{i,G+1}$ is compared to the target vector $x_{i,G}$ using the greedy criterion.

I'd say it is pretty unambiguous that author's intent was to split evolving agents' populations into "generations" indexed by $G$. A new generation $G+1$ is created by applying the DE algorithm to the previous generation $G$. No agents are changed within the generation $G$.

So, it looks like the answer to your question is "no" - the population of the current generation $G$ is not mutated. Your second approach is the correct one.

Some metaheuristics, like particle swarm optimization and bat algorithm, mutate their populations during the current generation; however, some like genetic algorithm doesn't. Thanks for clarifying, it seemed like it's closer in metaphor to the ones that do but it's nice having a declarative answer. — gator, Apr 17 '21 at 20:44

Does a differential evolution algorithm mutate its population during a generation?

1 Answers1