A genetic algorithm implemented in Python

Natural selection is, roughly, the likelihood of a given individual to survive long enough to reproduce, and thus continue its species. Factor in mutations—random changes in the genes—and the probability a given mutation has to help an individual survive (or not) in its environment and the result is that some individuals are more likely to reproduce than others. Those fitter individuals are more likely to pass on their mutations to the next generation, which will add mutations of its own, ultimately causing the population to slowly change as these mutations accumulate. Repeat this process over multiple generations across millions of years and we get evolution.

Turns out that implementing these ideas, or at least analogies, in software can be useful to solve certain problems, so let's write a simple program that exemplifies the process.

Seed

There are multiple types of genetic algorithms with multiple different uses, but usually they start with a data sample.

from collections.abc import Collection
from typing import Protocol


class Population[Individual](Collection, Protocol):
  def select_random(self) -> Individual: ...


def algorithm[Individual](population: Population[Individual]):
  parent_a = population.select_random()
  parent_b = population.select_random()

To keep things simple, we start with two parents that are selected randomly from the existing population, and we'll go from there.¹

Crossover

With our first pair in place, we can now produce the next "generation".

class Offspring[Individual](Protocol):
  def mutate(self) -> Individual: ...


class Population[Individual](Collection, Protocol):
  # ...
  def crossover(self, first: Individual, second: Individual)\
      -> Offspring[Individual]: ...

  def add(self, individual: Individual): ...


def algorithm[Individual](population: Population[Individual]):
  # ...
  base_offspring = population.crossover(parent_a, parent_b)
  real_offspring = base_offspring.mutate()
  population.add(real_offspring)

The crossover in genetic algorithms is the operation used to combine the data of the parents to produce offspring. But we can't just stop there, we need genetic variance to ensure the population actually evolves over time. One form of variance is of course that the parents contribute different characteristics selected at random from each parent, but even that isn't enough as it could leave us stuck².

Actual variance comes from the key element of mutation, the random chance that any given offspring individual will have genes not present in the parents.³

Finally, the new individual is, of course, a new member of the population so we add it⁴.

Natural Selection

At this point, we have parents and their offspring, what now? It's time to determine the goal. Genetic algorithms are commonly used to find a good enough solution to certain types of, often trial and error, problems that don't translate well to common normal algorithms. Fortunately, the only thing resembling a "goal" in nature is simply thriving, surviving long enough to reproduce... So let's do that, by introducing a "niche" and determining how well the individuals fit that niche.

# ...
class Population[Individual](Collection, Protocol):
  # ...
  def remove(self, individual: Individual): ...


class Niche[Individual](Protocol):
  def tournament(self, pop: Collection[Individual])\
    -> tuple[Individual, Individual]: ...


def algorithm[Individual](
  population: Population[Individual], niche: Niche[Individual]
):
  # ...
  fittest, unfit = niche.tournament(population)
  population.remove(unfit)

Nature is ruthless, and so is our algorithm. In nature, only the fittest perpetuate their genes, and in our algorithm, only that individual in a group⁵ that best fits the niche is the one to continue. This is usually called "tournament selection" in genetic algorithm jargon.

Finally, to maintain our analogy (and really to prevent our population from growing without bound) we remove the least fit individual from the population.

Generations

We have almost completed the algorithm, but the mere fact that we've found an individual that fits the niche better than others doesn't mean we've actually found one that thrives in the niche; the likelihood of achieving that in just the first generation is nil. We'll need many generations, so we need to repeat the process until we find such individual.

# ...
class Population[Individual](Collection, Protocol):
  # ...
  def find_mate(self, individual: Individual) -> Individual: ...


class Niche[Individual](Protocol):
  # ...
  def can_thrive(self, individual: Individual) -> bool: ...


def algorithm[Individual](
  population: Population[Individual], niche: Niche[Individual]
) -> int:
  parent_a = population.select_random()
  parent_b = population.select_random()

  generations = 0

  while not niche.can_thrive(parent_a):
    base_offspring = population.crossover(parent_a, parent_b)
    real_offspring = base_offspring.mutate()
    population.add(real_offspring)

    fittest, unfit = niche.tournament(population)
    population.remove(unfit)
    parent_a, parent_b = fittest, population.find_mate(fittest)

    generations += 1

  return generations

There are several options here, one commonly used in real genetic algorithms is to pick the two fittest instead of just one and make those "reproduce", producing an entirely new population and continue iterating from there. But to keep our natural analogy going, let's instead assume that our fittest finds a "suitable mate"⁶ in another member of the population, which also adds another source of variance.

Ultimately, the point here is iteration: continually doing the crossover and tournament selection until we meet our goal.

And there we have it, that algorithm function represents our full genetic algorithm, in a way I hope is self-explanatory enough. That function should work without change as long as it receives arguments that actually implement the protocols properly.

Here's a file with the complete definition, and here's a file with a string-based implementation of the algorithm, along with the function being run.

Now, before finishing, you'll notice that I talked very little about the actual problems that could be solved with this type of algorithm... Well that's true, because the point of this post was the algorithm itself. That said, I might write a follow up with a practical example.

Appendix (On implementation and testing)

I mentioned above that implementation doesn't matter and it indeed doesn't but for the sake of completeness—to fully explain the genetic algorithm—I wanted to go over what happens during crossover and tournament selection. However, we can write tests to do that instead of explaining the implementations line by line!⁷

from hypothesis import given, strategies as st

from implementation import Individual


st.register_type_strategy(Individual, st.builds(Individual, st.text(
  alphabet=Individual.POOL,
  min_size=Individual.LENGTH,
  max_size=Individual.LENGTH
)))

Before anything is done, we have to tell hypothesis how to create an Individual that actually fits our implementation. Only then we move onto the tests:

# ...
from implementation import Population

@given(...)
def test_crossover(parent_a: Individual, parent_b: Individual):
  offspring = Population().crossover(parent_a, parent_b)

  is_parent_a = is_parent_b = False

  for gene, a, b in zip(offspring, parent_a, parent_b):
    assert gene in (a, b)
    is_parent_a |= gene == a
    is_parent_b |= gene == b

  assert is_parent_a and is_parent_b

This test tells us everything we need to know about what happens in crossover without actually having to check the implementation: We don't care how it's done, but we do care that every gene in the offspring comes from one of the parents, and that both parents had an input.

# ...
from implementation import Niche


@given(...)
def test_tournament_selection(niche: Niche, population: Population):
  pop = set(population)
  winner, loser = niche.tournament(pop)

  while len(pop) > 1:
    assert winner in pop

    pop.remove(loser)
    _, loser = niche.tournament(pop)
  else:
    assert winner == loser

Tournament selection is a bit trickier to test because the calculation for each fittest is an implementation detail, but one the whole idea depends upon. We could simply repeat the implementation here and assert that the winner and loser were calculated correctly but then the test would no longer work if we changed the metric (or changed what an individual is entirely).

In these cases, we have to step back and think of invariants: what is always true about the tournament selection? As long as the winner remains in the population and no other individuals are added, it will always be the winner. And that's what we test: We systematically remove each loser until only one individual is left in the population; that individual must still be the original winner!