A simple genetic algorithm can be built from a few parts: a way to represent a candidate, a fitness function, parent selection, crossover, mutation, and a stopping rule. This walkthrough uses a binary genome and the OneMax objective, so you can see each step clearly—and avoid a common Python bug in which variation operators change selected parents in place.
What the algorithm does
A genetic algorithm (GA) searches by evolving a population of candidate solutions. It scores candidates with a fitness function, selects parents, creates offspring with variation operators, and repeats until it reaches a stopping condition such as a generation limit or evaluation budget. It is a search method, not a guarantee that every run will find the best possible answer.
For a small example, use OneMax: each candidate is a fixed-length list of zeroes and ones, and its fitness is the sum of its bits. With a 12-bit genome, for example, [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1] has fitness 6. The maximum possible fitness is 12, achieved by an all-ones genome. DEAP uses OneMax as an illustrative problem in its repository.
A complete from-scratch example
The following implementation uses tournament selection, one-point crossover, and bit-flip mutation. It copies selected parents before changing them, so the current population remains intact while offspring are prepared.
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import random
# Problem and run settings
GENOME_LENGTH = 12
POPULATION_SIZE = 40
GENERATIONS = 50
TOURNAMENT_SIZE = 3
CROSSOVER_PROBABILITY = 0.8
MUTATION_PROBABILITY = 0.02 # Probability for each bit
def make_individual():
return [random.randint(0, 1) for _ in range(GENOME_LENGTH)]
def fitness(individual):
return sum(individual)
def tournament_select(population):
contestants = random.sample(population, TOURNAMENT_SIZE)
return max(contestants, key=fitness)
def crossover(parent_a, parent_b):
"""Return two children made with one-point crossover."""
if len(parent_a) < 2:
return parent_a[:], parent_b[:]
point = random.randint(1, len(parent_a) - 1)
child_a = parent_a[:point] + parent_b[point:]
child_b = parent_b[:point] + parent_a[point:]
return child_a, child_b
def mutate(individual):
"""Flip each bit independently with MUTATION_PROBABILITY."""
for index in range(len(individual)):
if random.random() < MUTATION_PROBABILITY:
individual[index] = 1 - individual[index]
return individual
population = [make_individual() for _ in range(POPULATION_SIZE)]
evaluations = len(population)
for generation in range(GENERATIONS + 1):
best = max(population, key=fitness)
print(
f"generation={generation:02d} "
f"best_fitness={fitness(best)}/{GENOME_LENGTH} "
f"evaluations={evaluations}"
)
if fitness(best) == GENOME_LENGTH or generation == GENERATIONS:
break
next_population = [best[:]] # Elitism: preserve the current best candidate.
while len(next_population) < POPULATION_SIZE:
# Selection returns references to members of the existing population.
parent_a = tournament_select(population)[:]
parent_b = tournament_select(population)[:]
if random.random() < CROSSOVER_PROBABILITY:
child_a, child_b = crossover(parent_a, parent_b)
else:
child_a, child_b = parent_a, parent_b
mutate(child_a)
mutate(child_b)
next_population.append(child_a)
if len(next_population) < POPULATION_SIZE:
next_population.append(child_b)
population = next_population
evaluations += POPULATION_SIZE - 1 # The copied elite needs no new evaluation.
How each part works
Representation and fitness
make_individual() creates a fixed-length binary genome. fitness() assigns a score by counting the ones. For a different problem, these functions must reflect its decision variables and objective; a binary representation is appropriate only when the problem can sensibly be represented with bits.
Tournament selection
tournament_select() samples three candidates and returns the one with the highest fitness. A larger tournament makes selection more competitive because weaker candidates are less likely to win; it does not make a setting universally better. The sample size must not exceed the population size.
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Crossover and mutation
One-point crossover chooses a cut between bits and swaps the suffixes of two parents. The mutation function independently flips each bit with probability MUTATION_PROBABILITY. That is a per-bit probability, not the probability that an entire individual mutates. These operators fit binary lists; other representations need compatible operators.
Here, crossover probability is applied once to each parent pair. If the random draw is above the threshold, the copied parents become the children without crossover. Mutation is then attempted for every bit in both children, whether or not crossover occurred.
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Replacement, elitism, and stopping
Each iteration fills a new population and then replaces the old one. The first slot is a copy of the best current candidate, an elitism choice that prevents the best fitness from being lost during replacement. The run stops early if the maximum OneMax score is reached; otherwise it ends after the configured number of generations.
The example counts the initial population as evaluated and adds one evaluation for each newly created non-elite individual. Because this objective is inexpensive and deterministic, the code calls fitness() directly rather than storing scores. For costly or stochastic objectives, cache or explicitly recalculate fitness when a genome changes, and count actual objective calls.
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Why copying matters in Python
In Python, assigning an object to another variable does not duplicate it. A selection function that returns a population member returns a reference to that same list. If an in-place mutation changes it, the original population member changes too. DEAP explicitly notes that its selection operators return references and that its crossover and mutation operators modify individuals in place; see its operators tutorial.
This example copies each selected parent with [:] before variation, and its crossover function returns new child lists. Those choices isolate offspring from the old population. If you instead write operators that mutate a list in place, copy before passing selected individuals to them. In either design, a changed genome has a changed fitness and must not keep a stale cached score.
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Choose parameters as a starting point, not a recipe
Population size, generation count, selection pressure, crossover, mutation, and replacement policy influence the search. They depend on the representation, objective, and available compute, so this small OneMax example does not establish generally optimal values.
| Choice | Meaning in this example | How to adapt it |
|---|---|---|
| Population size | 40 candidates | Increase it when broader population diversity is useful and the evaluation budget permits; each generation then costs more evaluations. |
| Tournament size | 3 sampled candidates compete | Larger tournaments increase selection pressure; compare outcomes over repeated runs rather than assuming one size is best. |
| Crossover probability | 0.8 chance per parent pair | Controls whether a pair recombines. Keep it distinct from mutation probability. |
| Mutation probability | 0.02 chance per bit | This is a per-gene setting. A probability applied once to an individual would mean something different. |
| Replacement and elitism | New generation replaces the old; one best individual is copied forward | Choose whether to preserve top candidates and how many. Elitism protects strong solutions but can reduce diversity if overused. |
| Stopping condition | Maximum score or 50 generations | A generation cap is straightforward. An evaluation budget is useful when comparing approaches that evaluate different numbers of candidates. |
These are illustrative settings, not recommendations. The DEAP repository, for example, includes a 100-bit OneMax configuration with 300 individuals, 40 generations, crossover probability 0.5, mutation probability 0.1, and per-bit mutation probability 0.05. Those values describe that example only.
Track progress and make runs reproducible
The printed output records the generation, best fitness, and evaluation count. If the best score stops improving, that is useful diagnostic information, but it does not by itself show why progress stalled. Consider also recording average fitness and preserving the best candidate found across the run.
To reproduce a run while debugging, set a seed near the start of the script, such as random.seed(7). The same seed and code make the random choices repeatable in a given Python environment; changing parameters, code, or random-number implementation can change the result. For a fair comparison between settings, run multiple seeds and compare fitness against evaluations, rather than reporting a single favorable run.
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- Mutating the old population unintentionally: copy selected lists before any in-place operator, or design operators to return new lists.
- Using operators that do not match the genome: bit-flip mutation and one-point crossover are for binary sequences; other representations need suitable operations. DEAP advises checking the behavior of the selected crossover operator in its operator documentation.
- Confusing mutation probabilities: state whether a rate is per pair, per individual, or per gene. This code uses a pair-level crossover draw and a per-bit mutation draw.
- Keeping stale fitness: recompute or invalidate a candidate's score after changing its genome if fitness is cached.
- Comparing runs with different work budgets: generation counts alone can hide different numbers of evaluations. Track evaluations when comparing algorithms or configurations. DEAP's algorithm documentation describes generational evaluation, selection, variation, and reevaluation; the from-scratch handout by Denis Pallez illustrates evaluation budgets and progress observers.
When to use a library instead
Writing the loop yourself is helpful for learning and for a small, customized search. A library becomes useful when you need reusable operators, multiple evolutionary strategies, or established bookkeeping. DEAP's eaSimple documentation lays out a generational sequence of evaluation, stochastic selection, variation, and reevaluation. Its operator guidance also makes the reference and in-place modification behavior explicit, which remains important when adapting library examples.
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