A genetic algorithm (GA) searches for a good solution by evolving a population of candidate solutions. Instead of following one fixed path through the search space, it evaluates candidates, selects parents, and uses crossover and mutation to produce new candidates. Random choices help it explore, but also mean that improvement is not guaranteed on every run and an optimum may be missed. section 7.3 section 2.2
A basic GA repeats this cycle:
- Initialize a population. Encode each candidate in a form suited to the problem, such as a binary, real-valued, or permutation vector. section 7.2.3 section 7.3
- Evaluate each candidate with a fitness function, then select parents. Selection may be random or weighted by fitness. section 7.3 section 7.4
- Apply crossover to combine parents and mutation to introduce random changes. Check and repair offspring when the problem has constraints. section 7.2.3 section 7.3
- Evaluate offspring, select survivors, and repeat until a stopping condition is met, such as a generation limit, adequate fitness, or stalled improvement. section 7.3
Algorithm 7.1 Genetic algorithm
Initialization: Randomly generate an initial population M(0)
Evaluate all individuals: Compute and save the fitness f(m) for each individual in the current population M(t)
While termination criteria are not met
Select parents: Define selection probabilities p(m)for each individual p in M(t)
Apply crossover: Generate M(t+1) by probabilistically selecting individuals from M(t) to produce offspring via genetic operators
Apply mutation: Introduce random changes to individuals
Evaluate: evaluate the fitness of the new individuals
Select survivors: select individuals to form the next generation
The pseudocode is a compact guide to the order of evaluation, parent selection, variation, and survivor selection. section 7.3
Choosing a ticket price
Suppose a ticket price must be chosen from $75 to $235 to maximize profit. One Python implementation encodes prices as eight-bit chromosomes, evaluates each decoded price with profit(x) = −20x² + 6200x − 350000, and evolves the population. Its reported result is a $155 price with $130,500 profit. A second implementation defines the pricing problem in pymoo and configures its GA with sampling, crossover, mutation, and a 100-generation run; it reports the same price and profit. section 7.4
Match the representation and operators to the decision. A traveling-salesman route is a permutation, not a binary price: a pymoo example evaluates route length across 20 US cities and uses permutation sampling, order crossover, inversion mutation, and repair to fix the starting city. This changes the candidates and their variation operators without changing the evaluate–select–vary cycle. section 8.6 section 7.2.3
Tune population size, crossover, mutation, and stopping rules experimentally. Crossover shares traits between candidates; mutation maintains diversity and can help prevent premature convergence. A high crossover rate with a lower mutation rate is recommended as a starting balance between exploring new areas and refining existing solutions. Do not treat a found solution as proof of global optimality. section 7.5 section 2.2
