Roulette-wheel selection chooses candidates probabilistically: stronger candidates receive larger slices, while weaker candidates retain a smaller chance of selection. Imagine a casino wheel divided into slices, with each candidate occupying a slice sized according to its fitness. section 4.10 section 4.8
The technique is useful when an evolutionary algorithm should favor high-performing candidates without eliminating diversity entirely. A lower-fitness candidate may still carry a valuable gene, so occasional selection can support better future solutions. section 4.10 section 4.8
One spin of the wheel
Suppose a population has four candidates with fitness scores 1, 2, 3, and 4. Their total fitness is 10, so their selection probabilities are 0.1, 0.2, 0.3, and 0.4. The wheel divides the interval from 0 to 1 into corresponding ranges. A random spin landing in the largest range selects the candidate with fitness 4; a landing in the smallest range can still select the candidate with fitness 1. Repeat the spin until enough parents have been chosen. The same candidate may be selected more than once. section 4.10 section 4.8
A straightforward implementation follows these steps:
- Add the fitness scores to obtain the population total. section 4.10
- Divide each candidate’s fitness by that total to obtain its slice size. section 4.10
- Store each candidate’s cumulative start and end boundaries on the wheel. section 4.10
- Generate a random number between 0 and 1 and return the candidate whose slice contains it. section 4.10
def set_probabilities(population):
population_sum =
➥sum(individual[INDIVIDUAL_FITNESS_INDEX] #A
➥for individual in population)
for individual in population:
individual[INDIVIDUAL_PROBABILITY_INDEX] =
➥individual[INDIVIDUAL_FITNESS_INDEX]
➥/ population_sum #B
def roulette_wheel_selection(population,
➥number_of_selections):
set_probabilities(population)
slices = []
total = 0
for r in range(0, len(population)):
individual = population[r]
slices.append([r, total, total
➥+ individual[INDIVIDUAL_PROBABILITY_INDEX]]) #C
total += individual[INDIVIDUAL_PROBABILITY_INDEX]
chosen_ones = []
for r in range(number_of_selections):
spin = random.random()
result = [s[0] for s in slices if s[1]
➥< spin <= s[2]] #D
chosen_ones.append(population[result[0]]) #E
return chosen_ones
Python pseudocode shows probability assignment, cumulative slice construction, repeated spins, and selected-candidate lookup. section 4.10
The same mechanism can select the next attraction for an ant: available attractions receive probabilities, cumulative slices are built, and one random spin chooses the next visit. section 6.7
