Types of crossover in genetic algorithm

Crossover is a genetic operator used to introduce enhancement in the offspring’s genetic material. During the process of generating a population, there are chances that the fitness value of the new population stops improving, and one of the participating chromosomes could be a problem.

Crossover is a biological technique to mix the genetic material of the parent chromosomes and produce new offspring. There are chances that the children produced by this process are better than the previous ones and might possess better qualities and features.

There are many types of crossover available in the genetic algorithm. Let’s discuss the most widely used in this Answer.

One-point crossover

In this type of crossover, we mark a point on the parent chromosomes at the same position. The genes before this point remain, but the genes after this point are swapped. A random point of 3 is selected for a one-point crossover. The following illustration below shows the one-point crossover process.

One-point crossover
One-point crossover

Children’s genetic material is formed by inheriting one part of their genes from one parent and the other from the second parent.

Code example

Let’s see how we can implement a one-point crossover in Python. 

# Define the two parents as arrays
parent1 = [1, 2, 3, 4, 5, 6, 7, 8]
parent2 = [1, 3, 5, 7, 9, 11, 13, 15]
# Specify the crossover point (e.g., point 3)
crossover_point = 3
def one_point_crossover(parent1, parent2, crossover_point):
    "Perform one-point crossover between two parents at a specified point"
    
    # Create offspring by combining parent genes up to the specified crossover point
    offspring1 = parent1[:crossover_point] + parent2[crossover_point:]
    offspring2 = parent2[:crossover_point] + parent1[crossover_point:]
    
    return offspring1, offspring2
# Perform one-point crossover on the two parents at the specified point
offspring1, offspring2 = one_point_crossover(parent1, parent2, crossover_point)
# Print the results
print("Parent 1: ", parent1)
print("Parent 2: ", parent2)
print("\n")
print("Offspring 1: ", offspring1)
print("Offspring 2: ", offspring2)

Code explanation

  • Lines 2–3: We define the two parents as arrays parent1 and parent2 consisting of eight genes each.

  • Line 6: We specify the crossover point to swap the genes.

  • Lines 8–15: We define the one_point_crossover function that takes three parameters: two parents and a crossover point. We perform crossover at lines 12–13 and then return the children at line 15.

  • Line 18: We call the one_point_crossover() function.

  • Lines 21–25: We print both parents and offspring.

Two-point crossover

In this type of crossover, two random points are selected on the mating chromosomes, and the genes of the middle part are swapped. The following illustration below shows the two-point crossover process.

Two-point crossover
Two-point crossover

We can see that the genes before the first point and after the second point don’t change in the children while the genes between these two points get changed.

There can be a multipoint crossover where the alternative patches of genes are swapped.

Code example

Let’s see how we can implement a two-point crossover in Python. 

# Define the two parents as arrays
parent1 = [1, 2, 3, 4, 5, 6, 7, 8]
parent2 = [1, 3, 5, 7, 9, 11, 13, 15]
# Specify the crossover points
crossover_point1 = 2
crossover_point2 = 5
def two_point_crossover(parent1, parent2, point1, point2):
    "Perform a two-point crossover between two parents at specified points"
    # Create offspring by exchanging genetic material between parents at the specified points
    offspring1 = (
        parent1[:point1] + parent2[point1:point2] + parent1[point2:]
    )
    offspring2 = (
        parent2[:point1] + parent1[point1:point2] + parent2[point2:]
    )
    return offspring1, offspring2
# Perform two-point crossover on the two parents at the specified points
offspring1, offspring2 = two_point_crossover(parent1, parent2, crossover_point1, crossover_point2)
# Print the results
print("Parent 1: ", parent1)
print("Parent 2: ", parent2)
print("\n")
print("Offspring 1: ", offspring1)
print("Offspring 2: ", offspring2)

Code explanation

  • Lines 2–3: We define the two parents as arrays parent1 and parent2.

  • Lines 6–7: We specify two crossover points. The first one is 2, and the second is 5.

  • Lines 9–19: We define the two_point_crossover function that takes parents and crossover points and performs a two-point crossover operation. Line 19 returns the children generated after the two-point crossover process.

  • Line 22: We call the two_point_crossover function.

  • Lines 25–29: We print both parents and offspring.

Uniform crossover

In this type of crossover, we don’t swap the genes based on random pointers. We toss a coin for each gene in parent chromosomes. If the toss results in 1, we swap the genes, and if the toss is 0, then the original value of the genes passes to the children. The following illustration below shows the uniform crossover process.

Uniform crossover
Uniform crossover

We can see that the children’s genetic material depends on the toss’s value. We only swapped the genes where the toss value was 1.

Code example

Let’s see the implementation of the uniform crossover in Python.

import random
# Parent chromosomes
parent1 = [1, 2, 3, 4, 5]
parent2 = [6, 7, 8, 9, 10]
# Probability to swap genes
crossover_prob = 1
def uniform_crossover(parent1, parent2, crossover_prob):
    assert len(parent1) == len(parent2), "Parent chromosomes must have the same length"
    child1 = []
    child2 = []
    for gene1, gene2 in zip(parent1, parent2):
        bit = random.randint(0,1)
        if bit == crossover_prob:
            print("bit value=", bit)
            child1.append(gene2)
            child2.append(gene1)
        else:
            # Keep genes unchanged if no crossover occurs
            print("bit value=", bit)
            child1.append(gene1)
            child2.append(gene2)
    return child1, child2
child1, child2 = uniform_crossover(parent1, parent2, crossover_prob)
print("Parent 1:", parent1)
print("Parent 2:", parent2)
print("\n")
print("Child 1 after crossover:", child1)
print("Child 2 after crossover:", child2)

Code explanation

  • Lines 4–5: We define two parent chromosomes.

  • Line 8: We define crossover probability. This will control the crossover process.

  • Lines 10–28: We define the uniform_crossover function that takes parents and the crossover probability as parameters. We generate a random integer at line 18 and check if it equals the crossover_prob. If it is, we swap the genes otherwise, not.

  • Line 30: We call the uniform_crossover function.

  • Lines 32–36: We print the parent’s and children’s chromosomes.

Conclusion

In this Answer, we discussed a very important concept, crossover, of genetic algorithm. We discussed three types of crossover and saw their implementation in Python.

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