Crossover in genetic algorithms can be as simple as linear combination

Genetic algorithm is a powerful and simple global optimization algorithm. We learn from the best: from God!

Crossover is when two solutions are mixed up, for creating a second. This is evolution simulated on computers to solve problems!

Using a linear combination as a crossover method is a valid approach in genetic algorithms. Let’s break down how this process works:

1. Select Two Parents: Randomly choose two individuals (parents) from the current population.
2. Linear Combination:

• For each gene (locus) in the chromosome, create an offspring gene by combining the corresponding genes from the parents using a linear combination.
• The linear combination can be expressed as: [ \text{Offspring Gene} = \alpha \cdot \text{Gene from Parent 1} + (1 — \alpha) \cdot \text{Gene from Parent 2} ]
• Here, (\alpha) (alpha) is a parameter that determines the balance between the contributions of the two parents. It typically ranges from 0 to 1.

1. Repeat for All Genes:

• Apply the linear combination to each gene in the chromosome to create the complete offspring chromosome.

1. Mutation (Optional):

• After crossover, you can apply mutation to the offspring with a certain probability. Mutation introduces small random changes to the genes.

1. Create Offspring Population:

• Repeat the above steps to create a new population of offspring individuals.

Remember that the choice of (\alpha) affects how much influence each parent has on the offspring. Experimenting with different values of (\alpha) can lead to interesting results. Good luck with your genetic algorithm optimization! 🧬🔍🌱

Source: https://sl.bing.net/fCnwWsV5TIO