Whole Arithmetic Recombination

What is whole arithmetic recombination?

Whole arithmetic recombination is a crossover strategy for real-value chromosomes that mathematically mixes each gene of the parents to produce children. Whole arithmetic recombination takes a percentage of each parent gene and adds them to produce new solutions. The percentage of each parent gene present in the child gene is determined by an alpha parameter.

Whole arithmetic recombination combines genes according to the formula:

${\Large z = x * \alpha + y * (1 - \alpha)}$

Where $x$ and $y$ are parent genes, and $z$ is a resulting child gene.

That formula is applied to each corresponding gene in the parent chromosomes.

One thing to note is that an alpha of 0.5 will produce identical child chromosomes.

The image given below demonstrates the idea behind whole arithmetic recombination: