Whole arithmetic crossover creates offspring in a real-valued genetic algorithm by taking a weighted average of every corresponding value in two parent chromosomes. A weight α between 0 and 1 controls each parent’s contribution. section 8.2.1
| Child1Genei = α × Parent1Genei + (1 – α) × Parent2Genei Child2Genei = α × Parent2Genei + (1 – α) × Parent1Genei |
Use the formulas to compute both children: each child applies the same weight while reversing the parents’ roles. section 8.2.1
Worked chromosome example
For Parent1 = [1, 2, 3, 4], Parent2 = [2, 2, 2, 2], and α = 0.2, Child1 becomes [1.8, 2, 2.2, 2.4]. Reversing the parent contributions gives Child2 = [1.2, 2, 2.8, 3.6]. The first child can then undergo Gaussian mutation; with an added value of 0.43, it becomes [2.23, 2.43, 2.63, 2.83]. section 8.2.2
Apply the method as follows:
- Choose two real-valued parent chromosomes and a weight α in [0, 1]. section 8.2.1
- Average every corresponding gene to produce two complementary offspring. section 8.2.1
- Evaluate the offspring and optionally apply mutation within the genetic algorithm. section 8.2.2
