Crossover in Genetic Algorithms
— DNA Blending Explained

In biological reproduction, offspring inherit traits from both parents — a child might have their mother's eyes and their father's nose. Genetic Algorithms replicate this exact mechanism through crossover (recombination), the process of combining two parent DNA arrays to produce a new child individual.

Crossover is arguably the most important operator in a GA. Without it, a GA is little more than random search. With it, evolution can rapidly assemble beneficial building blocks from different parents into superior offspring.

1. Why Crossover Works: The Building Block Hypothesis

John Holland's Schema Theorem and the associated Building Block Hypothesis explain why crossover is so effective. Short, low-order, high-fitness gene sequences (called schemata or building blocks) tend to be preserved and combined across generations.

Imagine Parent A has excellent color genes and Parent B has excellent shape genes. Crossover can combine them, potentially producing a child that inherits both advantages simultaneously — something that random mutation alone would take exponentially longer to stumble upon.

2. Types of Crossover

Single-Point Crossover

The simplest form. A random cut point is chosen along the DNA string. The two parents exchange the tail segments after that cut point:

Simple and fast, but limited: genes on the same side of the cut always stay together.

Two-Point Crossover

Two cut points are chosen, and the middle segment is swapped. This allows more varied gene combinations than single-point crossover.

Uniform Crossover

For each gene position, flip a coin: inherit from Parent A or Parent B with equal probability. This produces the most diverse offspring and is used in gene46.

Real-Valued Crossover: BLX-α (Blend Crossover)

For real-numbered genes, simple segment swapping can be wasteful. BLX-α (Blend Crossover Alpha) instead samples child gene values from within — and slightly beyond — the range between the two parents' values:

The α parameter controls how far beyond the parents' range the child can explore. Higher α = more exploratory; lower α = more conservative blending.

3. Crossover Rate

Not every pair of parents undergoes crossover. The crossover rate (typically 0.6–0.9) determines the probability that two parents actually recombine versus simply copying themselves. A common configuration:

• Crossover rate: 0.8 (80% of pairs recombine)
• Mutation rate: 0.01–0.05 (1–5% chance per gene)

4. Crossover vs. Mutation: Complementary Roles

Crossover and mutation serve different evolutionary roles:

• Crossover explores new combinations of existing good genes — exploiting what evolution has already discovered.
• Mutation introduces genuinely new genetic material — exploring regions of the search space that no parent has visited.

A GA without crossover is slow to combine beneficial traits. A GA without mutation is vulnerable to premature convergence. Together, they balance exploitation and exploration.

5. What Crossover Looks Like in Practice (gene46)

When you right-swipe 8 individuals in gene46, those 8 become the parent pool. The system randomly pairs them and applies uniform crossover across all DNA parameters. The resulting children inherit a random mix of each parent's curve positions, color values, and shape parameters — creating visual offspring that genuinely resemble both parents while introducing novel combinations neither parent possessed.

This is why certain visual traits (a particular curve shape, a color family) can persist and strengthen across many generations: they are repeatedly selected and recombined into winning combinations.