Gain insights into building genetic algorithm frameworks in Elixir. Learn about statistics, genealogy tracking, and solving practical problems with customizable genetic algorithm frameworks.

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Elixir-genetic

Elixir-genetic-v1

Elixir-genetic-v2

Elixir-breaker

Mix-command

Elixir-encode

Elixir-evaluate

Elixir-encode-speller

Elixir-evaluate-complete

Elixir-evaluate-v2

Elixir-evaluate-v3

Elixir-evaluate-portfolio

Elixir-selection

Elixir-generate

Elixir-generate-orderone

Elixir-selection-random

Elixir-selection-tournament

Elixir-selection-roulette

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Elixir-prematureconverge

Elixir-prematureconverge-complete

Elixir-prematureconverge-complete-nqueens

Elixir-replacing

Elixir-tiger

Elixir-tiger_nogene

Elixir-tiger_gene

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Elixir-testing

Elixir-testing-credo

Elixir-testing-dialyzer

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Elixir-tetris-copy

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This course has been designed to introduce you to a field of programming you might have never been exposed to. In this course, you’ll learn everything you need to know to start working with genetic algorithms. As you work through the course, you’ll build a framework for problems using genetic algorithms. By the end, you’ll have a full-featured, customizable framework complete with statistics, genealogy tracking, and more, and you’ll have learned everything you need to solve practical problems with genetic algorithms.

Genetic Algorithms in Elixir

# What is crossover?

With the N-queens problem, we saw how much choosing the correct crossover strategy can affect our algorithms. Now, we need to develop an understanding of what crossover is and how it works.

Crossover is the process of combining the genes of two chromosomes to create new chromosomes. The idea is that solutions will combine to create even better solutions, like how evolution slowly optimizes organisms to adapt and become stronger in their environment.

While the parallels between biological reproduction and crossover are neither perfect nor sound, we can better understand crossover if we have a general understanding of biology. In biology, traits are passed down to children from parents. These traits, for example, include hair color, eye color, and muscle composition. If both parents possess the same traits, the child is more likely to inherit those traits from their parents.

Now, imagine two sets of parents. One set of parents consists of two world-class distance runners. The other set of parents consists of two world-class weightlifters. Which set of parents is more likely to produce a better distance runner? The set of distance runners, because they possess and are more likely to pass on traits that contribute to success in distance running.

The same idea applies to crossover in genetic algorithms. Our goal is to take the strongest traits present in two solutions and pass them on to child solutions. Over time, our strategy will produce a fitter population.

The crossover strategy we use can have a big impact on the performance of our algorithm. Strategies are very problem-dependent. Some strategies are designed with certain genotypes in mind. Other strategies are built for speed or simplicity. In the next section, we’ll see how crossover can impact the performance of a genetic algorithm.

# Implementing other common crossover strategies

The goal of crossover is to produce child solutions that are better than their parents. A good crossover strategy will produce, on average, better child solutions in the long run. Additionally, a good crossover strategy will respect the genotype of our chromosome. For example, if we’re using a permutation genotype, a good crossover strategy will maintain the integrity of the permutation. We don’t want to use a crossover strategy that will produce invalid solutions because, eventually, all of our solutions will become invalid, and our algorithm will never produce the best solution.

In this and the next couple of lessons, we’ll learn about several common crossover strategies that work on all of the genotypes we’ve learned about so far. With these crossover strategies in place, we’ll be able to effectively solve problems that use binary, permutation, and real-value genotypes. The crossover strategies we’ll implement are:


* Single-point crossover

* Uniform crossover
* Whole arithmetic recombination

Additionally, we a variety of more advanced crossover strategies will be introduced that can be researched and implemented individually.

# Single-point crossover

**Single-point crossover** is the most basic crossover strategy and the one we’ve been using since the lesson [The Evaluation, Selection, and Crossover Steps](https://www.educative.io/courses/genetic-algorithms-elixir/the-evaluation-selection-and-crossover-steps). John Holland proposed it as the crossover strategy in the original genetic algorithm. 

Single-point crossover is most commonly used in solving basic problems because it’s the easiest to implement. The basic algorithm for single-point crossover is:

1. Choose a random number `k` between `0` and `n-1` where `n` is the length of the parent chromosomes.

2. Split both parents at `k` to produce four slices of genes.
3. Swap the tails of each parent at `k` to produce two new children.

The following picture illustrates a single-point crossover:

Learn about crossover and how to implement single-point crossover strategy.

Exploring Crossover

Introduction

Writing Your First Genetic Algorithm

Breaking Down Genetic Algorithms

Encoding Problems and Solutions

Evaluating Solutions and Populations

Selecting the Best

Generating New Solutions

Preventing Premature Convergence

Replacing and Transitioning

Tracking Genetic Algorithms

Visualizing the Results

Optimizing Your Algorithms

Writing Tests and Code Quality

Moving Forward

Exploring Crossover

What is crossover?