Genetic algorithms and symbolic regression

A few months ago, I wrote a post about optimization using gradient descent, which involves searching for a model that best meets certain criteria by repeatedly making adjustments that improve things a little bit at a time. In many situations, this works quite well and will always or almost always finds the best solution. But in other cases, it's possible for this approach to fall into a locally optimal solution that isn't the overall best, but is better than any nearby solution. A common way to deal with this sort of situation is to add some randomness into the algorithm, making it possible to jump out of one of these locally optimal solutions into a slightly worse solution that is adjacent to a much better one. In this post, I want to explore one such approach, called a genetic algorithm (or an evolutionary algorithm), which I'll illustrate with a specific type of genetic algorithm called symbolic regression.