Genetic Algorithms: From Line Fitting to the Travelling Salesman

Imagine you're planning a road trip through 25 cities. The number of possible routes is 25!/2 — roughly 7.8 × 10²⁴, more than the number of stars in the observable universe. You can't try them all. And unlike fitting a line with gradient descent, there's no gradient to follow — the search space is discrete and rugged. Nature solved this class of problem billions of years ago. Evolution doesn't need gradients. It works through variation and selection: generate diverse candidates, keep the ones that work, combine their traits, add random mutations, and repeat. Genetic algorithms (GAs) formalise this process into a general-purpose optimiser. By the end of this post, you'll implement GAs from scratch for two problems: fitting a regression line (where we can verify the answer) and the Travelling Salesman Problem (where we can't). You'll understand the core operators — selection, crossover, and mutation — and see how a single evolutionary loop solves fundamentally different problems. This tu