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As I pointed out on the main page, evolution works. No-one can deny that, because we're here. If it works in real life, it should work on the computer too; and since genetic algorithms are just computer evolution, so should they. It's therefore easier to explain them to non-technical people than it is to explain fuzzy logic. I've therefore just linked to three introductions, at different levels of difficulty, which explain the main concepts associated with their computer implementation.
The first two are "How does a Genetic Algorithm work?" by Pico Technology for Finance, and "Evolutionary Algorithms: How Natural Selection Beats Human Design" by Derya Ozdemir, Interesting Engineering. The first is a straightforward description of a genetic algorithm's life cycle, in terms a programmer would understand. My code follows this pattern, so you may want to keep the article on hand in case the inspectors ask how it works. The second article, which you could also keep around, is more general. It explains some genetic-algorithm achievements, including designing communications antennae for NASA. It also explains why genetic algorithms, though capable of incredible invention, can be slow and hard to tune.
More technical is a set of tutorial slides, "Introduction To Genetic Algorithms, Cse634, Data Mining" by Anita Wasilewska. This goes into more detail. You don't need it for a basic understanding of what I'm doing, but you might find it interesting to think about the different variations on the idea that it discusses.