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I guess "local optimum" wasn't the right word. I got suck in a configuration in which my breed() method couldn't get closer to the goal, because it was just shuffling around characters that existed at the start. (I had started with 1001 randomly generated 13-byte sequences.)

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With GAs, you're frequently better allowing your breeding / mutation to make insane changes. Mimic reality: some changes flat-out kill the offspring immediately. Sure, you need letters... but allow breeding to slice the binary strings representing those letters. Otherwise you rely too heavily on mutation for changes, which is typically very slow.

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