We analyze the performance of a genetic algorithm (GA) we call Culling, and a variety of other algorithms, on a problem we refer to as the Additive Search Problem (ASP). We show that the problem of learning the Ising perceptron is reducible to a noisy version of ASP. Noisy ASP is the first problem we are aware of where a genetic-type algorithm bests all known competitors. We generalize ASP to k-ASP to study whether GAs will achieve “implicit parallelism” in a problem with many more schemata. GAs fail to achieve this implicit parallelism, but we describe an algorithm we call Explicitly Parallel Search that succeeds. We also compute the optimal culling point for selective breeding, which turns out to be independent of the fitness function or the population distribution. We also analyze a mean field theoretic algorithm performing similarly to Culling on many problems. These results provide insight into when and how GAs can beat competing methods.

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