Abstract
We study the asymptotic behavior of two mutation-selection genetic algorithms in random environments. First, the state space is a supercritical Galton-Watson tree conditioned upon non-extinction and the objective function is the distance from the root. In the second case, the state space is a regular tree and the objective function is a sample of a tree-indexed random walk. We prove that, after n steps, the algorithms find the maximum possible value of the objective function up to a finite random constant.
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