Drift Analysis and Evolutionary Algorithms Revisited

08/10/2016

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by   Johannes Lengler, et al.

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One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a boolean function f:{0,1}^n → R. The algorithm starts with a random search point ξ∈{0,1}^n, and in each round it flips each bit of ξ with probability c/n independently at random, where c>0 is a fixed constant. The thus created offspring ξ' replaces ξ if and only if f(ξ') > f(ξ). The analysis of the runtime of this simple algorithm on monotone and on linear functions turned out to be highly non-trivial. In this paper we review known results and provide new and self-contained proofs of partly stronger results.