Drift Analysis and Evolutionary Algorithms Revisited

One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a function f : {0,1}(n) -> R. The algorithm starts with a random search point..{0,1} n, and in each round it flips each bit of. with probability c/n independently at random, where c > 0 is a fixed constant. The thus created offspring. xi' replaces xi if and only if f (xi') >= f (xi). The analysis of the runtime of this simple algorithm for monotone and for 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.