Drift Analysis and Evolutionary Algorithms Revisited
This work addresses runtime analysis for evolutionary algorithms, which is incremental as it builds on and refines existing theoretical results in optimization.
The paper revisits the runtime analysis of a simple evolutionary algorithm on monotone and linear boolean functions, providing new and self-contained proofs that yield partly stronger results.
One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a boolean function $f:\{0,1\}^n \to {\mathbb R}$. The algorithm starts with a random search point $ξ\in \{0,1\}^n$, 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 $f(ξ') \ge f(ξ)$. 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.