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Drift Analysis and Evolutionary Algorithms Revisited

Published online by Cambridge University Press:  20 June 2018

J. LENGLER  and
A. STEGER
J. LENGLER
Affiliation:
Department of Computer Science, ETH Zürich, Zürich, Switzerland (e-mail: [email protected], [email protected])
A. STEGER
Affiliation:
Department of Computer Science, ETH Zürich, Zürich, Switzerland (e-mail: [email protected], [email protected])
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Abstract

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 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 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.

Keywords

Primary 68W2068W40Secondary 60G40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Special Issue 4: Special Issue: Oberwolfach Workshop , July 2018 , pp. 643 - 666
Copyright
Copyright © Cambridge University Press 2018 

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