Two-dimensional drift analysis: Optimizing two functions simultaneously can be hard
OPEN ACCESS
Author / Producer
Date
2023-09-06
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
Abstract
In this paper we show how to use drift analysis in the case of two random variables X1,X2, when the drift is approximatively given by A⋅(X1,X2)T for a matrix A. The non-trivial case is that X1 and X2 impede each other's progress, and we give a full characterization of this case. As an application, we develop and analyze a minimal example TWOLIN of a dynamic environment that can be hard. The environment consists of two linear functions f1 and f2 with positive weights, and in each generation selection is based on one of them at random. They only differ in the set of positions that have weight 1 and n. We show that the (1+1)-EA with mutation rate χ/n is efficient for small χ on TWOLIN, but does not find the shared optimum in polynomial time for large χ.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
971
Pages / Article No.
114072
Publisher
Elsevier
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Drift analysis; Runtime analysis; Theory of evolutionary algorithms; Dynamic environments
Organisational unit
08738 - Lengler, Johannes (Tit.-Prof.) / Lengler, Johannes (Tit.-Prof.)
03672 - Steger, Angelika / Steger, Angelika