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  Optimizing Monotone Functions Can Be Difficult

Doerr, B., Jansen, T., Sudholt, D., Winzen, C., & Zarges, C. (2010). Optimizing Monotone Functions Can Be Difficult. In R. Schaefer, C. Cotta, J. Kolodziej, & G. Rudolph (Eds.), Parallel Problem Solving from Nature, PPSN XI (pp. 42-51). Berlin: Springer. doi:10.1007/978-3-642-15844-5_5.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-16AC-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-2B4B-9
Genre: Conference Paper

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 Creators:
Doerr, Benjamin1, Author           
Jansen, Thomas2, Author
Sudholt, Dirk2, Author
Winzen, Carola1, Author           
Zarges, Christine2, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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 Abstract: Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions are easy to optimize. The choice of the constant $c$ in the mutation probability $p(n) = c/n$ can make a decisive difference. We show that if $c < 1$, then the \EA finds the optimum of every such function in $\Theta(n \log n)$ iterations. For $c=1$, we can still prove an upper bound of $O(n^{3/2})$. However, for $c > 33$, we present a strictly monotone function such that the \EA with overwhelming probability does not find the optimum within $2^{\Omega(n)}$ iterations. This is the first time that we observe that a constant factor change of the mutation probability changes the run-time by more than constant factors.

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Language(s): eng - English
 Dates: 20102010
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 536739
DOI: 10.1007/978-3-642-15844-5_5
URI: http://dx.doi.org/10.1007/978-3-642-15844-5_5
Other: Local-ID: C1256428004B93B8-FDE717515D9BDB45C12577AC00466269-DoerrJSWZ10
 Degree: -

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Title: 11th International Conference on Parallel Problem Solving from Nature
Place of Event: Krakow, Poland
Start-/End Date: 2010-09-11 - 2010-09-15

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Title: Parallel Problem Solving from Nature, PPSN XI
  Abbreviation : PPSN 2010
  Subtitle : 11th International Conference, Kraków, Poland, September 11-15, 2010, Proceedings, Part I
Source Genre: Proceedings
 Creator(s):
Schaefer, Robert1, Editor
Cotta, Carlos1, Editor
Kolodziej, Joanna1, Editor
Rudolph, Günter1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 42 - 51 Identifier: ISBN: 978-3-642-15843-8

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Title: Lecture Notes in Computer Science
  Abbreviation : LNCS
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 6238 Sequence Number: - Start / End Page: - Identifier: -