MPI-INF D1 Publications: Proceedings Article: Constructing Low Star Discrepancy Point Sets with Genetic Algorithms

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Author(s):

Doerr, Carola
De Rainville, François-Michel

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Not MPG Author(s):

De Rainville, François-Michel

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BibTeX cite key*:

DoerrDR2013

Title, Booktitle

Title*:	Constructing Low Star Discrepancy Point Sets with Genetic Algorithms
Booktitle*:	Proc. of Genetic and Evolutionary Computation Conference (GECCO 2013)

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Event Address*:	Amsterdam, Netherlands	Language:	English
Event Date* (no longer used):		Organization:
Event Start Date:	14 January 2014	Event End Date:	14 January 2014

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Name*:	ACM	URL:
Address*:	New York, USA	Type:

Vol, No, Year, pp.

Series:

Volume:		Number:
Month:		Pages:	789-796
Year*:	2013	VG Wort Pages:
ISBN/ISSN:		Sequence Number:
DOI:


(LaTeX) Abstract:	The recently active research area of black-box complexity revealed that for many optimization problems the best possible black-box optimization algorithm is significantly faster than all known evolutionary approaches. While it is not to be expected that a general-purpose heuristic competes with a problem-tailored algorithm, it still makes sense to look for the reasons for this discrepancy. In this work, we exhibit one possible reason---most optimal black-box algorithms profit also from solutions that are inferior to the previous-best one, whereas evolutionary approaches guided by the ``survival of the fittest'' paradigm often ignore such solutions. Trying to overcome this shortcoming, we design a simple genetic algorithm that first creates $\lambda$ offspring from a single parent by mutation with a mutation probability that is $k$ times larger than the usual one. From the best of these offspring (which often is worse than the parent) and the parent itself, we generate further offspring via a uniform crossover operator that takes bits from the winner offspring with probability $1/k$ only. A rigorous runtime analysis proves that our new algorithm for suitable parameter choices on the \onemax test function class is asymptotically faster (in terms of the number of fitness evaluations) than what has been shown for $(\mu \stackrel{+}{,} \lambda)$ EAs. This is the first time that crossover is shown to give an advantage for the $\onemax$ class that is larger than a constant factor. Using a fitness-dependent choice of $k$ and~$\lambda$, the optimization time can be reduced further to linear in~$n$. Our experimental analysis on several test function classes shows advantages already for small problem sizes and broad parameter ranges. Also, a simple self-adaptive choice of these parameters gives surprisingly good results.


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Correlation

MPG Unit:	Max-Planck-Institut für Informatik

MPG Subunit:	Algorithms and Complexity Group
Audience:	experts only
Appearance:	MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@INPROCEEDINGS{DoerrDR2013,
AUTHOR = {Doerr, Carola and De Rainville, François-Michel},
TITLE = {Constructing Low Star Discrepancy Point Sets with Genetic Algorithms},
BOOKTITLE = {Proc. of Genetic and Evolutionary Computation Conference (GECCO 2013)},
PUBLISHER = {ACM},
YEAR = {2013},
PAGES = {789--796},
ADDRESS = {Amsterdam, Netherlands},
}

Entry last modified by Carola Winzen, 02/17/2014

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	Editor(s) [Library]	Created 01/14/2014 04:02:07 PM
Revision 0.	Editor Carola Winzen	Edit Date 01/14/2014 04:02:07 PM