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  Constructing Low Star Discrepancy Point Sets with Genetic Algorithms

Doerr, C., & De Rainville, F.-M. (2013). Constructing Low Star Discrepancy Point Sets with Genetic Algorithms. In C. Blum, & E. Alba (Eds.), GECCO'13 (pp. 789-796). New York, NY: ACM.

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 Creators:
Doerr, Carola1, Author           
De Rainville, François-Michel2, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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 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 λ 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 (μ \stackrel+}{, λ) 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~λ, 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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Language(s): eng - English
 Dates: 2013
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: DoerrDR2013
DOI: 10.1145/2463372.2463469
Other: Local-ID: 33AADAC322A2C7E6C1257C600052979B-DoerrDR2013
 Degree: -

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Title: 15th Annual Conference on Genetic and Evolutionary Computation
Place of Event: Amsterdam, The Netherlands
Start-/End Date: 2013-07-06 - 2013-07-10

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Title: GECCO'13
  Abbreviation : GECCO 2013
  Subtitle : Proceedings of the 2013 Genetic and Evolutionary Computation Conference
Source Genre: Proceedings
 Creator(s):
Blum, Christian1, Editor
Alba, Enrique1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: New York, NY : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 789 - 796 Identifier: ISBN: 978-1-4503-1963-8