Single-Funnel and Multi-funnel Landscapes and Subthreshold-Seeking Behavior

  • Darrell WhitleyEmail author
  • Jonathan Rowe
Part of the Natural Computing Series book series (NCS)


Algorithms for parameter optimization display subthreshold-seeking behavior when the majority of the points that the algorithm samples have an evaluation less than some target threshold. Subthreshold-seeking algorithms avoid the curse of the general and Sharpened No Free Lunch theorems in the sense that they are better than random enumeration on a specific (but general) family of functions. In order for subthreshold-seeking search to be possible, most of the solutions that are below threshold must be localized in one or more regions of the search space. Functions with search landscapes that can be characterized as single-funnel or multi-funnel landscapes have this localized property. We first analyze a simple “Subthreshold-Seeker” algorithm. Further theoretical analysis details conditions that would allow a Hamming neighborhood local search algorithm using a Gray or binary representation to display subthreshold-seeking behavior. A very simple modification to local search is proposed that improves its subthreshold-seeking behavior.


Single Funnel Free Lunch Result Local Search Algorithm Hamming Neighborhood Search Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-07-1-0403. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. We would also like to thank Dagstuhl for giving us the chance to meet and exchange ideas.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceColorado State UniversityFort CollinsUSA
  2. 2.Department of Computer ScienceUniversity of BirminghamBirminghamUK

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