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Levy flights do not always optimize random blind search for sparse targets

  • It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.show moreshow less

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Metadaten
Author:Vladimir V. Palyulin, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
DOI:https://doi.org/10.1073/pnas.1320424111
ISSN:0027-8424 (print)
Pubmed Id:http://www.ncbi.nlm.nih.gov/pubmed?term=24516153
Parent Title (English):Proceedings of the National Academy of Sciences of the United States of America
Publisher:National Acad. of Sciences
Place of publication:Washington
Document Type:Article
Language:English
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
Tag:Levy foraging hypothesis; search optimization; stochastic processes
Volume:111
Issue:8
Pagenumber:6
First Page:2931
Last Page:2936
Funder:Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland (FiDiPro scheme)
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert