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Optimal Random Search, Fractional Dynamics and Fractional Calculus

[+] Author Affiliations
Caibin Zeng

South China University of Technology, Guangzhou, China

YangQuan Chen

University of California, Merced, CA

Paper No. DETC2013-12734, pp. V004T08A022; 7 pages
doi:10.1115/DETC2013-12734
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME

abstract

What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Levy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In the paper we propose the Continuous Time Random Walk (C-TRW) optimal search framework and find the optimum for both of search length’s and waiting time’s distributions. Based on fractional calculus technique, we further derive its master equation to show the mechanism of such complex fractional dynamics. Numerous simulations are provided to illustrate the non-destructive and destructive cases.

Copyright © 2013 by ASME

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