Levy Flight Algorithm for Optimization Problems - A Literature Review

This paper presents a literature review on applications of Levy flight. Nowadays, Levy flight laws has been used for a broad class of processes such as in physical, chemical, biological, statistical and also in financial. From the review, Levy flight technique has been applied mostly in physics area where the researchers use Levy flight technique to solve and optimize the problem regarding diffusive, scaling and transmission. This paper also reviews the latest researches using modified Levy flight technique such as truncated, smoothly truncated and gradually truncated Levy Flight for optimization. Finally, future trends of Levy flight are discussed.

[1]  Sanat Mohanty,et al.  A levy flight—random walk model for bioturbation , 2002, Environmental toxicology and chemistry.

[2]  Sergio Da Silva,et al.  Exponentially damped Lévy flights, multiscaling, and exchange rates , 2004 .

[3]  A. Davies,et al.  Evolution of fractal patterns during a classical-quantum transition. , 2001, Physical review letters.

[4]  Ikuo Matsuba,et al.  Generalized entropy approach to stable Lèvy distributions with financial application , 2003 .

[5]  Pushpa N. Rathie,et al.  Lévy flight approximations for scaled transformations of random walks , 2007, Comput. Stat. Data Anal..

[6]  D. R. Kulkarni,et al.  Evidence of Lévy stable process in tokamak edge turbulence , 2001 .

[7]  Yi-Sui Sun,et al.  Lévy flights in comet motion and related chaotic systems , 2001 .

[8]  N. F. Shul'ga,et al.  Anomalous diffusion and Lévy flights in channeling , 2004 .

[9]  Siegfried Stapf,et al.  Translational mobility in surface induced liquid layers investigated by NMR diffusometry , 1997 .

[10]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[11]  P. Barthelemy,et al.  A Lévy flight for light , 2008, Nature.

[12]  Emmanuel Hanert,et al.  Front dynamics in a two-species competition model driven by Lévy flights. , 2012, Journal of theoretical biology.

[13]  C. Houdr'e,et al.  Small-time expansions of the distributions, densities, and option prices of stochastic volatility models with Lévy jumps , 2010, 1009.4211.

[14]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[15]  H. M. Gupta,et al.  The gradually truncated Lévy flight: Stochastic process for complex systems , 2000 .

[16]  Ilya Pavlyukevich Lévy flights, non-local search and simulated annealing , 2007, J. Comput. Phys..

[17]  Geisel,et al.  Accelerated diffusion in Josephson junctions and related chaotic systems. , 1985, Physical review letters.

[18]  Stanley,et al.  Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. , 1994, Physical review letters.

[19]  Rosario N. Mantegna,et al.  Econophysics: Scaling and its breakdown in finance , 1997 .

[20]  V. Gonchar,et al.  Fluctuation-driven directed transport in the presence of Lévy flights , 2007, 0710.0883.

[21]  G. Viswanathan,et al.  Lévy flights and superdiffusion in the context of biological encounters and random searches , 2008 .

[22]  H. M. Gupta,et al.  The gradually truncated Levy flight for systems with power-law distributions , 1999 .

[23]  George M. Zaslavsky,et al.  Quantum manifestation of Lévy-type flights in a chaotic system , 2000, nlin/0012028.

[24]  B. Dubrulle,et al.  Truncated Lévy laws and 2D turbulence , 1998 .