Lévy flights, non-local search and simulated annealing

Pavlyukevich, Ilya

doi:10.1016/j.jcp.2007.06.008

Cited by 616 publications

(278 citation statements)

References 26 publications

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“…These observations may be of particular importance to swimming or airborne searchers, because streams occur most naturally there, or when the searcher itself prefers one direction, for instance owing to prior experience. Our findings may also be relevant for computational search algorithms in biased landscapes (42). Of course, more quantitative statements need a detailed investigation for a given, concrete system.…”

Section: Discussionmentioning

confidence: 78%

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

Palyulin

Chechkin

Metzler

2014

Proc. Natl. Acad. Sci. U.S.A.

190

213

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It is generally believed that random search processes based on scalefree, Lévy stable jump length distributions (Lévy 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 Lévy 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 Lévy 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 Lévy flights with a critical exponent α = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal α may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.search optimization | stochastic processes | Lévy foraging hypothesis H ow do you find the proverbial needle in the haystack or an enemy submarine in the vast expanse of the sea? Scientists have studied the dynamics and optimization of search processes for decades, their interests ranging from military tasks such as locating enemy vessels or mines in the ocean and search strategies of animals for food to diffusion control of molecular processes in biological cells (1-4). Without prior knowledge about the location of the target, a searcher randomly explores the search space. However, as already argued by Shlesinger and Klafter (5), instead of performing a Brownian walk a better search strategy for sparse targets is that of a Lévy flight (LF): The agent moves randomly with a power-law distribution λðxÞ ' jxj −1−α of relocation lengths. Owing to their scale-free, fractal character, LFs combine local exploration with decorrelating, long-range excursions. These effect a reduced oversampling compared with Brownian search (i.e., the forager is less likely to return to previously visited sites). In the field of movement ecology (6), such random jump-like search processes are often referred to as "blind search" using saltatory motion, which is typical for predators hunting at spatial scales that exceed their sensory range (7-10). Such blind search, inter alia, was observed for fully aquatic marine vertebrate predators including plankton-feeding basking sharks (Cetorhinus maximus) (11), jellyfish predators, leatherback turtles (Dermochelys coriacea) (12), and southern elephant seals (13). This is the kind of search motion we investigate here.How commonly are LFs actually observed in nature? Apart from the flight of the albatross (14, 15), power-law relocation...

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Section: Discussionmentioning

confidence: 78%

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

Palyulin

Chechkin

Metzler

2014

Proc. Natl. Acad. Sci. U.S.A.

190

213

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“…In addition, bees and birds may behave as Lévy flight behaviour [13], with jump or fly distance steps obey a Lévy distribution. Furthermore, flower constancy can be used an increment step using the similarity or difference of two flowers.…”

Section: Characteristics Of Flower Pollinationmentioning

confidence: 99%

“…The parameter L is the strength of the pollination, which essentially is a step size. Since insects may move over a long distance with various distance steps, we can use a Lévy flight to mimic this characteristic efficiently [13,15]. That is, we draw L > 0 from a Levy distribution Here Γ(λ) is the standard gamma function, and this distribution is valid for large steps s > 0.…”

Section: Flower Pollination Algorithmmentioning

confidence: 99%

Flower Pollination Algorithm for Global Optimization

Yang

2012

Lecture Notes in Computer Science

1,685

970

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Flower pollination is an intriguing process in the natural world. Its evolutionary characteristics can be used to design new optimization algorithms. In this paper, we propose a new algorithm, namely, flower pollination algorithm, inspired by the pollination process of flowers. We first use ten test functions to validate the new algorithm, and compare its performance with genetic algorithms and particle swarm optimization. Our simulation results show the flower algorithm is more efficient than both GA and PSO. We also use the flower algorithm to solve a nonlinear design benchmark, which shows the convergence rate is almost exponential.

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“…Thus, we draw L > 0 from levy distribution which is valid for large steps i.e. s > 0 [39] and it can be represented as:…”

Section: A Flower Pollination Algorithmmentioning

confidence: 99%

Nature Inspired Range Based Wireless Sensor Node Localization Algorithms

Kaur¹,

Arora²

2017

IJIMAI

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Localization is one of the most important factors highly desirable for the performance of Wireless Sensor Network (WSN). Localization can be stated as the estimation of the location of the sensor nodes in sensor network. In the applications of WSN, the data gathered at sink node will be meaningless without localization information of the nodes. Due to size and complexity factors of the localization problem, it can be formulated as an optimization problem and thus can be approached with optimization algorithms. In this paper, the nature inspired algorithms are used and analyzed for an optimal estimation of the location of sensor nodes. The performance of the nature inspired algorithms viz. Flower pollination algorithm (FPA), Firefly algorithm (FA), Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) for localization in WSN is analyzed in terms of localization accuracy, number of localized nodes and computing time. The comparative analysis has shown that FPA is more proficient in determining the coordinates of nodes by minimizing the localization error as compared to FA, PSO and GWO.

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Lévy flights, non-local search and simulated annealing

Cited by 616 publications

References 26 publications

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

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

Flower Pollination Algorithm for Global Optimization

Nature Inspired Range Based Wireless Sensor Node Localization Algorithms

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