scholarly journals Optimal Lévy-flight foraging in a finite landscape

2015 ◽  
Vol 12 (104) ◽  
pp. 20141158 ◽  
Author(s):  
Kun Zhao ◽  
Raja Jurdak ◽  
Jiajun Liu ◽  
David Westcott ◽  
Branislav Kusy ◽  
...  
Keyword(s):  
Power Law ◽  
Animal Movement ◽  
Foraging Strategy ◽  
Foraging Strategies ◽  
Foraging Efficiency ◽  
Lévy Flight ◽  
Step Size ◽  
Levy Flight ◽  
Ballistic Motion ◽  
Wide Range

We present a simple model to study Lévy-flight foraging with a power-law step-size distribution in a finite landscape with countable targets. We find that different optimal foraging strategies characterized by a wide range of power-law exponent μ opt , from ballistic motion ( μ opt → 1) to Lévy flight (1 < μ opt < 3) to Brownian motion ( μ opt ≥ 3), may arise in adaptation to the interplay between the termination of foraging, which is regulated by the number of foraging steps, and the environmental context of the landscape, namely the landscape size and number of targets. We further demonstrate that stochastic returning can be another significant factor that affects the foraging efficiency and optimality of foraging strategy. Our study provides a new perspective on Lévy-flight foraging, opens new avenues for investigating the interaction between foraging dynamics and the environment and offers a realistic framework for analysing animal movement patterns from empirical data.

scholarly journals Apparent power-law distributions in animal movements can arise from intraspecific interactions

2015 ◽  
Vol 12 (103) ◽  
pp. 20140927 ◽  
Author(s):  
Greg A. Breed ◽  
Paul M. Severns ◽  
Andrew M. Edwards
Keyword(s):  
Power Law ◽  
Animal Movement ◽  
Step Length ◽  
Switching Process ◽  
Gps Tracking ◽  
Lévy Flight ◽  
Intraspecific Interactions ◽  
Levy Flight ◽  
State Switching ◽  
Best Fit

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species ( Euphydryas editha taylori ) was best fit by a bounded PL, evidence of a Lévy flight, while the other ( Euphydryas phaeton ) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori ). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.

scholarly journals A Swarm Robotic Exploration Strategy Based on an Improved Random Walk Method

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bao Pang ◽  
Yong Song ◽  
Chengjin Zhang ◽  
Hongling Wang ◽  
Runtao Yang
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Swarm Robotics ◽  
Search Strategy ◽  
Lévy Flight ◽  
Step Size ◽  
Levy Flight ◽  
Random Walk Method ◽  
Robotic Exploration ◽  
Exploration Mission

An environment can be searched far more efficiently if the appropriate search strategy is used. Because of the limited individual abilities of swarm robots, namely, local sensing and low processing power, random searching is the main search strategy used in swarm robotics. The random walk methods that are used most commonly are Brownian motion and Lévy flight, both of which mimic the self-organized behavior of social insects. However, both methods are somewhat limited when applied to swarm robotics, where having the robots search repeatedly can result in highly inefficient searching. Therefore, by analyzing the characteristics of swarm robotic exploration, this paper proposes an improved random walk method in which each robot adjusts its step size adaptively to reduce the number of repeated searches by estimating the density of robots in the environment. Simulation experiments and experiments with actual robots are conducted to study the effectiveness of the proposed method and evaluate its performance in an exploration mission. The experimental results presented in this paper show that an area is covered more efficiently using the proposed method than it is using either Brownian motion or Lévy flight.

scholarly journals A random walk description of individual animal movement accounting for periods of rest

2016 ◽  
Vol 3 (11) ◽  
pp. 160566 ◽  
Author(s):  
Paulo F. C. Tilles ◽  
Sergei V. Petrovskii ◽  
Paulo L. Natti
Keyword(s):  
Brownian Motion ◽  
Animal Movement ◽  
Cauchy Distribution ◽  
Gaussian Kernel ◽  
Lévy Flight ◽  
Levy Flight ◽  
Theoretical Approaches ◽  
Actual Movement ◽  
Baseline Probability ◽  
Probability Density Function Pdf

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.

scholarly journals Levy Flight and Chaos Theory Based Gravitational Search Algorithm for Global Optimization

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Performance Metrics ◽  
Chaotic Maps ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Lévy Flight ◽  
Step Size ◽  
Levy Flight ◽  
Statistical Measures ◽  
Engineering Design Problems ◽  
Gravitational Search

The Gravitational Search Algorithm (GSA) is one of the highly regarded population-based algorithms. It has been reported that GSA has a powerful global exploration capability but suffers from the limitations of getting stuck in local optima and slow convergence speed. In order to resolve the aforementioned issues, a modified version of GSA has been proposed based on levy flight distribution and chaotic maps (LCGSA). In LCGSA, the diversification is performed by utilizing the high step size value of levy flight distribution while exploitation is carried out by chaotic maps. The LCGSA is tested on well-known 23 classical benchmark functions. Moreover, it is also applied to three constrained engineering design problems. Furthermore, the analysis of results is performed through various performance metrics like statistical measures, convergence rate, and so on. Also, a signed Wilcoxon rank-sum test has also been conducted. The simulation results indicate that LCGSA provides better results as compared to standard GSA and most of the competing algorithms.

scholarly journals Modification of Fish Swarm Algorithm Based on Lévy Flight and Firefly Behavior

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Zhenrui Peng ◽  
Kangli Dong ◽  
Hong Yin ◽  
Yu Bai
Keyword(s):  
Dynamic Parameter ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Value Functions ◽  
Lévy Flight ◽  
Step Size ◽  
Levy Flight ◽  
Artificial Fish Swarm Algorithm ◽  
Searching Strategy ◽  
Swarm Algorithm

Artificial fish swarm algorithm easily converges to local optimum, especially in solving the global optimization problem of multidimensional and multiextreme value functions. To overcome this drawback, a novel fish swarm algorithm (LFFSA) based on Lévy flight and firefly behavior is proposed. LFFSA incorporates the moving strategy of firefly algorithm into two behavior patterns of fish swarm, i.e., chasing behavior and preying behavior. Furthermore, Lévy flight is introduced into the searching strategy. To limit the search band, nonlinear view and step size based on dynamic parameter are considered. Finally, the proposed algorithm LFFSA is validated with several benchmark problems. Numerical results demonstrate that LFFSA has a better performance in convergence speed and optimization accuracy than the other test algorithms.

scholarly journals Influence of hunting strategy on foraging efficiency in Galapagos sea lions

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11206
Author(s):  
Jessica-Anne Blakeway ◽  
John P.Y. Arnould ◽  
Andrew J. Hoskins ◽  
Patricia Martin-Cabrera ◽  
Grace J. Sutton ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Energy Expenditure ◽  
Foraging Strategy ◽  
Foraging Strategies ◽  
Foraging Efficiency ◽  
Flat Bottom ◽  
Sea Lions ◽  
Dive Behaviour ◽  
Zalophus Wollebaeki ◽  
Depth Ranges

The endangered Galapagos sea lion (GSL, Zalophus wollebaeki) exhibits a range of foraging strategies utilising various dive types including benthic, epipelagic and mesopelagic dives. In the present study, potential prey captures (PPC), prey energy consumption and energy expenditure in lactating adult female GSLs (n = 9) were examined to determine their foraging efficiency relative to the foraging strategy used. Individuals displayed four dive types: (a) epipelagic (<100 m; EP); or (b) mesopelagic (>100 m; MP) with a characteristic V-shape or U-shape diving profile; and (c) shallow benthic (<100 m; SB) or (d) deep benthic (>100 m; DB) with square or flat-bottom dive profiles. These dive types varied in the number of PPC, assumed prey types, and the energy expended. Prey items and their energetic value were assumed from previous GSL diet studies in combination with common habitat and depth ranges of the prey. In comparison to pelagic dives occurring at similar depths, when diving benthically, GSLs had both higher prey energy consumption and foraging energy expenditure whereas PPC rate was lower. Foraging efficiency varied across dive types, with benthic dives being more profitable than pelagic dives. Three foraging trip strategies were identified and varied relative to prey energy consumed, energy expended, and dive behaviour. Foraging efficiency did not significantly vary among the foraging trip strategies suggesting that, while individuals may diverge into different foraging habitats, they are optimal within them. These findings indicate that these three strategies will have different sensitivities to habitat-specific fluctuations due to environmental change.

scholarly journals Chaos and Lévy flights in the three-body problem

2020 ◽  
Vol 497 (3) ◽  
pp. 3694-3712
Author(s):  
Viraj Manwadkar ◽  
Alessandro A Trani ◽  
Nathan W C Leigh
Keyword(s):  
Power Law ◽  
Body Problem ◽  
Lifetime Distribution ◽  
Lévy Flight ◽  
Three Body Problem ◽  
Power Law Distribution ◽  
Lévy Flights ◽  
Levy Flight ◽  
Levy Flights ◽  
Three Body

ABSTRACT We study chaos and Lévy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $\mathcal {S}$ and the Lévy flight (LF) index $\mathcal {L}$, that are derived from the Agekyan–Anosova maps and homology radius $R_{\mathcal {H}}$. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Lévy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distributions from the different kinds of interactions. We observe that ergodic interactions follow an exponential decay distribution similar to that of radioactive decay. Meanwhile, Lévy flight interactions follow a power-law distribution. Lévy flights in fact dominate the tail of the general three-body lifetime distribution, providing conclusive evidence for the speculated connection between power-law tails and Lévy flight interactions. We propose a new physically motivated model for the lifetime distribution of three-body systems and discuss how it can be used to extract information about the underlying ergodic and Lévy flight interactions. We discuss ejection probabilities in three-body systems in the ergodic limit and compare it to previous ergodic formalisms. We introduce a novel mechanism for a three-body relaxation process and discuss its relevance in general three-body systems.

Performance Enhancement of Differential Evolution by Incorporating Lévy Flight and Chaotic Sequence for the Cases of Satellite Images

2015 ◽  
Vol 6 (3) ◽  
pp. 69-81 ◽  
Author(s):  
Krishna Gopal Dhal ◽  
Md. Iqbal Quraishi ◽  
Sanjoy Das
Keyword(s):  
Differential Evolution ◽  
Satellite Image ◽  
Chaotic Sequence ◽  
Population Diversity ◽  
Lévy Flight ◽  
Step Size ◽  
Levy Flight ◽  
De Algorithm ◽  
Image Contrast Enhancement ◽  
Modified Algorithm

Differential Evolution (DE) is a simple but powerful evolutionary algorithm. Crossover Rate (CR) and Mutation Factor (F) are the most important control parameters in DE. Mutation factor controls the diversification. In traditional DE algorithm CR and F are kept constant. In this paper, the values of CR and F are modified to enhance the capability of traditional DE algorithm. In the first modified algorithm chaotic sequence is used to perform this modification. In the next modified algorithm Lévy Flight with chaotic step size is used for such enhancement. In the second modified DE, population diversity has been used to build population in every generation. As a result the algorithm does not converge prematurely. Both modified algorithms have been applied to optimize parameters of the parameterized contrast stretching function. The algorithms are tested for satellite image contrast enhancement and the results are compared, which show that DE via chaotic Lévy and population diversity information outperforms the traditional and chaotic DE in the image enhancement domain.

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