Beyond Brownian Motion: A levy flight in magic boots

Resonance ◽  
2004 ◽  
Vol 9 (1) ◽  
pp. 50-60 ◽  
Author(s):  
Nalini Chakravarti
Keyword(s):  
Brownian Motion ◽  
Lévy Flight ◽  
Levy 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 Cyclical game coupling with Levy flight and Brownian motion and stable coexistence conditions of species

2014 ◽  
Vol 63 (16) ◽  
pp. 168701
Author(s):  
Wang Dong ◽  
Tang Chang-Qing ◽  
Tian Bao-Guo ◽  
Qu Liang-Sheng ◽  
Zhang Jin-Chun ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Lévy Flight ◽  
Levy Flight ◽  
Stable Coexistence ◽  
And Brownian Motion

scholarly journals LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION

2008 ◽  
Vol 18 (09) ◽  
pp. 2649-2672 ◽  
Author(s):  
A. A. DUBKOV ◽  
B. SPAGNOLO ◽  
V. V. UCHAIKIN
Keyword(s):  
Brownian Motion ◽  
Characteristic Function ◽  
Lévy Process ◽  
Levy Process ◽  
Lévy Flight ◽  
Lévy Flights ◽  
Levy Flight ◽  
Barrier Crossing ◽  
Lévy Motion ◽  
Levy Flights

After a short excursion from the discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the Lévy flight superdiffusion as a self-similar Lévy process. The condition of self-similarity converts the infinitely divisible characteristic function of the Lévy process into a stable characteristic function of the Lévy motion. The Lévy motion generalizes the Brownian motion on the base of the α-stable distributions theory and fractional order derivatives. Further development on this idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. This leads to the Kolmogorov's equation for arbitrary Markovian processes. As a particular case we obtain the fractional Fokker–Planck equation for Lévy flights. Some results concerning stationary probability distributions of Lévy motion in symmetric smooth monostable potentials, and a general expression to calculate the nonlinear relaxation time in barrier crossing problems are derived. Finally, we discuss the results on the same characteristics and barrier crossing problems with Lévy flights, recently obtained by different approaches.

Robot Swarm for Efficient Area Coverage Inspired by Ant Foraging: The Case of Adaptive Switching Between Brownian Motion and Lévy Flight

2017 ◽  
Author(s):  
Aditya Deshpande ◽  
Manish Kumar ◽  
Subramanian Ramakrishnan
Keyword(s):  
Brownian Motion ◽  
Performance Metrics ◽  
Research Area ◽  
Area Coverage ◽  
Lévy Flight ◽  
Levy Flight ◽  
Ant Foraging ◽  
Robot Swarm ◽  
Potential Applications ◽  
Active Research

Design of robot swarms inspired by self-organization in social insect groups is currently an active research area with a diverse portfolio of potential applications. In this work, the authors propose a control law for efficient area coverage by a robot swarm in a 2D spatial domain, inspired by the unique dynamical characteristics of ant foraging. The novel idea pursued in the effort is that dynamic, adaptive switching between Brownian motion and Lévy flight in the stochastic component of the search increases the efficiency of the search. Influence of different pheromone (the virtual chemotactic agent that drives the foraging) threshold values for switching between Lévy flights and Brownian motion is studied using two performance metrics — area coverage and visit entropy. The results highlight the advantages of the switching strategy for the control framework, particularly in cases when the object of the search is scarce in quantity or getting depleted in real-time.

Feature Selection for Histopathological Image Classification using levy Flight Salp Swarm Optimizer

2019 ◽  
Vol 12 (4) ◽  
pp. 329-337 ◽  
Author(s):  
Venubabu Rachapudi ◽  
Golagani Lavanya Devi
Keyword(s):  
Feature Selection ◽  
Image Classification ◽  
Feature Selection Method ◽  
Selection Method ◽  
Lévy Flight ◽  
Levy Flight ◽  
Local Optima ◽  
Histopathological Image ◽  
Surf Features ◽  
Histopathological Image Classification

Background: An efficient feature selection method for Histopathological image classification plays an important role to eliminate irrelevant and redundant features. Therefore, this paper proposes a new levy flight salp swarm optimizer based feature selection method. Methods: The proposed levy flight salp swarm optimizer based feature selection method uses the levy flight steps for each follower salp to deviate them from local optima. The best solution returns the relevant and non-redundant features, which are fed to different classifiers for efficient and robust image classification. Results: The efficiency of the proposed levy flight salp swarm optimizer has been verified on 20 benchmark functions. The anticipated scheme beats the other considered meta-heuristic approaches. Furthermore, the anticipated feature selection method has shown better reduction in SURF features than other considered methods and performed well for histopathological image classification. Conclusion: This paper proposes an efficient levy flight salp Swarm Optimizer by modifying the step size of follower salp. The proposed modification reduces the chances of sticking into local optima. Furthermore, levy flight salp Swarm Optimizer has been utilized in the selection of optimum features from SURF features for the histopathological image classification. The simulation results validate that proposed method provides optimal values and high classification performance in comparison to other methods.

Salp swarm algorithm with crossover scheme and Lévy flight for global optimization

2021 ◽  
pp. 1-12
Author(s):  
Heming Jia ◽  
Chunbo Lang
Keyword(s):  
Global Optimization ◽  
Heuristic Algorithm ◽  
Experimental Results ◽  
High Dimensional ◽  
Lévy Flight ◽  
Test Functions ◽  
Levy Flight ◽  
Salp Swarm Algorithm ◽  
Swarm Algorithm ◽  
Accuracy And Stability

Salp swarm algorithm (SSA) is a meta-heuristic algorithm proposed in recent years, which shows certain advantages in solving some optimization tasks. However, with the increasing difficulty of solving the problem (e.g. multi-modal, high-dimensional), the convergence accuracy and stability of SSA algorithm decrease. In order to overcome the drawbacks, salp swarm algorithm with crossover scheme and Lévy flight (SSACL) is proposed. The crossover scheme and Lévy flight strategy are used to improve the movement patterns of salp leader and followers, respectively. Experiments have been conducted on various test functions, including unimodal, multimodal, and composite functions. The experimental results indicate that the proposed SSACL algorithm outperforms other advanced algorithms in terms of precision, stability, and efficiency. Furthermore, the Wilcoxon’s rank sum test illustrates the advantages of proposed method in a statistical and meaningful way.

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