Related papers: L\'evy flights as an underlying mechanism for glob…
This paper studies a class of enhanced diffusion processes in which random walkers perform L\'evy flights and apply it for global optimization. L\'evy flights offer controlled balance between exploitation and exploration. We develop four…
Most global optimization problems are nonlinear and thus difficult to solve, and they become even more challenging when uncertainties are present in objective functions and constraints. This paper provides a new two-stage hybrid search…
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
Nature-inspired algorithms such as Particle Swarm Optimization and Firefly Algorithm are among the most powerful algorithms for optimization. In this paper, we intend to formulate a new metaheuristic algorithm by combining Levy flights with…
We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative heavy-tailed L\'evy noise. The scheme is designed to prevent…
L\'{e}vy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that L\'{e}vy flights can maximize the efficiency of resource searching in uncertain environments, and also…
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are…
Portfolio optimization is a financial task which requires the allocation of capital on a set of financial assets to achieve a better trade-off between return and risk. To solve this problem, recent studies applied multi-objective…
L\'evy flights represent the best strategy to randomly search for a target in an unknown environment, and have been widely observed in many animal species. Here, we inspect and discuss recent results concerning human behavior and cognition.…
Optimal random foraging strategy has gained increasing concentrations. It is shown that L\'evy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard L\'evy flight generally cannot be…
All swarm-intelligence-based optimization algorithms use some stochastic components to increase the diversity of solutions during the search process. Such randomization is often represented in terms of random walks. However, it is not yet…
In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter…
Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. We demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also…
This book chapter introduces to the problem to which extent search strategies of foraging biological organisms can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight…
An efficient search algorithm is very crucial in robotic area, especially for exploration missions, where the target availability is unknown and the condition of the environment is highly unpredictable. In a very large environment, it is…
We present a simple model to study L\'{e}vy-flight foraging in a finite landscape with countable targets. In our approach, foraging is a step-based exploratory random search process with a power-law step-size distribution $P(l) \propto…
The L\'evy flight foraging hypothesis asserts that biological organisms have evolved to employ (truncated) L\'evy flight searches due to such strategies being more efficient than those based on Brownian motion. However, we provide here a…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…