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In this paper, we develop a new method to obtain the accessibility of stochastic partial differential equations driven by additive pure jump noise. An important novelty of this paper is to allow the driving noises to be degenerate. As an application, for the first time, we obtain the accessibility of a class of stochastic equations driven by pure jump (possibly degenerate) noise, including stochastic 2D Navier-Stokes equations, stochastic Burgers equations, stochastic singular p-Laplace equations, and stochastic fast diffusion equations. As a further application, we establish the ergodicity of stochastic singular p-Laplace equations and stochastic fast diffusion equations driven by additive pure jump noise, and we remark that the driving noises could be Compound Poisson processes or Lévy processes with heavy tails. [ABSTRACT FROM AUTHOR]

Due to the intermittent and unstable nature of PV systems, maximum power point tracking (MPPT) of PV systems is necessary in practice. At the same time, PV cells are also shaded by objects such as trees and houses in the environment causing local shadows, so the Lévy flight particle swarm optimisation (LFPSO) is proposed in this paper. The random walk process of Lévy flight is added to the particle swarm optimisation (PSO) to increase the diversity of the search, which can avoid falling into local optimal solutions. The experimental simulation results show that the algorithm proposed in this paper can still accurately track the global maximum power in the case of partial shading, which well avoids falling into the local maximum power. The performance is much higher than the traditional maximum power point tracking algorithm, which improves the efficiency of the PV system. [ABSTRACT FROM AUTHOR]

In this paper, we study one-dimensional hyperbolic Anderson models (HAM) driven by space-time pure-jump Lévy white noise in a finite-variance setting. Motivated by recent active research on limit theorems for stochastic partial differential equations driven by Gaussian noises, we present the first study in this Lévy setting. In particular, we first establish the spatial ergodicity of the solution and then a quantitative central limit theorem (CLT) for the spatial averages of the solution to HAM in both Wasserstein distance and Kolmogorov distance, with the same rate of convergence. To achieve the first goal (i.e. spatial ergodicity), we exploit some basic properties of the solution and apply a Poincaré inequality in the Poisson setting, which requires delicate moment estimates on the Malliavin derivatives of the solution. Such moment estimates are obtained in a soft manner by observing a natural connection between the Malliavin derivatives of HAM and a HAM with Dirac delta velocity. To achieve the second goal (i.e. CLT), we need two key ingredients: (i) a univariate second-order Poincaré inequality in the Poisson setting that goes back to Last, Peccati, and Schulte (Probab. Theory Related Fields, 2016) and has been recently improved by Trauthwein (arXiv:2212.03782); (ii) aforementioned moment estimates of Malliavin derivatives up to second order. We also establish a corresponding functional CLT by (a) showing the convergence in finite-dimensional distributions and (b) verifying Kolmogorov's tightness criterion. Part (a) is made possible by a linearization trick and the univariate second-order Poincaré inequality, while part (b) follows from a standard moment estimate with an application of Rosenthal's inequality. [ABSTRACT FROM AUTHOR]

In order to overcome the difficulty of parameter tuning caused by the large lag and time-varying nonlinearity of the tank for lysozyme fermentation, a temperature control method based on LRWOA-LSTM-PID is proposed in this paper. Firstly, according to the intrinsic mechanism of the fermenter, a temperature mechanism model based on a dynamic equation is designed, which can better reflect the temperature changes in the fermenter. Secondly, a Proportional Integral Derivative (PID) parameter tuning method based on a Long-Short Term Memory Network (LSTM) is proposed, which takes advantage of the ability of LSTM to learn time sequence information and obtains the variation trend between error sequences under continuous time sampling, thereby adjusting network weights more reasonably and accelerating PID parameter tuning. Finally, a Whale Optimization Algorithm (WOA) based on the Lévy flight and random walk strategy (LRWOA) is proposed for the initialization of LSTM parameters; this algorithm has excellent optimization capabilities and overcomes the problem of LSTM falling into local optimal solutions prematurely during parameter randomization. The results show that the method proposed in this paper can achieve rapid tuning of PID parameters, thereby improving the convergence speed of the system and reducing system overshoot. [ABSTRACT FROM AUTHOR]

Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm's diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm. [ABSTRACT FROM AUTHOR]

We aimed to improve the detection accuracy of laser methane sensors in expansive temperature application environments. In this paper, a large-scale dataset of the measured concentration of the sensor at different temperatures is established, and a temperature compensation model based on the ISSA-BP neural network is proposed. On the data side, a large-scale dataset of 15,810 sets of laser methane sensors with different temperatures and concentrations was established, and an Improved Isolation Forest algorithm was used to clean the large-scale data and remove the outliers in the dataset. On the modeling framework, a temperature compensation model based on the ISSA-BP neural network is proposed. The quasi-reflective learning, chameleon swarm algorithm, Lévy flight, and artificial rabbits optimization are utilized to improve the initialization of the sparrow population, explorer position, anti-predator position, and position of individual sparrows in each generation, respectively, to improve the global optimization seeking ability of the standard sparrow search algorithm. The ISSA-BP temperature compensation model far outperforms the four models, SVM, RF, BP, and PSO-BP, in model evaluation metrics such as MAE, MAPE, RMSE, and R-square for both the training and test sets. The results show that the algorithm in this paper can significantly improve the detection accuracy of the laser methane sensor under the wide temperature application environment. [ABSTRACT FROM AUTHOR]

Harris Hawks Optimization (HHO) is a novel meta-heuristic algorithm that imitates the predation characteristics of Harris Hawk and combines Lévy flight to solve complex multidimensional problems. Nevertheless, the basic HHO algorithm still has certain limitations, including the tendency to fall into the local optima and poor convergence accuracy. Coot Bird Optimization (CBO) is another new swarm-based optimization algorithm. CBO originates from the regular and irregular motion of a bird called Coot on the water’s surface. Although the framework of CBO is slightly complicated, it has outstanding exploration potential and excellent capability to avoid falling into local optimal solutions. This paper proposes a novel enhanced hybrid algorithm based on the basic HHO and CBO named Enhanced Harris Hawks Optimization Integrated with Coot Bird Optimization (EHHOCBO). EHHOCBO can provide higher-quality solutions for numerical optimization problems. It first embeds the leadership mechanism of CBO into the population initialization process of HHO. This way can take full advantage of the valuable solution information to provide a good foundation for the global search of the hybrid algorithm. Secondly, the Ensemble Mutation Strategy (EMS) is introduced to generate the mutant candidate positions for consideration, further improving the hybrid algorithm’s exploration trend and population diversity. To further reduce the likelihood of falling into the local optima and speed up the convergence, Refracted Opposition-Based Learning (ROBL) is adopted to update the current optimal solution in the swarm. Using 23 classical benchmark functions and the IEEE CEC2017 test suite, the performance of the proposed EHHOCBO is comprehensively evaluated and compared with eight other basic meta-heuristic algorithms and six improved variants. Experimental results show that EHHOCBO can achieve better solution accuracy, faster convergence speed, and a more robust ability to jump out of local optima than other advanced optimizers in most test cases. Finally, EHHOCBOis applied to address four engineering design problems.Our findings indicate that the proposed method also provides satisfactory performance regarding the convergence accuracy of the optimal global solution. [ABSTRACT FROM AUTHOR]

This paper introduces a novel metaheuristic algorithm named the opposition-based cooperation search algorithm with Nelder–Mead (OCSANM). This enhanced algorithm builds upon the cooperation search algorithm (CSA) by incorporating opposition-based learning (OBL) and the Nelder–Mead simplex search method. The primary application of this algorithm is the design of a fractional-order proportional–integral–derivative (FOPID) controller for a buck converter system. A comprehensive evaluation is conducted using statistical boxplot analysis, nonparametric statistical tests and convergence response comparisons to assess the algorithm's performance and confirm its superiority over CSA. Furthermore, the FOPID-controlled buck converter system based on OCSANM is compared with two top-performing algorithms: one using a hybridized approach of Lévy flight distribution with simulated annealing (LFDSA) and the other employing the improved hunger games search (IHGS) algorithm. This comparison encompasses transient and frequency responses, performance indices and robustness analysis. The results reveal the notable advantages of the proposed OCSANM-based system, including 25.8% and 8.7% faster rise times, 26% and 8.8% faster settling times compared with the best-performing approaches, namely LFDSA and IHGS, respectively. In addition, the OCSANM-based system exhibits a 34.7% and 9.6% wider bandwidth than the existing approaches-based systems. Incorporating voltage and current responses of the buck converter's switched circuit with the OCSANM-based FOPID controller further underscores the algorithm's effectiveness. To provide a comprehensive assessment, the paper also compares the proposed approach's time and frequency domain responses with those of 17 other state-of-the-art approaches attempting to control buck converter systems similarly. These findings affirm the effectiveness of the OCSANM in designing FOPID controllers for buck converter systems. [ABSTRACT FROM AUTHOR]

To address the anti-swing issue of the payload in bridge cranes, Proportional–Integral–Derivative (PID) control is a commonly used method. However, parameter tuning of the PID controller relies on empirical knowledge and often leads to system overshoot. This paper proposes an Improved Sparrow Search Algorithm (ISSA) to optimize the gains of PID controllers, alleviating adverse effects on payload oscillation and trolley positioning during the operation of overhead cranes. First, tent map chaos mapping is introduced to initialize the sparrow population, enhancing the algorithm's global search capability. Then, by integrating sine and cosine concepts along with nonlinear learning factors, the updating mechanism of discoverer positions is dynamically adjusted, expediting the solving process. Finally, the Lévy flight strategy is employed to update follower positions, thereby enhancing the algorithm's local escape capability. Additionally, a fitness function containing overshoot penalties is proposed to address overshoot issues. Simulation results indicate that the overshoot rates of all algorithms remain less than 3%. Moreover, compared with the Sparrow Search Algorithm (SSA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Whale optimization Algorithm (WOA), the optimized PID control system with the ISSA algorithm exhibits superior control performance and possesses certain robustness and adaptability. [ABSTRACT FROM AUTHOR]

Temperature and humidity as the key factors affecting the storage and ripening of fruits and vegetables directly determine the quality of fruits and vegetables. In this paper, a temperature and humidity model was constructed based on an integrated device of controlled atmosphere storage and ripening. Aiming at the shortcomings of the temperature and humidity model such as large inertia, nonlinearity, and model uncertainty, a fuzzy‐PID controller based on the improved Lévy flight particle swarm algorithm (LFPSO) is proposed. Initially, a mathematical model of temperature and humidity is developed through mechanism research and parameter estimation. Subsequently, a temperature and humidity fuzzy‐PID control strategy is proposed for regulating temperature and humidity. An improved LFPSO is then introduced to optimize the key parameters of the fuzzy‐PID controller, such as the quantization factor and the scale factor. The superiority of the improved LFPSO algorithm is verified by comparing the test functions. Finally, the improved LFPSO‐fuzzy‐PID controller, fuzzy‐PID controller, and Smith‐PID controller are applied to the simulation model for comparison using the MATLAB Simulink simulation platform. The results show that the improved LFPSO‐fuzzy‐PID control algorithm has a good control effect in the temperature and humidity simulation system of controlled atmosphere (CA) ripening container, which provides a reference for solving the optimization problem of actual engineering design. Practical applications: In order to reduce the postharvest cold chain losses of fruits and vegetables, this paper proposes a containerized style device that combines fruits and vegetables storage and ripening for simplifying the losses caused by transshipment at cold chain nodes. Since temperature and humidity play a key role in fruits and vegetables storage and ripening, which directly affect the product quality, this paper establishes a complete mathematical model of CA ripening temperature and humidity system by combining mechanism modeling and parameter identification. In order to keep the temperature and humidity within the ideal range, Smith‐PID controller, fuzzy‐PID controller, and fuzzy‐PID control method based on improved Lévy flight particle swarm optimization are proposed to regulate the air conditioner and humidifier. The performance of three different types of controllers was tested on the MATLAB. The simulation results demonstrate that the improved LFPSO‐fuzzy‐PID controller is superior and more effective than Smith‐PID and fuzzy‐PID controllers. [ABSTRACT FROM AUTHOR]

Introduction: Eye movement is one of the cues used in human--machine interface technologies for predicting the intention of users. The developing application in eye movement event detection is the creation of assistive technologies for paralyzed patients. However, developing an effective classifier is one of the main issues in eye movement event detection. Methods: In this paper, bidirectional long short-term memory (BILSTM) is proposed along with hyperparameter tuning for achieving effective eye movement event classification. The Lévy flight and interactive crossoverbased reptile search algorithm (LICRSA) is used for optimizing the hyperparameters of BILSTM. The issues related to overfitting are avoided by using fuzzy data augmentation (FDA), and a deep neural network, namely, VGG- 19, is used for extracting features from eye movements. Therefore, the optimization of hyperparameters using LICRSA enhances the classification of eye movement events using BILSTM. Results and Discussion: The proposed BILSTM--LICRSA is evaluated by using accuracy, precision, sensitivity, F1-score, area under the receiver operating characteristic (AUROC) curve measure, and area under the precision--recall curve (AUPRC) measure for four datasets, namely, Lund2013, collected dataset, GazeBaseR, and UTMultiView. The gazeNet, human manual classification (HMC), and multi-source information-embedded approach (MSIEA) are used for comparison with the BILSTM--LICRSA. The F1-score of BILSTM--LICRSA for the GazeBaseR dataset is 98.99%, which is higher than that of the MSIEA. [ABSTRACT FROM AUTHOR]

This paper studies a stochastic two-species Schoener's competitive model with Lévy jumps by the mean-reverting Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process is illustrated. After that, we show the existence and uniqueness of the global solution. Moment estimates for the global solution of the stochastic model are then given. Moreover, by constructing the Lyapunov function and applying Itô's formula and Chebyshev's inequality, it is found that the model is stochastic and ultimately bounded. In addition, we give sufficient conditions for the extinction of species. Finally, numerical simulations are employed to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid algorithm based on the slime mould algorithm (SMA) and the mixed dandelion optimizer. The hybrid algorithm improves the convergence speed and prevents the algorithm from falling into the local optimal. (1) The Bernoulli chaotic mapping is added in the initialization phase to enrich the population diversity. (2) The Brownian motion and Lévy flight strategy are added to further enhance the global search ability and local exploitation performance of the slime mould. (3) The specular reflection learning is added in the late iteration to improve the population search ability and avoid falling into local optimality. The experimental results show that the convergence speed and precision of the improved algorithm are improved in the standard test functions. At last, this paper optimizes the parameters of the Extreme Learning Machine (ELM) model with the improved method and applies it to the power load forecasting problem. The effectiveness of the improved method in solving practical engineering problems is further verified. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Lévy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic. [ABSTRACT FROM AUTHOR]

This paper studies an insurer's optimal investment portfolio under the mean-variance criterion. The financial market consists of a riskless bond and a risky asset, and the latter's volatility is random. We are extending the Cox–Ingersoll–Ross (CIR) model to the case with jumps, where it is modeled by a jump-diffusion stochastic differential equation (SDE). We use a Lévy SDE to describe the risk process we have, in which we extend the classic Cramér-Lundberg model to the Lévy process, and additionally introduce the stochastic volatility into this model. We assume that the insurer in question is a mean-variance optimizer. In other words, the decision that this insurer faces is to simultaneously maximize and minimize the mean and variance of his/her terminal wealth by selecting an optimal portfolio. We have uncovered closed-form solutions to the mean-variance problem with respect to the efficient strategy and efficient frontier by solving for expected utility maximization of a quadratic function through the martingale method. Finally, we give a numerical example that analyzes the economic behavior of the efficient frontier. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced whale optimization algorithm based on virtual force to optimize coverage and address the problem of uneven coverage during the deployment of underwater sensor networks. This method is guided by the Lévy flight and virtual force algorithms and adopts a differential mutation strategy based on random walks. This improves the fitness of the initial population and population richness of the algorithm. The effectiveness of this method was verified through simulation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy. [ABSTRACT FROM AUTHOR]

The Artificial Electric Field Algorithm (AEFA) stands out as a physics-inspired metaheuristic, drawing inspiration from Coulomb's law and electrostatic force; however, while AEFA has demonstrated efficacy, it can face challenges such as convergence issues and suboptimal solutions, especially in high-dimensional problems. To overcome these challenges, this paper introduces a modified version of AEFA, named mAEFA, which leverages the capabilities of Lévy flights, simulated annealing, and the Adaptive s-best Mutation and Natural Survivor Method (NSM) mechanisms. While Lévy flights enhance exploration potential and simulated annealing improves search exploitation, the Adaptive s-best Mutation and Natural Survivor Method (NSM) mechanisms are employed to add more diversity. The integration of these mechanisms in AEFA aims to expand its search space, enhance exploration potential, avoid local optima, and achieve improved performance, robustness, and a more equitable equilibrium between local intensification and global diversification. In this study, a comprehensive assessment of mAEFA is carried out, employing a combination of quantitative and qualitative measures, on a diverse range of 29 intricate CEC'17 constraint benchmarks that exhibit different characteristics. The practical compatibility of the proposed mAEFA is evaluated on five engineering benchmark problems derived from the civil, mechanical, and industrial engineering domains. Results from the mAEFA algorithm are compared with those from seven recently introduced metaheuristic algorithms using widely adopted statistical metrics. The mAEFA algorithm outperforms the LCA algorithm in all 29 CEC'17 test functions with 100% superiority and shows better results than SAO, GOA, CHIO, PSO, GSA, and AEFA in 96.6%, 96.6%, 93.1%, 86.2%, 82.8%, and 58.6% of test cases, respectively. In three out of five engineering design problems, mAEFA outperforms all the compared algorithms, securing second place in the remaining two problems. Results across all optimization problems highlight the effectiveness and robustness of mAEFA compared to baseline metaheuristics. The suggested enhancements in AEFA have proven effective, establishing competitiveness in diverse optimization problems. [ABSTRACT FROM AUTHOR]

With the development of the integration of aviation safety and artificial intelligence, research on the combination of risk assessment and artificial intelligence is particularly important in the field of risk management, but searching for an efficient and accurate risk assessment algorithm has become a challenge for the civil aviation industry. Therefore, an improved risk assessment algorithm (PS-AE-LSTM) based on long short-term memory network (LSTM) with autoencoder (AE) is proposed for the various supervised deep learning algorithms in flight safety that cannot adequately address the problem of the quality on risk level labels. Firstly, based on the normal distribution characteristics of flight data, a probability severity(PS)model is established to enhance the quality of risk assessment labels. Secondly, autoencoder is introduced to reconstruct the flight parameter data to improve the data quality. Finally, utilizing the time-series nature of flight data, a long and short-term memory network is used to classify the risk level and improve the accuracy of risk assessment. Thus, a risk assessment experiment was conducted to analyze a fleet landing phase dataset using the PS-AE-LSTM algorithm to assess the risk level associated with aircraft hard landing events. The results show that the proposed algorithm achieves an accuracy of 86.45% compared with seven baseline models and has excellent risk assessment capability. [ABSTRACT FROM AUTHOR]

With the continuous development of rail transportation worldwide, the safety and economy of metro trains have become essential standards. The door system is one of the most frequently used components in the process of train operation, so the fault rate is much higher than other systems. In view of the above problems, a preventive maintenance (PM) model for critical components of metro train door system is established based on reliability in this paper. Firstly, the Pareto chart analysis method and failure mode effect and criticality analysis method are adopted to determine that the lower retaining pin assembly and balanced pressing wheel are the main fault components in the door system. The parameter values of the three-parameter Weibull model of the door components are accurately obtained through the improved dung beetle optimizer algorithm, which provides an essential theoretical basis for optimizing preventive maintenance decisions. Secondly, a PM model of metro door components is established, and Lévy flight is added to PSO to enhance the optimization performance of the algorithm and solve the preventive maintenance model. Finally, the model is verified by sorting out the historical fault maintenance data of the metro door system in a city. The experimental results show that the PM strategy has economic, safety and task performance advantages compared to traditional maintenance methods. [ABSTRACT FROM AUTHOR]

The paper examines the valuation and hedging of life insurance obligations in the presence of mortality risk using the local risk-minimizing hedging approach. Roughly speaking, it is assumed that the lifetime of policyholders in an insurance portfolio is modeled by a point process whose stochastic intensity is controlled by a diffusion process. The stock price process is assumed to be a regime-switching Lévy process with non-zero regime-switching drift, where the parameters are assumed to depend on the economic states. Using the Föllmer–Schweizer decomposition, the main valuation and hedging results for a conditional payment process are determined. Some specific situations have been considered in which the local risk-minimizing strategies for a stream of liability payments or a unit-linked contract are presented. [ABSTRACT FROM AUTHOR]

It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both + 1 and − 1. In this paper, we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case (i.e. gapless case). We make use of a natural extension of the Fredholm index to the non-Fredholm case, known as the Witten index. The aim of this paper is to fully classify the Witten index of the split-step quantum walk by employing the spectral shift function for a rank one perturbation of a fourth-order difference operator. It is also shown in this paper that the Witten index can take half-integer values in the non-Fredholm case. [ABSTRACT FROM AUTHOR]

This paper builds a multivariate Lévy‐driven Ornstein‐Uhlenbeck process for the management of non‐maturing deposits, that are a major source of funding for banks. The contribution of the paper is both theoretical and operational. On the theoretical side, the novelty of this model is to include three independent sources of randomness in a Lévy framework: market interest rates, deposit rates and deposit volumes. The choice of a Lévy background driving process allows us to model rare but severe events. On the operational side, we propose a procedure to include severe volume outflows with positive probability in future scenarios simulation, explaining its implementation with an illustrative example using Italian banking sector data. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new type of tasks for control theory for stochastic dynamical systems — programmed control with Probability 1 (PCP1). PCP1 is an application of an invariant theory. We use the PCP1 concept for dynamical processes described by a system of Itô differential equations with jump-diffusion (GSDES). The considered equations include the drift, the diffusion, and the jumps, together or not. Features of our approach are both a wide set of dynamical systems and investigation of such systems for their unique trajectories. Our method is based on the concept of a stochastic first integral (SFI) for GSDES and its equations which author studied before. The purpose of the present paper is to construct a differential equation system (both stochastic and deterministic) using a known set of FIs for the investigating process. Several examples are given. [ABSTRACT FROM AUTHOR]

This paper proposes a new data clustering method using the advantages of metaheuristic (MH) optimization algorithms. A novel MH optimization algorithm, called arithmetic optimization algorithm (AOA), was proposed to address complex optimization tasks. Math operations inspire the AOA, and it showed significant performance in dealing with different optimization problems. However, the traditional AOA faces some limitations in its search process. Thus, we develop a new variant of the AOA, namely, Augmented AOA (AAOA), integrated with the opposition-based learning (OLB) and Lévy flight (LF) distribution. The main idea of applying OLB and LF is to improve the traditional AOA exploration and exploitation trends in order to find the best clusters. To evaluate the AAOA, we implemented extensive experiments using twenty-three well-known benchmark functions and eight data clustering datasets. We also evaluated the proposed AAOA with extensive comparisons to different optimization algorithms. The outcomes verified the superiority of the AAOA over the traditional AOA and several MH optimization algorithms. Overall, the applications of the LF and OLB have a significant impact on the performance of the conventional AOA. [ABSTRACT FROM AUTHOR]

This paper provides a real application of a popular swarm-intelligence optimisation method. The aim is to analyse the efficiency of various settings of the marine predator algorithm (MPA). Four crucial numerical parameters of the MPA are statistically analysed to propose the most efficient setting for solving engineering problems. Besides population size, particle velocity parameter P, Lévy flight parameter β , and fish aggregating device (FAD) probabilities are studied. Finally, 193 various settings, including fixed values and dynamic changes of the MPA parameters, are experimentally compared when solving 13 engineering problems. Standard statistical approaches are employed to highlight significant differences in various MPA settings. The setting of two MPA parameters (P, FADs) significantly influences MPA performance. Three newly proposed MPA settings outperform the original variant significantly. The best results provide the MPA variant with the dynamic linear change of P from 0.5 to 0. These parameters influence the velocity of prey and predator individuals in all three stages of the MPA search process. Decreasing the value of P showed that decreasing the velocity of individuals during the search provides good performance. Further, lower efficiency of the MPA with higher FAD values was detected. It means that more occasional use of fish aggregating devices (FADs) can increase the solvability of engineering problems. Regarding population size, lower values ( N = 10 ) provided significantly better results compared with the higher values ( N = 500 ). [ABSTRACT FROM AUTHOR]

This paper studies the stochastic pantograph model, which is considered a subcategory of stochastic delay differential equations. A more general jump process, which is called the Lévy process, is added to the model for better performance and modeling situations, having sudden changes and extreme events such as market crashes in finance. By utilizing the truncation technique, we propose the diffused split-step truncated Euler–Maruyama method, which is considered as an explicit scheme, and apply it to the addressed model. By applying the Khasminskii-type condition, the convergence rate of the proposed scheme is attained in L p (p ≥ 2) sense where the non-jump coefficients grow super-linearly while the jump coefficient acts linearly. Also, the rate of convergence of the proposed scheme in L p (0 < p < 2) sense is addressed where all the three coefficients grow beyond linearly. Finally, theoretical findings are manifested via some numerical examples. [ABSTRACT FROM AUTHOR]

To fully harness the burgeoning array of in-orbit satellite resources and augment the efficacy of dynamic surveillance of densely clustered terrestrial targets, this paper delineates the following methodologies. Initially, we leverage the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering algorithm to aggregate the concentrated terrestrial targets, taking into account the field-of-view peculiarities of agile staring satellites. Subsequently, we architect a model for a synergistic multiple angle earth observation satellites (AEOSs) mission planning with the optimization objectives of observational revenue, minimal energy expenditure, and load balancing, factoring in constraints such as target visibility time window, AEOSs maneuverability, and satellite storage. To tackle this predicament, we propose an improved heuristic ant colony optimization (ACO) algorithm, utilizing the task interval, task priority, and the length of time a task can start observation as heuristic information. Furthermore, we incorporate the notion of the max–min ant system to regulate the magnitude of pheromone concentration, and we amalgamate global and local pheromone update strategies to expedite the convergence rate of the algorithm. We also introduce the Lévy flight improved pheromone evaporation coefficient to bolster the algorithm's capacity to evade local optima. Ultimately, through a series of simulation experiments, we substantiate the significant performance improvements achieved by the improved heuristic ant colony algorithm compared to the standard ant colony algorithm. We furnish proof of its efficacy in resolving the planning of multiple AEOS staring observation missions. [ABSTRACT FROM AUTHOR]

Risk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is required to prevent loss from uncertainty. In this paper, we assume that risk factors follow the Lévy process, and propose a stylized model, based on regression, that can estimate the risk of a complicated system under the framework of nest simulation. Specifically, portfolio risk estimation using the Lévy process is discussed as an example. The stylized model simplifies the risk factors artificially, and provides useful basis functions to fit the portfolio loss with little computational effort. Numerical experiments showed the good performance of the stylized model in estimating risk for the Variance Gamma process and the Normal Inverse Gaussian process, which are two examples of the Lévy process. [ABSTRACT FROM AUTHOR]

This paper introduces a power-law subordinator and a power-law Lévy process whose Laplace transform and characteristic function are simply made up of power functions or the ratio of power functions, respectively, and proposes a power-law vector random field whose finite-dimensional characteristic functions consist merely of a power function or the ratio of two power functions. They may or may not have first-order moment, and contain Linnik, variance Gamma, and Laplace Lévy processes (vector random fields) as special cases. For a second-order power-law vector random field, it is fully characterized by its mean vector function and its covariance matrix function, just like a Gaussian vector random field. An important feature of the power-law Lévy processes (random fields) is that they can be used as the building blocks to construct other Lévy processes (random fields), such as hyperbolic secant, cosine ratio, and sine ratio Lévy processes (random fields). [ABSTRACT FROM AUTHOR]

In recent years, forecasting has received increasing attention since it provides an important basis for the effective operation of power systems. In this paper, a hybrid method, composed of kernel principal component analysis (KPCA), tree seed algorithm based on Lévy flight (LTSA) and extreme learning machine (ELM), is proposed for short-term load forecasting. Specifically, the randomly generated weights and biases of ELM have a significant impact on the stability of prediction results. Therefore, in order to solve this problem, LTSA is utilized to obtain the optimal parameters before the prediction process is executed by ELM, which is called LTSA-ELM. Meanwhile, the input data is extracted by KPCA considering the sparseness of the electric load data and used as the input of LTSA-ELM model. The proposed method is tested on the data from European network on intelligent technologies (EUNITE) and experimental results demonstrate the superiority of the proposed approaches compared to the other methods involved in the paper. [ABSTRACT FROM AUTHOR]

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Multilevel thresholding segmentation of color images plays an important role in many fields. The pivotal procedure of this technique is determining the specific threshold of the images. In this paper, an improved mayfly algorithm (IMA)-based color image segmentation method is proposed. Tent mapping initializes the female mayfly population to increase population diversity. Lévy flight is introduced in the wedding dance iterative formulation to make IMA jump from the local optimal solution quickly. Two nonlinear coefficients were designed to speed up the convergence of the algorithm. To better verify the effectiveness, eight benchmark functions are used to test the performance of IMA. The average fitness value, standard deviation, and Wilcoxon rank sum test are used as evaluation metrics. The results show that IMA outperforms the comparison algorithm in terms of search accuracy. Furthermore, Kapur entropy is used as the fitness function of IMA to determine the segmentation threshold. 10 Berkeley images are segmented. The best fitness value, peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and other indexes are used to evaluate the effect of segmented images. The results show that the IMA segmentation method improves the segmentation accuracy of color images and obtains higher quality segmented images. [ABSTRACT FROM AUTHOR]

The object of the present paper is the study of the joint lifetime of d components subject to a common stressful external environment. Out of the stressing environment, the components are independent and the lifetime of each component is characterized by its failure (hazard) rate function. The impact of the external environment is modelled through an increase in the individual failure rates of the components. The failure rate increments due to the environment increase over time and they are dependent among components. The evolution of the joint failure rate increments is modelled by a non negative multivariate additive process, which include Lévy processes and non-homogeneous compound Poisson processes, hence encompassing several models from the previous literature. A full form expression is provided for the multivariate survival function with respect to the intensity measure of a general additive process, using the construction of an additive process from a Poisson random measure (or Poisson point process). The results are next specialized to Lévy processes and other additive processes (time-scaled Lévy processes, extended Lévy processes and shock models), thus providing simple and easily computable expressions. All results are provided under the assumption that the additive process has bounded variations, but it is possible to relax this assumption by means of approximation procedures, as is shown for the last model of this paper. [ABSTRACT FROM AUTHOR]

Moth search (MS) is a nature-inspired metaheuristic optimization algorithm based on the most representative characteristics of moths, Lévy flights and phototaxis. Phototaxis signifies a movement which organism towards or away from a source of light, which is the representative features for moths. The best moth individual is seen as the light source in Moth search. The moths that have a smaller distance from the best one will fly around the best individual by Lévy flights. For reasons of phototaxis, the moths, far from the fittest one, will fly towards the best one with a big step. These two features, Lévy flights and phototaxis, correspond to the processes of exploitation and exploration for metaheuristic optimization. The superiority of the moth search has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the moth search was conducted in this paper, which included the three sections: statistical research studies about moth search, different variants of moth search, and engineering optimization/applications. The future insights and development direction in the area of moth search are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of stochastic functional differential equations driven by the time-changed Lévy process. Using the Lyapunov technique, we obtain some sufficient conditions to ensure that the solutions of the considered equations are h-stable in p-th moment sense. Subsequently, using time-changed Itô formula and a proof by reduction ad absurdum, we capture some new criteria for the h-stability in mean square of the considered equations. In the end, we analyze some illustrative examples to show the interest and usefulness of the major results. [ABSTRACT FROM AUTHOR]

In recent years, due to the growing complexity of real-world problems, researchers have been favoring stochastic search algorithms as their preferred method for problem solving. The slime mould algorithm is a high-performance, stochastic search algorithm inspired by the foraging behavior of slime moulds. However, it faces challenges such as low population diversity, high randomness, and susceptibility to falling into local optima. Therefore, this paper presents an enhanced slime mould algorithm that combines multiple strategies, called the ESMA. The incorporation of selective average position and Lévy flights with jumps in the global exploration phase improves the flexibility of the search approach. A dynamic lens learning approach is employed to adjust the position of the optimal slime mould individual, guiding the entire population to move towards the correct position within the given search space. In the updating method, an improved crisscross strategy is adopted to reorganize the slime mould individuals, which makes the search method of the slime mould population more refined. Finally, the performance of the ESMA is evaluated using 40 well-known benchmark functions, including those from CEC2017 and CEC2013 test suites. It is also recognized by Friedman's test as statistically significant. The analysis of the results on two real-world engineering problems demonstrates that the ESMA presents a substantial advantage in terms of search capability. [ABSTRACT FROM AUTHOR]

In the face of fire in buildings, people need to quickly plan their escape routes. Intelligent optimization algorithms can achieve this goal, including the sparrow search algorithm (SSA). Despite the powerful search ability of the SSA, there are still some areas that need improvements. Aiming at the problem that the sparrow search algorithm reduces population diversity and is easy to fall into local optimum when solving the optimal solution of the objective function, a hybrid improved sparrow search algorithm is proposed. First, logistic-tent mapping is used to initialize the population and enhance diversity in the population. Also, an adaptive period factor is introduced into the producer's update position equation. Then, the Lévy flight is introduced to the position of the participant to improve the optimization ability of the algorithm. Finally, the adaptive disturbance strategy is adopted for excellent individuals to strengthen the ability of the algorithm to jump out of the local optimum in the later stage. In order to prove the improvement of the optimization ability of the improved algorithm, the improved sparrow algorithm is applied to five kinds of maps for evacuation path planning and compared with the simulation results of other intelligent algorithms. The ultimate simulation results show that the optimization algorithm proposed in this paper has better performance in path length, path smoothness, and algorithm convergence, showing better optimization performance. [ABSTRACT FROM AUTHOR]

This paper proposes binary versions of artificial rabbits optimization (ARO) for feature selection (FS) with medical diagnosis data. ARO is a recent swarm-based optimization algorithm that mimics rabbits' natural survival tactics and eating habits. It was modeled in an optimization context to tackle optimization problems of continuous search spaces. In this paper, ARO is improved to deal with the binary domain of FS. The improvements include three additions: First, different alternatives of transfer functions were used to convert ARO from continuous to binary; second, the global-best concept was added to the binary ARO to improve the exploitation capability of the proposed algorithm; and finally, Lévy flight and opposition-based learning strategies were injected into the proposed algorithm to enhance its diversity and thus improve the balance between global exploration and local exploitation during all stages of the search process. Six binary variants of ARO were designed across an extensive set of experiments to study the impact of using the proposed amendments on the performance of the proposed ARO algorithm. These variants are: binary ARO with S-shaped transfer function (BAROS), binary ARO with V-shaped transfer function (BAROV), BAROS with the global-best concept (BGAROS), BGAROV with the global-best concept (BGAROV), BGAROS with Lévy flight and opposition-based learning strategies (BGAROSLO), and BGAROV with Lévy flight and opposition-based learning strategies (BGAROVLO). The proposed binary ARO versions were evaluated using 23 medical FS datasets. In addition, the proposed algorithm was applied to detect coronavirus disease using a real COVID-19 dataset. Five performance measures were used: classification accuracy, sensitivity, specificity, fitness value, and the number of selected features. In a nutshell, the proposed binary ARO versions were able to achieve success rates for these performance metrics as follows: 66.7%, 50%, 33.3%, 66.7%, and 83.3%, respectively. In conclusion, the success of the proposed ARO versions was realized due to the suitable design of the parameters of the proposed ARO version, such as transfer functions, global-best concept, Lévy flight, and opposition-based learning strategies. A comprehensive comparative evaluation was studied against ten well-established methods using the same datasets with a high preference for the proposed ARO versions, especially BGAROSLO which can achieve the best accuracy for the majority of the FS datasets. This is proven using Friedman's statistical test ad-hocked by Holm's test. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence/non-existence of ground states for the following type of elliptic equations with mixed local and nonlocal operators and general nonlinearity:  (− ▵) s u − ▵ u + λ u = f (u) , x ∈ R N , which is driven by the superposition of Brownian and Lévy processes. By considering a constrained variational problem, under suitable assumptions on f, we manage to establish a sharp existence of the ground state solutions to the equation considered. These results improve the ones in the existing reference. [ABSTRACT FROM AUTHOR]

In this paper, a two‐way relay‐aided cognitive satellite terrestrial network (TR‐CSTN) model is proposed, where primary users are located at the edge of the base station. In the TR‐CSTN, one of satellite terminal users (STUs) is selected by the fusion center as the TR to forward information between two edge primary users with power of the TR. Meanwhile, these edge primary users share the licensed frequency band with the selected TR to send information to the satellite. Then, given the limited spectrum utilization and energy efficiency (EE) of the communication system, the cooperative spectrum sensing is employed to realize green communication. Specifically, the fusion center threshold, energy detection threshold, sensing duration and number of STUs are jointly optimized to enhance EE. Furthermore, considering that the node's energy shortage results in a short network lifetime, absolute EE gets improved. In detail, a power allocation scheme named normalized power aided Lévy flight trajectory‐based whale optimization algorithm (NP‐LWOA) is provided, which fulfills effective energy compensation among STUs to prolong the network lifetime notably. Finally, numerical results confirm the theoretical analysis and show the effectiveness of the TR‐CSTN and the NP‐LWOA in efficiently achieving the concept of green communication compared with other methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is threefold. Firstly, we prove the existence and uniqueness of a global strong (in both the probabilistic and the PDE senses) H¹2-valued solution to the 2D stochastic Navier--Stokes equations (SNSEs) driven by a multiplicative Lévy noise under the natural Lipschitz condition on balls and linear growth assumptions on the jump coefficient. Secondly, we prove a Girsanov-type theorem for Poisson random measures and apply this result to a study of the wellposedness of the corresponding stochastic controlled problem for these SNSEs. Thirdly, we apply these results to establish a Freidlin--Wentzell-type large deviation principle for the solutions of these SNSEs by employing the weak convergence method introduced by Budhiraja et al. (2011, 2013). [ABSTRACT FROM AUTHOR]