Search

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]

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]

A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index κ (0 < κ < 2). Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change. [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]

Path planning is an important research direction in the field of robotics; however, with the advancement of modern science and technology, the study of efficient, stable, and safe path-planning technology has become a realistic need in the field of robotics research. This paper introduces an improved sparrow search algorithm (ISSA) with a fusion strategy to further improve the ability to solve challenging tasks. First, the sparrow population is initialized using circle chaotic mapping to enhance diversity. Second, the location update formula of the northern goshawk is used in the exploration phase to replace the sparrow search algorithm's location update formula in the security situation. This improves the discoverer model's search breadth in the solution space and optimizes the problem-solving efficiency. Third, the algorithm adopts the Lévy flight strategy to improve the global optimization ability, so that the sparrow jumps out of the local optimum in the later stage of iteration. Finally, the adaptive T-distribution mutation strategy enhances the local exploration ability in late iterations, thus improving the sparrow search algorithm's convergence speed. This was applied to the CEC2021 function set and compared with other standard intelligent optimization algorithms to test its performance. In addition, the ISSA was implemented in the path-planning problem of mobile robots. The comparative study shows that the proposed algorithm is superior to the SSA in terms of path length, running time, path optimality, and stability. The results show that the proposed method is more effective, robust, and feasible in mobile robot path planning. [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]

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]

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 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]

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]

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]

In this paper, we study the speed of extinction of continuous state branching processes in subcritical Lévy environments. More precisely, when the associated Lévy process to the environment drifts to -8 and, under a suitable exponential change of measure (Esscher transform), the environment either drifts to -8 or oscillates. We extend recent results of Palau et al. (2016) and Li and Xu (2018), where the branching term is associated to a spectrally positive stable Lévy process and complement the recent article of Bansaye et al. (2021) where the critical case was studied. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes and the asymptotic behaviour of exponential functionals of Lévy processes. As an application of the aforementioned results, we characterise the process conditioned to survival also known as the Q-process. [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]

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]

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]

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]

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]

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]

Henry gas solubility optimization (HGSO) algorithm is a physical heuristic algorithm based on Henry's law. It is a heuristic algorithm proposed to simulate the process of gas solubility in liquid changing with temperature. In this paper, Lévy's flight operator and Brown motion operator are introduced respectively, which are inspired by the flight trajectory of animals and the thermal motion of particles. This increases the diversity of search strategies and enhances the ability of local search. It greatly improves the shortcoming of the original HGSO algorithm, which has a single position updating method and sometimes slow convergence speed. Lévy motion based Henry gas solubility optimization algorithm (Lévy-HGSO), Brown motion based Henry gas solubility optimization algorithm (Brown-HGSO) are proposed in this paper. It is worth mentioning that in this paper, an improved Henry gas solubility optimization algorithm (BL-HGSO) based on the Lévy and Brown motion is proposed by combining the Lévy flight operator and Brown motion operator. Different from the former two, the effective combination of different motion modes can more accurately find the optimal solution, which not only guarantees the original global search ability, but also strengthens the local search strategy, and is not easy to fall into the local optimal value. In order to verify the performance of the proposed algorithms, 40 benchmark functions were optimized by this algorithm, and two practical engineering design problems were solved. The sine and cosine algorithm (SCA), whale optimization algorithm (WOA), lightning search algorithm (LSA), water cycle algorithm(WCA)and HGSO algorithms were used in comparison experiments. The simulation results show that three improved HGSO algorithms proposed in this paper have strong ability of balancing exploration and exploitation, fast convergence speed and high precision. [ABSTRACT FROM AUTHOR]

The paper suggests a hybrid numerical method to price barrier options under Levy processes. As the main ingredient of our approach, we model the values of the Wiener-Hopf factors using artificial neural networks in the exact formula for the solution. The numerical Wiener-Hopf factorization typically reduces the problem to the factorization of the polynomial of exp(iξ), which is interpreted as the characteristic function of the random variable that approximates the Lévy process at the exponentially distributed time moment. We design and train a feedforward neural network with one hidden layer that approximates the coefficients of factors based on the input vector of the factorized polynomial coefficients. We implemented in the software a training data generator and a generalized loss function to factorize a polynomial of arbitrary degree. We demonstrate the performance of our approach using examples of factorization of second-, sixth- and 254th-degree polynomials. It takes a fraction of a second for our trained artificial neural networks to calculate the factors. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of stochastic Riemann-Liouville type fractional differential equations driven by Lévy noise. By using Itô formula for the considered equation, we attempt to explore the non-confluence property of solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions which is novel in exploring the non-confluence property of differential equations. [ABSTRACT FROM AUTHOR]

Lévy flight is a random walk mechanism which can make large jumps at local locations with a high probability. The probability density distribution of Lévy flight was characterized by sharp peaks, asymmetry, and trailing. Its movement pattern alternated between frequent short-distance jumps and occasional long-distance jumps, which can jump out of local optimal and expand the population search area. The metaheuristic algorithms are inspired by nature and applied to solve NP-hard problems. Lévy flight is used as an operator in the cuckoo algorithm, monarch butterfly optimization, and moth search algorithms. The superiority for the Lévy flight-based metaheuristic algorithms has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the Lévy flight-based metaheuristic algorithms is conducted in this paper. The research includes the following sections: statistical analysis about Lévy flight, metaheuristic algorithms with a Lévy flight operator, and classification of Lévy flight used in metaheuristic algorithms. The future insights and development direction in the area of Lévy flight are also discussed. [ABSTRACT FROM AUTHOR]

In contrast to their seemingly simple and shared structure of independence and stationarity, Lévy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes. Inspired by the recent paper of Ghourchian, Amini, and Gohari, we characterize their compressibility by studying the entropy of their double discretization (both in time and amplitude) in the regime of vanishing discretization steps. For a Lévy process with absolutely continuous marginals, this reduces to understanding the asymptotics of the differential entropy of its marginals at small times, for which we obtain a new local central limit theorem. We generalize known results for stable processes to the non-stable case, with a special focus on Lévy processes that are locally self-similar, and conceptualize a new compressibility hierarchy of Lévy processes, captured by their Blumenthal–Getoor index. [ABSTRACT FROM AUTHOR]

This paper examines the problem of hedging banks interest rate margins. We assume that the demand's deposits follow an exponential Lévy process with potential jumps. The forward market rates are assumed to follow the standard market model introduced by Brace et al. (Math Finance 7(2):127–155, 1997). As Adam et al. (Hedging interest rate margins on demand deposits, Université Paris 1 Panthéon-Sorbonne working paper, 2012), we consider that deposit rates depend linearly on market rates. Face to incompleteness, the liability manager must hedge both interest rate and demand deposit risks. For this purpose, we introduce various quadratic hedging criteria, allowing us to provide explicit hedging strategies that we further analyze. We illustrate in particular the impact of both the trends and the volatilities of interest rates and demand deposits. [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]

This paper overviews our recent results of energy market modeling, including The option pricing formula for a mean-reversion asset, variance and volatility swaps on energy markets, applications of weather derivatives on energy markets, pricing crude oil options using the Lévy processes, energy contracts modeling with delayed and jumped volatilities, applications of mean-reverting processes on Alberta energy markets, and alternatives to the Black-76 model for options valuation of futures contracts. We will also consider the clean renewable energy prospective in Canada, and, in particular, in Alberta and Calgary. [ABSTRACT FROM AUTHOR]

The wireless sensor network (WSN) is an essential technology of the Internet of Things (IoT) but has the problem of low coverage due to the uneven distribution of sensor nodes. This paper proposes a novel enhanced whale optimization algorithm (WOA), incorporating Lévy flight and a genetic algorithm optimization mechanism (WOA-LFGA). The Lévy flight technique bolsters the global search ability and convergence speed of the WOA, while the genetic optimization mechanism enhances its local search and random search capabilities. WOA-LFGA is tested with 29 mathematical optimization problems and a WSN coverage optimization model. Simulation results demonstrate that the improved algorithm is highly competitive compared with mainstream algorithms. Moreover, the practicality and the effectiveness of the improved algorithm in optimizing wireless sensor network coverage are confirmed. [ABSTRACT FROM AUTHOR]

An Enhanced Chameleon Swarm Algorithm (ECSA) by integrating roulette wheel selection and Lé vy flight methods is presented to solve non-convex Economic Load Dispatch (ELD) problems. CSA has diverse strategies to move towards the optimal solution. Even so, this algorithm's performance faces some hurdles, such as early convergence and slumping into local optimum. In this paper, several enhancements were made to this algorithm. First, it's position updating process was slightly tweaked and took advantage of the chameleons' randomization as well as adopting several time-varying functions. Second, the Lévy flight operator is integrated with roulette wheel selection method and both are combined with ECSA to augment the exploration behavior and lessen its bias towards exploitation. Finally, an add-on position updating strategy is proposed to develop a further balance between exploration and exploitation conducts. The optimization performance of ECSA is shown by testing it on five various real ELD cases with a generator having 3, 13, 40, 80 and 140 units, each with different constraints. The results of the ELD systems' analysis depict that ECSA is better than the parent CSA and other state-of-the art methods. Further, the efficacy of ECSA was experimented on several benchmark test functions, and its performance was compared to other well-known optimization methods. Experimental results show that ECSA surpasses other methods on complex benchmark functions with modest computational burdens. The superiority and practicality of ECSA is demonstrated by getting new best solutions for large-scale ELD cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

The whale optimization algorithm (WOA) is a simple structured and easily implemented swarm-based algorithm inspired by the unique bubble-net feeding method of humpback whales. Past studies have shown that WOA performs well in a number of optimization problems. However, it is difficult for WOA to completely free itself from the problems of insufficient convergence accuracy and premature convergence when solving global optimization problems. To address these issues, a hybrid whale optimization algorithm based on symbiotic strategy (HWOAMS) is proposed in this paper. The main idea of the proposed method is to combine the improved symbiotic organisms search algorithm (SOS) with the whale optimization algorithm thus enhancing the search ability of WOA. First, an improved symbiotic phase based on Lévy flight and chaos strategy is introduced into the exploration process to enhance the global search capability; Second, an improved mutualism phase based on Brownian motion is used instead of the original shrinking encircling phase to achieve better local exploitation. Third, an improved parasitic phase based on a modified global optimal spiral operator strategy is embedded in the spiral updating position phase to help the algorithm further improve the exploitation efficiency and convergence accuracy. Finally, a global search strategy is proposed to help the algorithm better balance exploration and exploitation. To establish the effectiveness of the new algorithm, extensive simulation experiments are conducted on HWOAMS using the classical function test set, the CEC 2019 function set and four classical engineering problems. Numerical evaluation results indicate that HWOAMS outperforms 18 other algorithms in terms of local optimum avoidance ability and convergence accuracy in a majority of cases, and has better search performance. [ABSTRACT FROM AUTHOR]

In this paper, we study a Lévy risk process consisting of Brownian component together with premiums and claims that are phase type with many phases. Our aim is to approximate the probability of ruin without touching an upper barrier a. In line with this, the study demonstrates that the described Lévy risk process can essentially be replaced with a simpler risk process in which both premiums and claims are phase-type with just few phases. [ABSTRACT FROM AUTHOR]

The price V of a contingent claim in finance, insurance and economics is defined as an expectation of a stochastic expression. If the underlying uncertainty is modeled as a strong Markov process X, the Feynman–Kac theorem suggests that V is the unique solution of a boundary problem for a parabolic equation. In the case of PDO with constant symbols, simple probabilistic tools explained in this paper can be used to explicitly calculate expectations under very weak conditions on the process and study the regularity of the solution. Assuming that the Feynman–Kac theorem holds, and a more general boundary problem can be localized, the local results can be used to study the existence and regularity of solutions, and derive efficient numerical methods. In the paper, difficulties for the realization of this program are analyzed, several outstanding problems are listed, and several closely efficient methods are outlined. [ABSTRACT FROM AUTHOR]

Inertial weight adaptive quantum particle swarm optimization (DCWQPSO) algorithm can effectively improve the problem of particle falling into local extreme value. But the particle is still possible to fall into local extreme value in the later stage of particle evolution. When it is applied to photovoltaic multi‐peak maximum power tracking (MPPT), the tracking efficiency is not only reduced, but also may lead to tracking failure under the condition of sudden tracking of photovoltaic light intensity. To solve the above problems, this paper proposes a photovoltaic maximum power tracking (MPPT) control algorithm combining Lévy flight strategy with DCWQPSO algorithm. Lévy flight is a non‐Gaussian random process. The algorithm introduces Lévy flight strategy to change the mutation formula of particles and uses the characteristics of Lévy flight short step and occasionally long step jump search to improve the diversity of particles in the algorithm population. The algorithm proposed in this paper enhances the particle diversity, improves the convergence accuracy and speed of the algorithm, and overcomes the defects of the DCWQPSO algorithm. Simulation results demonstrate that the MPPT control algorithm proposed in this paper has fast‐tracking speed and high precision, which can effectively improve the maximum power tracking efficiency and dynamic quality of photovoltaic power generation system under uncertain environment, and it also has good robustness. [ABSTRACT FROM AUTHOR]

In response to the problems of easily falling into local optima, low path planning accuracy, and slow convergence speed when applying the traditional pelican optimization algorithm to the mobile robot path planning problem, a multi-strategy improved pelican optimization algorithm (MPOA) is proposed. In the initialization stage, chaotic mapping is used to increase the diversity of the pelican population individuals. In the exploration stage, an adaptive feedback adjustment factor is proposed to adjust the local optima of pelican individuals’ positions and balance the algorithm’s local development capability. In the development stage, the Lévy flight strategy is introduced to adjust the domain radius of the pelican population individuals, and the Gaussian mutation mechanism is used to disturb individuals that have fallen into local optima. Simulation experimental results show that the improved algorithm has significantly improved and effectively shortened the length of the planned path. [ABSTRACT FROM AUTHOR]

A novel theoretical result on estimation of the local time and the occupation time measure of an α-stable Lévy process with α ∈ (1, 2) is presented. The approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L²-optimal statistic by construction. The corresponding stable central limit theorems are proved and a statistical application is discussed. In particular, this work extends the results of [20], which investigated the case of the Brownian motion. [ABSTRACT FROM AUTHOR]

The moth search algorithm (MS) is a relatively new metaheuristic optimization algorithm which mimics the phototaxis and Lévy flights of moths. Being an NP-hard problem, the 0–1 multidimensional knapsack problem (MKP) is a classical multi-constraint complicated combinatorial optimization problem with numerous applications. In this paper, we present a hybrid learning MS (HLMS) by incorporating two learning mechanisms, global-best harmony search (GHS) learning and Baldwinian learning for solving MKP. (1) GHS learning guides moth individuals to search for more valuable space and the potential dimensional learning uses the difference between two random dimensions to generate a large jump. (2) Baldwinian learning guides moth individuals to change the search space by making full use of the beneficial information of other individuals. Hence, GHS learning mainly provides global exploration and Baldwinian learning works for local exploitation. We demonstrate the competitiveness and effectiveness of the proposed HLMS by conducting extensive experiments on 87 benchmark instances. The experimental results show that the proposed HLMS has better or at least competitive performance against the original MS and some other state-of-the-art metaheuristic algorithms. In addition, the parameter sensitivity of Baldwinian learning is analyzed and two important components of HLMS are investigated to understand their impacts on the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Chimp optimization algorithm (ChOA) is a meta-heuristic algorithm inspired by individual intelligence and sexual motivation during group hunting. It is designed to speed up the convergence of the optimal solution. Because of its simplicity and low computational cost, the algorithm has been widely used to solve complex global optimization problem. But in the process of searching, it is easy to fall into the local optima, and the balance between exploitation and exploration cannot be realized well. In this paper, an adaptive chimp optimization algorithm called AChOA is proposed. Firstly, the Tent chaotic map is firstly used to initialize the chimp population to obtain a better initial solutions and improve convergence precision. Secondly, adaptive non linear convergence factor and adaptive weight are introduced in the global search stage, and the parameters vary adaptively according to the number of iterations and population diversity, so as to improve the population diversity. Thirdly, the Lévy flight strategy is introduced into the position update formula to mitigate the shortcomings of ChOA algorithm, such as finding the local optima rather than the global optima, and lack of balance between the exploitation and exploration process. Finally, a comparison with 10 famous algorithms on 19 benchmark functions of the solving accuracy and convergence speed of AChOA is presented. The results show that AChOA has the advantages of fast convergence speed, high solution accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC'20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon's rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems. [ABSTRACT FROM AUTHOR]

This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical solution is chosen to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. We model market data using a stable distribution to demonstrate the relationships between the tails and the new fractional Fokker–Planck model, as well as develop an R code that can be used to draw figures from real data. [ABSTRACT FROM AUTHOR]

In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation. [ABSTRACT FROM AUTHOR]

The paper studies the global dynamics and probability density function for a class of stochastic SVI epidemic models with white noise, Lévy jumps and nonlinear incidence. The stability of disease-free and endemic equilibria for the corresponding deterministic model is first obtained. The threshold criteria on the stochastic extinction, persistence and stationary distribution are established. That is, the disease is extinct with probability one if the threshold value ..., and the disease is persistent in the mean and any positive solution is ergodic and has a unique stationary distribution if ... . Furthermore, the approximate expression of the log-normal probability density function around the quasi-endemic equilibrium of the stochastic model is calculated. A new technique for the calculation of the probability density function is proposed. Lastly, the numerical examples and simulations are presented to verify the main results. [ABSTRACT FROM AUTHOR]

The application of Lévy processes including major movements or jumps over a small period of time has proved to be an effective technique in financial research to catch certain unusual or extreme cases in stock price dynamics. Models that follow the Lévy process are The FMLS, Kobol, and CGMY models. These models gradually grow the interest for study among researchers because of some of the best choices them. Therefore the topic of approaching these three different models has drawn yet more attention. In the current paper, we present these models' numerical method. At first, The Riemann-Liouville tempered fractional derivative (RLTFD) with arbitrary order is approximated by using the basis function of the shifted Chebyshev polynomials of the fourth kind (SCPFK). In the second step, we gain the semi-discrete design to solve the tempered fractional B-S model (TFBSM) by applying finite difference approximation. We're going to show that this system is stable and O (δ τ) is the convergence order. In fact, a fast stabilized method will obtain to reduce the time from processing and the computation time per repetition. Then to get the full scheme, we use SCPFK to approximate the spatial fractional derivative. Finally, two numerical examples are presented to demonstrate the accuracy and usefulness of the developed system. [ABSTRACT FROM AUTHOR]