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To achieve the optimal solution between construction costs and carbon emissions in the multi-target optimization scheduling, this paper proposes a multi-objective optimization scheduling design for wind–solar energy storage microgrids based on an improved oppositional gradient grey wolf optimization (OGGWO) algorithm. First, two new features were added to the traditional grey wolf optimization (GWO) algorithm to solve the multi-target optimization scheduling of grid-connected microgrids, aiming to improve solution quality and convergence speed. Furthermore, Gaussian walk and Lévy flight are introduced to enhance the search capability of the proposed OGGWO algorithm. This method expands the search range while sacrificing only a small amount of search speed, contributing to obtaining the global optimal solution. Finally, the gradient direction is considered in the feature search process, allowing for a comprehensive understanding of the search space, which facilitates achieving the global optimum. Experimental results indicate that, compared to traditional methods, the proposed improved OGGWO algorithm can achieve standard deviations of 4.88 and 4.46 in two different scenarios, demonstrating significant effectiveness in reducing costs and pollution. [ABSTRACT FROM AUTHOR]

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures the market expectations of future volatility, but traditional methods based on second-moment shocks and the time-varying volatility of the VIX often do not effectively to capture the non-Gaussian, heavy-tailed nature of asset returns. To address this, we constructed a revised VIX by fitting a double-subordinated Normal Inverse Gaussian Lévy process to S&P 500 log returns, to provide a more comprehensive measure of volatility that captures the extreme movements and heavy tails observed in financial data. Using an axiomatic framework, we developed a family of risk–reward ratios that, when computed with our revised VIX and fitted to a long-memory time series model, provide a more precise identification of uncertainty shocks in financial markets. [ABSTRACT FROM AUTHOR]

Currently, numerous intelligent maximum power point tracking (MPPT) algorithms are capable of tackling the global optimization challenge of multi-peak photovoltaic output power under partial shading conditions, yet they often face issues such as slow convergence, low tracking precision, and substantial power fluctuations. To address these challenges, this paper introduces a hybrid algorithm that integrates an improved salp swarm algorithm (SSA) with the perturb and observe (P&O) method. Initially, the SSA is augmented with a dynamic spiral evolution mechanism and a Lévy flight strategy, expanding the search space and bolstering global search capabilities, which in turn enhances the tracking precision. Subsequently, the application of a Gaussian operator for distribution calculations allows for the adaptive adjustment of step sizes in each iteration, quickening convergence and diminishing power oscillations. Finally, the integration with P&O facilitates a meticulous search with a small step size, ensuring swift convergence and further mitigating post-convergence power oscillations. Both the simulations and the experimental results indicate that the proposed algorithm outperforms particle swarm optimization (PSO) and grey wolf optimization (GWO) in terms of convergence velocity, tracking precision, and the reduction in iteration power oscillation magnitude. [ABSTRACT FROM AUTHOR]

To address the issues of poor population diversity, low accuracy, and susceptibility to local optima in the Butterfly Optimization Algorithm (BOA), an Improved Butterfly Optimization Algorithm with multiple strategies (IBOA) is proposed. The algorithm employs SPM mapping and reverse learning methods to initialize the population, enhancing its diversity; utilizes Lévy flight and trigonometric search strategies to update individual positions during global and local search phases, respectively, expanding the search scope of the algorithm and preventing it from falling into local optima; and finally, it introduces a simulated annealing mechanism to accept worse solutions with a certain probability, enriching the diversity of solutions during the optimization process. Simulation experimental results comparing the IBOA with Particle Swarm Optimization, BOA, and three other improved BOA algorithms on ten benchmark functions demonstrate that the IBOA has improved convergence speed and search accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes an Improved Spider Wasp Optimizer (ISWO) to address inaccuracies in calculating the population (N) during iterations of the SWO algorithm. By innovating the population iteration formula and integrating the advantages of Differential Evolution and the Crayfish Optimization Algorithm, along with introducing an opposition-based learning strategy, ISWO accelerates convergence. The adaptive parameters trade-off probability (TR) and crossover probability (Cr) are dynamically updated to balance the exploration and exploitation phases. In each generation, ISWO optimizes individual positions using Lévy flights, DE's mutation, and crossover operations, and COA's adaptive update mechanisms. The OBL strategy is applied every 10 generations to enhance population diversity. As the iterations progress, the population size gradually decreases, ultimately yielding the optimal solution and recording the convergence process. The algorithm's performance is tested using the 2017 test set, modeling a mountainous environment with a Gaussian function model. Under constraint conditions, the objective function is updated to establish a mathematical model for UAV flight. The minimal cost for obstacle-avoiding flight within the specified airspace is obtained using the fitness function, and the flight path is smoothed through cubic spline interpolation. Overall, ISWO generates high-quality, smooth paths with fewer iterations, overcoming premature convergence and the insufficient local search capabilities of traditional genetic algorithms, adapting to complex terrains, and providing an efficient and reliable solution. [ABSTRACT FROM AUTHOR]

With advancements in integrated space–air–ground global observation capabilities, the volume of remote sensing data is experiencing exponential growth. Traditional computing models can no longer meet the task processing demands brought about by the vast amounts of remote sensing data. As an important means of processing remote sensing data, distributed cluster computing's task scheduling directly impacts the completion time and the efficiency of computing resource utilization. To enhance task processing efficiency and optimize the allocation of computing resources, this study proposes a Multi-Strategy Improved Siberian Tiger Optimization (MSSTO) algorithm based on the original Siberian Tiger Optimization (STO) algorithm. The MSSTO algorithm integrates the Tent chaotic map, the Lévy flight strategy, Cauchy mutation, and a learning strategy, showing significant advantages in convergence speed and global optimal solution search compared to the STO algorithm. By combining stochastic key encoding schemes and uniform allocation encoding schemes, taking the task scheduling of aerosol optical depth retrieval as a case study, the research results show that the MSSTO algorithm significantly shortens the completion time (21% shorter compared to the original STO algorithm and an average of 15% shorter compared to nine advanced algorithms, such as a particle swarm algorithm and a gray wolf algorithm). It demonstrates superior solution accuracy and convergence speed over various competing algorithms, achieving the optimal execution sequence and machine allocation scheme for task scheduling. [ABSTRACT FROM AUTHOR]

Coverage control is a fundamental and critical issue in plentiful wireless sensor network (WSN) applications. Aiming at the high-dimensional optimization problem of sensor node deployment and the complexity of the monitoring area, an orthogonal learning multi-strategy bald eagle search (OLMBES) algorithm is proposed to optimize the location deployment of sensor nodes. This paper incorporates three kinds of strategies into the bald eagle search (BES) algorithm, including Lévy flight, quasi-reflection-based learning, and quadratic interpolation, which enhances the global exploration ability of the algorithm and accelerates the convergence speed. Furthermore, orthogonal learning is integrated into BES to improve the algorithm's robustness and premature convergence problem. By this way, population search information is fully utilized to generate a more superior position guidance vector, which helps the algorithm jump out of the local optimal solution. Simulation results on CEC2014 benchmark functions reveal that the optimization performance of the proposed approach is better than that of the existing method. On the WSN coverage optimization problem, the proposed method has greater network coverage ratio, node uniformity, and stronger optimization stability when compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The inverse kinematics of robotic manipulators involves determining an appropriate joint configuration to achieve a specified end-effector position. This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the Lévy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10 − 18 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the Lévy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems. [ABSTRACT FROM AUTHOR]

Aiming at the problems of chameleon swarm algorithm (CSA), such as slow convergence speed, poor robustness, and ease of falling into the local optimum, a multi-strategy improved chameleon optimization algorithm (ICSA) is herein proposed. Firstly, logistic mapping was introduced to initialize the chameleon population to improve the diversity of the initial population. Secondly, in the prey-search stage, the sub-population spiral search strategy was introduced to improve the global search ability and optimization accuracy of the algorithm. Then, considering the blindness of chameleon's eye turning to find prey, the Lévy flight strategy with cosine adaptive weight was combined with greed strategy to enhance the guidance of random exploration in the eyes' rotation stage. Finally, a nonlinear varying weight was introduced to update the chameleon position in the prey-capture stage, and the refraction reverse-learning strategy was used to improve the population activity in the later stage so as to improve the ability of the algorithm to jump out of the local optimum. Eighteen functions in the CEC2005 benchmark test set were selected as an experimental test set, and the performance of ICSA was tested and compared with five other swarm intelligent optimization algorithms. The analysis of the experimental results of 30 independent runs showed that ICSA has stronger convergence performance and optimization ability. Finally, ICSA was applied to the UAV path-planning problem. The simulation results showed that compared with other algorithms, the paths generated by ICSA in different terrain scenarios are shorter and more stable. [ABSTRACT FROM AUTHOR]

Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay differential equations, due to the fact that the delays cause very complicated correction terms. In this paper, we identify Marcus stochastic delay differential equations with some Marcus stochastic differential equations without delays but subject to extra constraints. This helps us to obtain the following two main results: (i) we establish a sufficient condition for the existence and uniqueness of the solution to the Marcus delay differential equations; and (ii) we establish a representation formula for the probability density of the Marcus stochastic delay differential equations. In the representation formula, the probability density for Marcus stochastic differential equations with memory is analytically expressed in terms of probability density for the corresponding Marcus stochastic differential equations without memory. [ABSTRACT FROM AUTHOR]

The paper considers a bidimensional continuous-time risk model with subexponential claims and Brownian perturbations, in which the price processes of the investment portfolio of the two lines of business are two geometric Lévy processes and the two lines of business share a common claim-number process, which is a renewal counting process. The paper mainly considers the claims of each line of business having a dependence structure. When the claims have subexponential distributions, the asymptotics of the finite-time ruin probabilities ψ a n d (x 1 , x 2 ; T) and ψ s i m (x 1 , x 2 ; T) have been obtained. When the distributions of claims belong to the intersection of long-tailed and dominatedly varying-tailed distribution classes, the asymptotics of the finite-time ruin probability ψ o r (x 1 , x 2 ; T) is given. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is a classic and challenging optimization task in most machine learning and data mining projects. Recently, researchers have attempted to develop more effective methods by using metaheuristic methods in FS. To increase population diversity and further improve the effectiveness of the beluga whale optimization (BWO) algorithm, in this paper, we propose a multi-strategies improved BWO (MSBWO), which incorporates improved circle mapping and dynamic opposition-based learning (ICMDOBL) population initialization as well as elite pool (EP), step-adaptive Lévy flight and spiral updating position (SLFSUP), and golden sine algorithm (Gold-SA) strategies. Among them, ICMDOBL contributes to increasing the diversity during the search process and reducing the risk of falling into local optima. The EP technique also enhances the algorithm′s ability to escape from local optima. The SLFSUP, which is distinguished from the original BWO, aims to increase the rigor and accuracy of the development of local spaces. Gold-SA is introduced to improve the quality of the solutions. The hybrid performance of MSBWO was evaluated comprehensively on IEEE CEC2005 test functions, including a qualitative analysis and comparisons with other conventional methods as well as state-of-the-art (SOTA) metaheuristic approaches that were introduced in 2024. The results demonstrate that MSBWO is superior to other algorithms in terms of accuracy and maintains a better balance between exploration and exploitation. Moreover, according to the proposed continuous MSBWO, the binary MSBWO variant (BMSBWO) and other binary optimizers obtained by the mapping function were evaluated on ten UCI datasets with a random forest (RF) classifier. Consequently, BMSBWO has proven very competitive in terms of classification precision and feature reduction. [ABSTRACT FROM AUTHOR]

Catch fish optimization algorithm (CFOA) is a newly proposed meta-heuristic algorithm based on human behaviors. CFOA shows better performance on multiple test functions and clustering problems. However, CFOA shows poor performance in some cases, and there is still room for improvement in convergence accuracy, getting rid of local traps, and so on. To further enhance the performance of CFOA, a multi-strategy improved catch fish optimization algorithm (MICFOA) is proposed in this paper. In the exploration phase, we propose a Lévy-based differential independent search strategy to enhance the global search capability of the algorithm while minimizing the impact on the convergence speed. Secondly, in the exploitation phase, a weight-balanced selection mechanism is used to maintain population diversity, enhance the algorithm's ability to get rid of local optima during the search process, and effectively boost the convergence accuracy. Furthermore, the structure of CFOA is also modified in this paper. A fishermen position replacement strategy is added at the end of the algorithm as a way to strengthen the robustness of the algorithm. To evaluate the performance of MICFOA, a comprehensive comparison with nine other metaheuristic algorithms is performed on the 10/30/50/100 dimensions of the CEC 2017 test functions and the 10/20 dimensions of the CEC2022 test functions. Statistical experiments show that MICFOA has more significant dominance in numerical optimization problems, and its overall performance outperforms the CFOA, PEOA, TLBO, COA, ARO, EDO, YDSE, and other state-of-the-art algorithms such as LSHADE, JADE, IDE-EDA, and APSM-jSO. [ABSTRACT FROM AUTHOR]

The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a Lévy flight strategy, a Brownian motion strategy and an RFDB selection method. The Lévy flight strategy and Brownian motion strategy are used to enhance the algorithm's exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively. [ABSTRACT FROM AUTHOR]

In the realm of urban logistics, optimizing vehicle routes for varied cargo types—including refrigerated, fragile, and standard cargo—poses significant challenges amid complex urban infrastructures and heterogeneous vehicle capacities. This research paper introduces a novel model for the multi-type capacitated vehicle routing problem (MT-CVRP) that harnesses an advanced ant colony optimization algorithm, dubbed Lévy-EGACO. This algorithm integrates Lévy flights and elitist guiding principles, enhancing search efficacy and pheromone update processes. The primary objective of this study is to minimize overall transportation costs while optimizing the efficiency of intricate route planning for vehicles with diverse load capacities. Through rigorous simulation experiments, we corroborated the validity of the proposed model and the effectiveness of the Lévy-EGACO algorithm in optimizing urban cargo transportation routes. Lévy-EGACO demonstrated a consistent reduction in transportation costs, ranging from 1.8% to 2.5% compared to other algorithms, across different test scenarios following base data modifications. These findings reveal that Lévy-EGACO substantially improves route optimization, presenting a robust solution to the challenges of MT-CVRP within urban logistics frameworks. [ABSTRACT FROM AUTHOR]

An active stabiliser bar significantly enhances the anti-roll capabilities of vehicles. The control strategy is a crucial factor in enabling the active stabiliser bar to function effectively. This paper investigates an active disturbance rejection control (ADRC) strategy. Given the numerous parameters of the ADRC and their significant mutual influence, optimising these parameters is challenging. To address this, an improved chicken flock optimisation algorithm is proposed to optimise the ADRC parameters and enhance its performance. First, a three-degree-of-freedom dynamic model of the vehicle is established, and an active disturbance rejection control-based optimisation model utilising a chicken flock optimisation algorithm is constructed. To tackle the issues of getting stuck in local optima and low precision when dealing with complex problems in the traditional chicken flock optimisation (CFO) algorithm, several strategies, including improved Lévy flight, have been adopted. Subsequently, the twelve parameters of the ADRC are optimised using the improved chicken flock optimisation algorithm. Comprehensive testing on multiple benchmark functions demonstrates that the improved chicken flock optimisation (ICFO) algorithm is distinctly superior to other advanced algorithms in terms of solution quality and robustness. Simulation results show that the ICFO-ADRC controller is significantly superior. In four different complex road condition tests, the ICFO-ADRC controller shows an average performance improvement of 8% compared to the fuzzy PI-PD controller, an average improvement of 82% compared to the non-optimised ADRC controller, and an average improvement of 18% compared to the CFO-ADRC controller. Our findings confirm that this paper was able to provide new solutions for vehicle stability control whilst opening up new possibilities for the application of metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

A simple self-experiment allows for the measurement of individual pedestrian movements, aiming to understand the deviations from intended directions seen in heterogeneous human crowds. The method involves pedestrian self-observations using the GPS sensor of a smartphone, providing a unique perspective on individual behavior within a crowd and offering a means to evaluate average pedestrian speed. The study is focused on individual mobility in the context of a heterogeneous crowd rather than the behavior of a crowd composed of similar types of people. With this study, an important contribution to the understanding of interpersonal distances in heterogeneous crowds is made. [ABSTRACT FROM AUTHOR]

In coastal areas, coconuts are a common crop. Everyone from farmers to lawmakers and businesses would benefit from an accurate forecast of coconut production. Internet of Things (IoT) sensors are strategically positioned to continuously monitor the environment and gather production statistics to obtain accurate agricultural output predictions. To effectively estimate coconut prediction, this study presents an enhanced deep learning classifier called Bi-directional Long Short-Term Memory (BILSTM) with the integrated Lévy Flight and Seagull Optimization Algorithm (LFSOA). LASSO feature selection is applied to eliminate the superfluous characteristics in the yield estimation. To further enhance the coconut yield estimate, the optimal set of hyperparameters for BILSTM is tuned by the LFSOA, which helps to avoid the overfitting issue. For the results, the BILSTM is compared against different classifiers such as Recurrent Neural Network (RNN), Random Forest Classifier (RFC), and LSTM. Similarly, LFSOA-based hyperparameter tuning is contrasted with different optimization algorithms. The outputs show that LFSOA-based hyperparameter tuning in BILSTM achieved accuracy, precision, recall, and f1-score of 98.963%, 99.026%, 99.155%, and 95.758%, respectively, which are higher when compared to existing methods. Similarly, the BILSTM-LFSOA accomplished better results in statistical measures, including the Root Mean Square Error (RMSE) of 0.105, Mean Squared Error (MSE) of 0.011, Mean Absolute Error (MAE) of 0.094, and coefficient of determination (R2) of 0.954, respectively. From the overall analysis, the proposed BILSTM-LFSOA improves coconut yield prediction by achieving better results in all the performance measures when compared with existing models. The results of this study are important to many stakeholders, including but not limited to policymakers, farmers, banks, and insurance companies. As coconuts are an important crop in developing countries, accurate coconut yield forecasting will lead to greater financial and food security in these regions. [ABSTRACT FROM AUTHOR]

Addressing real-time optimization problems becomes increasingly challenging as their complexity continues to escalate over time. So bio-optimization algorithms (BoAs) come into the picture to solve such problems due to their global search capability, adaptability, versatility, parallelism, and robustness. This article aims to perform hyperparameter tuning of machine learning (ML) models by integrating them with BoAs. Aiming to maximize the accuracy of the hybrid bio-optimized defect prediction (HBoDP) model, this research paper develops four novel hybrid BoAs named the gravitational force Lévy flight grasshopper optimization algorithm (GFLFGOA), the gravitational force Lévy flight grasshopper optimization algorithm–sparrow search algorithm (GFLFGOA-SSA), the gravitational force grasshopper optimization algorithm–sparrow search algorithm (GFGOA-SSA), and the Lévy flight grasshopper optimization algorithm–sparrow search algorithm (LFGOA-SSA). These aforementioned algorithms are proposed by integrating the good exploration capacity of the SSA with the faster convergence of the LFGOA and GFGOA. The performances of the GFLFGOA, GFLFGOA-SSA, GFGOA-SSA, and LFGOA-SSA are verified by conducting two different experiments. Firstly, the experimentation was conducted on nine benchmark functions (BFs) to assess the mean, standard deviation (SD), and convergence rate. The second experiment focuses on boosting the accuracy of the HBoDP model through the fine-tuning of the hyperparameters in the artificial neural network (ANN) and XGBOOST (XGB) models. To justify the effectiveness and performance of these hybrid novel algorithms, we compared them with four base algorithms, namely the grasshopper optimization algorithm (GOA), the sparrow search algorithm (SSA), the gravitational force grasshopper optimization algorithm (GFGOA), and the Lévy flight grasshopper optimization algorithm (LFGOA). Our findings illuminate the effectiveness of this hybrid approach in enhancing the convergence rate and accuracy. The experimental results show a faster convergence rate for BFs and improvements in software defect prediction accuracy for the NASA defect datasets by comparing them with some baseline methods. [ABSTRACT FROM AUTHOR]

We consider two different time fractional telegrapher's equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal. [ABSTRACT FROM AUTHOR]

In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism's posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently. [ABSTRACT FROM AUTHOR]

The recently introduced coati optimization algorithm suffers from drawbacks such as slow search velocity and weak optimization precision. An enhanced coati optimization algorithm called CMRLCCOA is proposed. Firstly, the Sine chaotic mapping function is used to initialize the CMRLCCOA as a way to obtain better-quality coati populations and increase the diversity of the population. Secondly, the generated candidate solutions are updated again using the convex lens imaging reverse learning strategy to expand the search range. Thirdly, the Lévy flight strategy increases the search step size, expands the search range, and avoids the phenomenon of convergence too early. Finally, utilizing the crossover strategy can effectively reduce the search blind spots, making the search particles constantly close to the global optimum solution. The four strategies work together to enhance the efficiency of COA and to boost the precision and steadiness. The performance of CMRLCCOA is evaluated on CEC2017 and CEC2019. The superiority of CMRLCCOA is comprehensively demonstrated by comparing the output of CMRLCCOA with the previously submitted algorithms. Besides the results of iterative convergence curves, boxplots and a nonparametric statistical analysis illustrate that the CMRLCCOA is competitive, significantly improves the convergence accuracy, and well avoids local optimal solutions. Finally, the performance and usefulness of CMRLCCOA are proven through three engineering application problems. A mathematical model of the hypersonic vehicle cruise trajectory optimization problem is developed. The result of CMRLCCOA is less than other comparative algorithms and the shortest path length for this problem is obtained. [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]

This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model's solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus. [ABSTRACT FROM AUTHOR]

Underground coal seam mining significantly reduces the stability of slopes, especially soil slopes, and an accurate evaluation of the stability of soil slopes under underground mining conditions is crucial for mining safety. In this study, the impact of coal seam mining is considered as the additional horizontal and vertical stresses acting on the slope, and an equation for calculating the safety factor of soil slopes under underground mining conditions is derived based on the rigorous Janbu method. Then, the Improved Radial Movement Optimization (IRMO) algorithm is introduced and combined with Lévy flight optimization to conduct global optimization searches, obtaining the critical sliding surface and corresponding safety factor of the soil slope under underground coal seam mining. Through comparisons with the numerical simulation results in three different case studies, the feasibility of applying the IRMO algorithm with Lévy flight to analyze the stability of soil slopes under underground mining is demonstrated. This ensures the accuracy and stability of the calculation results while maintaining a high convergence efficiency. Furthermore, the effects of the mining thickness and mining direction on slope stability are analyzed, and the results indicate that a smaller mining thickness and mining along the slope are advantageous for slope stability. The method proposed in this study provides valuable insights for preventing the slope instability hazards caused by underground coal seam mining. [ABSTRACT FROM AUTHOR]

The precise mathematical description of gaze patterns remains a topic of ongoing debate, impacting the practical analysis of eye-tracking data. In this context, we present evidence supporting the appropriateness of a Lévy flight description for eye-gaze trajectories, emphasizing its beneficial scale-invariant properties. Our study focuses on utilizing these properties to aid in diagnosing Attention-Deficit and Hyperactivity Disorder (ADHD) in children, in conjunction with standard cognitive tests. Using this method, we found that the distribution of the characteristic exponent of Lévy flights statistically is different in children with ADHD. Furthermore, we observed that these children deviate from a strategy that is considered optimal for searching processes, in contrast to non-ADHD children. We focused on the case where both eye-tracking data and data from a cognitive test are present and show that the study of gaze patterns in children with ADHD can help in identifying this condition. Since eye-tracking data can be gathered during cognitive tests without needing extra time-consuming specific tasks, we argue that it is in a prime position to provide assistance in the arduous task of diagnosing ADHD. [ABSTRACT FROM AUTHOR]

We propose a doubly subordinated Lévy process, the normal double inverse Gaussian (NDIG), to model the time series properties of the cryptocurrency bitcoin. By using two subordinated processes, NDIG captures both the skew and fat-tailed properties of, as well as the intrinsic time driving, bitcoin returns and gives rise to an arbitrage-free option pricing model. In this framework, we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Chicago Board Options Exchange VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both volatility measures are compared to the volatility based on the historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures the observed in-sample volatility. [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]

Advances built into recent sUASs (drones) offer a compelling possibility for field-based data collection in logistically challenging and GPS-denied environments. sUASs-based photogrammetry generates 3D models of features and landscapes, used extensively in archaeology as well as other field sciences. Until recently, navigation has been limited by the expertise of the pilot, as objects, like trees, and vertical or complex environments, such as cliffs, create significant risks to successful documentation. This article assesses sUASs' capability for autonomous obstacle avoidance and 3D flight planning using data collection scenarios carried out in Black Mesa, Oklahoma. Imagery processed using commercial software confirmed that the collected data can build photogrammetric models suitable for general archaeological documentation. The results demonstrate that new capabilities in drones may open up new field environments previously considered inaccessible, too risky, or costly for fieldwork, especially for all but the most expert pilots. Emerging technologies for drone-based photogrammetry, such as the Skydio 2+ considered here, place remote, rugged terrain within reach of many archaeological research units in terms of commercial options and cost. [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]

Rapid coal mining results in a series of mining subsidence damages. Predicting surface movement and deformation accurately is essential to reducing mining damage. The accurate determination of parameters for a mining subsidence prediction model is crucial for accurately predicting mining subsidence. In this research, with the incorporation of the Sobol sequence and Lévy flight strategy, we propose an improved whale optimization algorithm (IWOA), thereby enhancing its global optimization capability and mitigating local optimization issues. Our simulation experiment results demonstrate that the IWOA achieved a root mean square error and relative error of less than 0.42 and 0.27%, respectively, indicating its superior accuracy compared to a basic algorithm. The IWOA inversion model also exhibits superior performance compared to a basic algorithm in mitigating gross error interference, Gaussian noise interference, and missing observation point interference. Additionally, it demonstrates enhanced global search capabilities. The IWOA was employed to perform parameter inversion for the working face 1414(1) in Guqiao Coal Mine. The root mean square error of the inversion results did not exceed 6.03, while the subsidence coefficient q, tangent of the main influence angle tanβ, horizontal movement coefficient b, and mining influence propagation angle θ were all below 0.32. The average value of the fitted root mean square error for the subsidence value's fitted root mean square error and horizontal movement value's fitted root mean square error of the IWOA was 91.51 mm, which satisfies the accuracy requirements for general engineering applications. [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]

Wind-power generators around the world face two risks, one due to changes in wind intensity impacting energy production, and the second due to changes in electricity retail prices. To hedge these risks simultaneously, the quanto option is an ideal financial tool. The natural logarithm of electricity prices of the study will be modeled with a variance gamma (VG) and normal inverse Gaussian (NIG) processes, while wind speed and power series will be modeled with an Ornstein–Uhlenbeck (OU) process. Since the risk from changing wind-power production and spot prices is highly correlated, we must model this correlation as well. This is reproduced by replacing the small jumps of the Lévy process with a Brownian component and correlating it with wind power and speed OU processes. Then, we will study the income of the wind-energy company from a stochastic point of view, and finally, we will price the quanto option of European put style for the wind-energy producer. We will compare quanto option prices obtained from the VG process and NIG process. The novelty brought into this study is the use of a new dataset in a new geographic location and a new Lévy process, VG, apart from NIG. [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]

We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. [ABSTRACT FROM AUTHOR]

Cloud Manufacturing (CMfg) has attracted lots of attention from scholars and practitioners. The purpose of quality of service (QoS)-aware manufacturing cloud service composition (MCSC), as one of the key issues in CMfg, is to combine different available manufacturing cloud services (MCSs) to generate an optimized MCSC that can meet the diverse requirements of customers. However, many available MCSs, deployed in the CMfg platform, have the same function but different QoS attributes. It is a great challenge to achieve optimal MCSC with a high QoS. In order to obtain better optimization results efficiently for the QoS-MCSC problems, a whale optimization algorithm (WOA) with adaptive weight, Lévy flight, and adaptive crossover strategies (ASWOA) is proposed. In the proposed ASWOA, adaptive crossover inspired by the genetic algorithm is developed to balance exploration and exploitation. The Lévy flight is designed to expand the search space of the WOA and accelerate the convergence of the WOA with adaptive crossover. The adaptive weight is developed to extend the search scale of the exploitation. Simulation and comparison experiments are conducted on various benchmark functions and different scale QoS-MCSC problems. The QoS attributes of the problems are randomly and symmetrically generated. The experimental results demonstrate that the proposed ASWOA outperforms other compared cutting-edge algorithms. [ABSTRACT FROM AUTHOR]

To overcome the limitations of the sparrow search algorithm and the challenges of dynamic obstacle avoidance in mobile robots, an integrated method combining the enhanced sparrow search algorithm with the dynamic window approach is introduced. First, logistic–tent chaotic mapping is utilized for the initialization of the sparrow population, thereby achieving a uniform distribution of the sparrow population and simultaneously enhancing the exploratory capability of the algorithm. The implementation of the elite reverse learning strategy aims to diversify the sparrow population, thus improving the quality of initial solutions and the algorithm's search accuracy. Additionally, the position update dynamic self-adaptive adjustment strategy is adopted to enhance the optimization capability of the algorithm by refining the position update formulas for both producers and scroungers. By combining the Lévy flight strategy and the optimal position perturbation strategy, the algorithm's efficacy in escaping local optima can be improved. Second, an adaptive velocity adjustment strategy is presented for the dynamic window approach and optimized for its evaluation function to enhance the safety of the path. Third, the enhanced sparrow search algorithm is integrated with the dynamic window approach to tackle the problems of the non-smooth global path and inadequate dynamic obstacle avoidance capability. Both simulation and experimental results show the superiority of the enhanced sparrow search algorithm in comparison to other algorithms in terms of the path length, total rotation angle, and algorithm execution time. Notably, in comparison to the basic sparrow search algorithm, there is a decrease in average path lengths by 15.31% and 11.92% in the improved sparrow search algorithm. The integrated algorithm not only crafts local paths rooted in global paths but also adeptly facilitates real-time dynamic obstacle evasion, ensuring the robot's safe arrival at its destination. [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]

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]

In order to improve the operation reliability and new energy consumption rate of the combined wind–solar storage system, an optimal allocation method for the capacity of the energy storage system (ESS) based on the improved sand cat swarm optimization algorithm is proposed. First, based on the structural analysis of the combined system, an optimization model of energy storage configuration is established with the objectives of the lowest total investment cost of the ESS, the lowest load loss rate and the lowest new energy abandonment rate, which not only takes into account the economy of energy storage construction for investors and builders, but also reduces the probability of blackout for users to protect their interests and improves the utilization rate of the natural resources of wind and light, which can achieve a multi-win–win situation. The model can realize the win–win situation in many aspects. Secondly, an improved k-means clustering algorithm is used to cluster the renewable energy power and load data to realize the typical day data extraction. Then, for the proposed multi-objective optimization model, an SCSO is proposed based on the triangular wandering strategy, Lévy flight strategy and lens imaging reverse learning improvement, which can help the algorithm to jump out of the local optimum while improving its global optimization ability, and these improvements can significantly improve the optimization effect of the SCSO. Finally, simulation analysis is carried out in combination with typical daily extraction data, and the results verify the advantages and effectiveness of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

Despite having some fluctuations and the impact of the COVID-19 crisis, the demand for flights had a general growing trend for the past years. As the airspace is limited, efforts to better manage the total number of flights are noteworthy. In addition, volatility (i.e., unpredicted changes) in the number of flights has been observed to be increasing. Efforts to improve flight forecasting are thus necessary to improve air traffic efficiency and reduce costs. In this study, volatility in the number of flights is estimated based on past trends, and the outcomes are used to project future levels. This enables risk situations such as having to manage unexpectedly high numbers of flights to be predicted. The methodological approach analyses the Functional Airspace Block of Central Europe (FABEC). Based on the number of flights for 2015–2019, the following are calculated: historic mean, variance, volatility, 95th percentile, flights per hour and flights per day of the week in different time zones in six countries. Due to the nature of air traffic and the overdispersion observed, this study uses counting data models such as negative binomial regressions. This makes it possible to calculate risk measures including expected shortfall (ES) and value at risk (VaR), showing for each hour that the number of flights can exceed planned levels by a certain number. The study finds that in Germany and Belgium at 13:00 h there is a 5% worst-case possibility of having averages of 683 and 246 flights, respectively. The method proposed is useful for planning under uncertainties. It is conducive to efficient airspace management, so risk indicators help Air Navigation Service Providers (ANSPs) to plan for low-probability situations in which there may be large numbers of flights. [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]

We investigate ground states of a (nonlocal) nonlinear Schrödinger equation which generalizes classical (fractional, relativistic, etc.) Schrödinger equations, so that we extend relevant results and study common properties of these equations in a uniform way. To obtain the existence of ground states, we first solve a minimization problem and then prove that the solution of the minimization problem is a ground state of the equation. After examining the regularity of the solutions to the equation, we demonstrate that any ground state is sign-definite. [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]

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 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]

A multi-strategy crazy sparrow search algorithm (LTMSSA) for logic-tent hybrid chaotic maps is given in the research to address the issues of poor population diversity, slow convergence, and easily falling into the local optimum of the sparrow search algorithm (SSA). Firstly, the LTMSSA employs an elite chaotic backward learning strategy and an improved discoverer-follower ratio factor to improve the population's quality and diversity. Secondly, the LTMSSA updates the positions of discoverers and followers by the crazy operator and the Lévy flight strategy to expand the selection range of target following individuals. Finally, during the algorithm's optimization search, the LTMSSA introduces the tent hybrid and Corsi variable perturbation strategies to improve the population's ability to jump out of the local optimum. Different types and dimensions of test functions are used as performance benchmark functions to test the performance of the LTMSSA with SSA variants and other algorithms. The simulation results show that the LTMSSA can jump out of the optimal local solution, converge faster, and have higher accuracy. Its overall performance is better than the other seven algorithms, and the LTMSSA can find smaller optimal values than other algorithms in the welded beam and reducer designs. The results confirm that the LTMSSA is an effective aid for computationally complex practical tasks, provides high-quality solutions, and outperforms other algorithms. [ABSTRACT FROM AUTHOR]

With the swift advancement of the geometric modeling industry and computer technology, traditional generalized Ball curves and surfaces are challenging to achieve the geometric modeling of various complex curves and surfaces. Constructing an interpolation curve for the given discrete data points and optimizing its shape have important research value in engineering applications. This article uses an improved golden eagle optimizer to design the shape-adjustable combined generalized cubic Ball interpolation curves with ideal shape. Firstly, the combined generalized cubic Ball interpolation curves are constructed, which have global and local shape parameters. Secondly, an improved golden eagle optimizer is presented by integrating Lévy flight, sine cosine algorithm, and differential evolution into the original golden eagle optimizer; the three mechanisms work together to increase the precision and convergence rate of the original golden eagle optimizer. Finally, in view of the criterion of minimizing curve energy, the shape optimization models of combined generalized cubic Ball interpolation curves that meet the C1 and C2 smooth continuity are instituted. The improved golden eagle optimizer is employed to deal with the shape optimization models, and the combined generalized cubic Ball interpolation curves with minimum energy are attained. The superiority and competitiveness of improved golden eagle optimizer in solving the optimization models are verified through three representative numerical experiments. [ABSTRACT FROM AUTHOR]