Search Results (55)

In some problems, partial differential equations are reduced to ordinary differential equations. In special cases, when incorporating randomness, equations can be reduced to systems of stochastic differential Equations (SDEs). Stochastic averaging for a class of stochastic differential equations with fractional Brownian motion and non-Gaussian Lévy noise is considered. Stability criteria for systems of stochastic differential equations with fractional Brownian motion and non-Gaussian Lévy noise do not currently exist. Usually, studies on determining the sensitivity of solutions to the accuracy of setting the initial conditions are being conducted to explain the phenomenon of deterministic chaos. These studies show both convergence in mean square and convergence in probability to averaged systems of stochastic differential equations driven by fractional Brownian motion and Lévy process. The solutions to systems can be approximated by solutions to averaged stochastic differential equations by using the stochastic averaging. Full article

This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-state distributions are, respectively, Gauss and Levy. As the Levy-driven OUP: the motions can display the Noah effect (heavy-tailed amplitudal fluctuations); and their memory structure is tunable. And, as Gaussian-stationary processes: the motions can display the Joseph effect (long-ranged temporal dependencies); and their correlation structure is tunable. The motions have two parameters: a critical exponent which determines the Noah effect and the memory structure; and a clock function which determines the Joseph effect and the correlation structure. The novel class is a compelling stochastic model due to the following combination of facts: on the one hand the motions are tractable and amenable to analysis and use; on the other hand the model is versatile and the motions display a host of both regular and anomalous features. Full article

Robotic tack welding poses challenges in path optimization due to local optimum entrapment, limited adaptability, and high-dimensional complexity. To overcome these challenges, a Lévy flight-enhanced improved whale optimization algorithm (LF-IWOA) was developed. The algorithm combines elite opposition-based learning (EOBL), differential evolution (DE), and Lévy flight (LF) to improve global exploration capability, increase population diversity, and improve convergence. Additionally, a dynamic trajectory optimization model is designed to consider joint-level constraints, including velocity, acceleration, and jerk. The performance of LF-IWOA was evaluated using two industrial workpieces with varying welding point distributions. Comparative experiments with metaheuristic algorithms, such as the genetic algorithm (GA), WOA and other recent nature-inspired methods, show that LF-IWOA consistently achieves shorter paths and faster convergence. For Workpiece 1, the algorithm reduces the welding path by up to 25.53% compared to the genetic algorithm, with an average reduction of 14.82% across benchmarks. For Workpiece 2, the optimized path is 18.41% shorter than the baseline. Moreover, the dynamic trajectory optimization strategy decreases execution time by 26.83% and reduces mechanical energy consumption by 15.40% while maintaining smooth and stable joint motion. Experimental results demonstrated the effectiveness and practical applicability of the LF-IWOA in robotic welding tasks. Full article

Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time series’s next value by analysing its past. The input financial data are assumed to be consistent with an $\alpha$-stable Lévy motion. The computation of the scaling exponent and the value of $\alpha$, which characterises the type of the $\alpha$-stable Lévy motion, are crucial for the iterative scheme. These two indices can be determined at each iteration from the form of the structure function, for the computation of which we use the method of generalised moments. Their values are used for the creation of the corresponding $\alpha$-stable Lévy noise, which acts as a seed for the stochastic component. Furthermore, the drift and diffusion terms are calculated at each iteration. The proposed model is general, allowing the kind of stochastic process to vary from one iterative step to another, and its applicability is not restricted to financial data. As a case study, we consider Greece’s stock market general index over a period of five years, from September 2019 to September 2024, after the completion of bailout programmes. Greece’s economy changed from a restricted to a free market over the chosen era, and its stock market trading increments are likely to be describable by an $\alpha$-stable L’evy motion. We find that $\alpha =2$ and the scaling exponent H varies over time for every iterative step we perform. The forecasting points follow the same trend, are in good agreement with the actual data, and for most of the forecasts, the percentage error is less than 2%. Full article

Software testing identifies potential errors and defects in software. A crucial component of software testing is integration testing, and the generation of class integration test orders (CITOs) is a critical topic in integration testing. The research shows that search-based algorithms can solve this problem effectively. As a novel search-based algorithm, the sparrow search algorithm (SSA) is good at finding the optimal to optimization problems, but it has drawbacks like weak population variety later on and the tendency to easily fall into the local optimum. To overcome its shortcomings, a modified sparrow search algorithm (MSSA) is developed and applied to the CITO generation issue. The algorithm is initialized with a good point set strategy, which distributes the sparrows evenly in the solution space. Then, the discoverer learning strategy of Brownian motion is introduced and the Levy flight is utilized to renew the positions of the followers, which balances the global search and local search of the algorithm. Finally, the optimal solution is subjected to random wandering to increase the probability of the algorithm jumping out of the local optimum. Using the overall stubbing complexity as a fitness function to evaluate different class test sequences, experiments are conducted on open-source Java systems, and the experimental results demonstrate that the MSSA generates test orders with lower stubbing cost in a shorter time than other novel intelligent algorithms. The superiority of the proposed algorithm is verified by five evaluation indexes: the overall stubbing complexity, attribute complexity, method complexity, convergence speed, and running time. The MSSA has shown significant advantages over the BSSA in all aspects. Among the nine systems, the total overall stubbing complexity of the MSSA is 13.776% lower than that of the BSSA. Total time is reduced by 23.814 s. Full article

Path planning is of great research significance as it is key to affecting the efficiency and safety of mobile robot autonomous navigation task execution. The traditional gray wolf optimization algorithm is widely used in the field of path planning due to its simple structure, few parameters, and easy implementation, but the algorithm still suffers from the disadvantages of slow convergence, ease of falling into the local optimum, and difficulty in effectively balancing exploration and exploitation in practical applications. For this reason, this paper proposes a multi-strategy improved gray wolf optimization algorithm (MSIAR-GWO) based on reinforcement learning. First, a nonlinear convergence factor is introduced, and intelligent parameter configuration is performed based on reinforcement learning to solve the problem of high randomness and over-reliance on empirical values in the parameter selection process to more effectively coordinate the balance between local and global search capabilities. Secondly, an adaptive position-update strategy based on detour foraging and dynamic weights is introduced to adjust the weights according to changes in the adaptability of the leadership roles, increasing the guiding role of the dominant individual and accelerating the overall convergence speed of the algorithm. Furthermore, an artificial rabbit optimization algorithm bypass foraging strategy, by adding Brownian motion and Levy flight perturbation, improves the convergence accuracy and global optimization-seeking ability of the algorithm when dealing with complex problems. Finally, the elimination and relocation strategy based on stochastic center-of-gravity dynamic reverse learning is introduced for the inferior individuals in the population, which effectively maintains the diversity of the population and improves the convergence speed of the algorithm while avoiding falling into the local optimal solution effectively. In order to verify the effectiveness of the MSIAR-GWO algorithm, it is compared with a variety of commonly used swarm intelligence optimization algorithms in benchmark test functions and raster maps of different complexities in comparison experiments, and the results show that the MSIAR-GWO shows excellent stability, higher solution accuracy, and faster convergence speed in the majority of the benchmark-test-function solving. In the path planning experiments, the MSIAR-GWO algorithm is able to plan shorter and smoother paths, which further proves that the algorithm has excellent optimization-seeking ability and robustness. Full article

In this paper, we consider a class of stochastic differential equations driven by multiplicative $\alpha$-stable ($0<\alpha <2$) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster–Lyapunov criteria. Full article

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents $\{{\gamma }_1,{\gamma }_2,\dots \}$ under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI. Full article

Oilfield Sewage System Scheduling is a complicated, large-scale, nonlinear system problem with multiple variables. The complexity of the sewage system pipeline network connection grows along with the ongoing building of oilfield stations, and the shortcomings of the sewage system water quantity scheduling program based on human experience decision-making become increasingly apparent. The key to solving this problem is to realize the digital and intelligent scheduling of sewage systems. Taking the sewage system of an oil production plant in Daqing oilfield as the research object, the water scheduling model of the sewage system is established in this paper. Aiming at the complex nonlinear characteristics of the model, the Levy flight speed updating operator, the adaptive stochastic offset operator, and the Brownian motion selection optimization operator are established by taking advantage of the particle swarm optimization (PSO) and the cuckoo search (CS) algorithm. Based on these operators, a hybrid PSO-CS algorithm is proposed, which jumps out of the local optimum and has a strong global search capability. Comparing PSO-CS with other algorithms on the CEC2022 test set, it was found that the PSO-CS algorithm ranked first in all 12 test functions, proving the excellent solving performance of the PSO-CS algorithm. Finally, the PSO-CS is applied to solve a water scheduling model for the sewage system of an oil production plant in Daqing Oilfield. It is found that the scheduling plan optimized by PSO-CS has a 100% water supply rate to the downstream water injection station, and the total energy consumption of the scheduling plan on the same day is reduced from 879.95 × 10⁶ m⁵/d to 712.84 × 10⁶ m⁵/d, which is a 19% reduction in energy consumption. The number of water balance stations in the sewage station increased by 7, which effectively improved the water resource utilization rate of the sewage station. Full article

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. Full article

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems. Full article

Aiming at the problem of path planning for autonomous underwater vehicle (AUV) to cope with the influence of obstacles and eddies in complex marine environments, a path planning method based on an improved salp swarm algorithm (ISSA) is proposed. Firstly, the motion model of the AUV and eddy current model are constructed, including the relationship between position, velocity, attitude, and control inputs. Secondly, the improved SSA is proposed, which introduces the Levy flight strategy to enhance the algorithm’s optimization seeking ability and adds a nonlinear convergence factor to enhance the convergence ability of the algorithm. The stability and robustness of the improved algorithm are verified by test functions. Finally, the ISSA is applied to AUV path planning, which optimizes the AUV travel distance, improves the search efficiency and accuracy, and avoids the local optimum of the algorithm. The ISSA enhances the adaptive ability and robustness of the algorithm by introducing a dynamic adjustment strategy and feedback mechanism. Experimental verification is carried out using a simulated marine environment. The results show that the ISSA is better than the traditional algorithm in terms of path length as well as algorithm stability, and can effectively improve the navigation performance of AUV. Full article

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. Full article

The rapid advancement of artificial intelligence technology has significantly enhanced the intelligence of mobile robots, facilitating their widespread utilization in unmanned driving, smart home systems, and various other domains. As the scope, scale, and complexity of robot deployment continue to expand, there arises a heightened demand for enhanced computational power and real-time performance, with path planning emerging as a prominent research focus. In this study, we present an adaptive Lévy flight–rotation slime mold algorithm (LRSMA) for global robot motion planning, which incorporates LRSMA with the cubic Hermite interpolation. Unlike traditional methods, the algorithm eliminates the need for a priori knowledge of appropriate interpolation points. Instead, it autonomously detects the convergence status of LRSMA, dynamically increasing interpolation points to enhance the curvature of the motion curve when it surpasses the predefined threshold. Subsequently, it compares path lengths resulting from two different objective functions to determine the optimal number of interpolation points and the best path. Compared to LRSMA, this algorithm reduced the minimum path length and average processing time by (2.52%, 3.56%) and (38.89%, 62.46%), respectively, along with minimum processing times. Our findings demonstrate that this method effectively generates collision-free, smooth, and curvature-constrained motion curves with the least processing time. Full article

The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows for the detection of jumps in segmented trajectories with non-Gaussian confined parts. The value of each parameter indicates the contribution of confined segments. Non-Gaussian features in mRNA trajectories are attributed to trajectory segmentation. Each segment can be in one of the following diffusion modes: free diffusion, confined motion, and immobility. When free diffusion segments alternate with confined or immobile segments, the mean square displacement of the segmented trajectory resembles subdiffusion. Confined segments have both Gaussian (normal) and non-Gaussian statistics. If random trajectories are estimated as FLSM, they can exhibit either subdiffusion or Lévy diffusion. This approach can be useful for analyzing empirical data with non-Gaussian behavior, and statistical classification of diffusion trajectories helps reveal anomalous dynamics. Full article