Search Results (255)

This study presents a comparative analysis of two bio-inspired optimization techniques: the Dragonfly Algorithm (DA) and Cuckoo Search (CS). The DA models the collective behavior of dragonflies, replicating dynamic processes such as foraging, evasion, and synchronized movement to effectively explore and exploit the solution space. In contrast, the CS algorithm draws inspiration from the brood parasitism strategy observed in certain Cuckoo species, where eggs are laid in the nests of other birds, thereby leveraging randomization and selection mechanisms for optimization. To enhance the performance of both algorithms, Type-2 fuzzy logic systems were integrated into their structures. Specifically, the DA was fine-tuned through the adjustment of its inertia weight (W) and attraction coefficient (Beta), while the CS algorithm was optimized by calibrating the Lévy flight distribution parameter. A comprehensive set of benchmark functions, F1 through F10, was employed to evaluate and compare the effectiveness and convergence behavior of each method under fuzzy-enhanced configurations. Results indicate that the fuzzy-based adaptations consistently improved convergence stability and accuracy, demonstrating the advantage of integrating Type-2 fuzzy parameter control into swarm-based optimization frameworks. Full article

To overcome the limitations of traditional multi-objective evolutionary algorithms—which often become trapped in local optima when addressing complex optimization problems and face challenges in balancing convergence efficiency with population diversity—this study proposes an enhanced NSGA-II algorithm that incorporates Lévy flight and simulated annealing strategies. The proposed algorithm enhances global exploration via Lévy flight mutation, improves local search precision through simulated annealing, and dynamically coordinates the search process using adaptive parameter strategies. Experiments conducted on the ZDT and DTLZ test function series demonstrated that the proposed algorithm achieves performance comparable to or better than that of NSGA-II and other benchmark algorithms, as measured by inverted generational distance and hypervolume metrics. It also exhibited superior convergence, distribution uniformity, and robustness. Furthermore, the algorithm was applied to the multi-objective optimization of electric winch trajectories for oil drilling rigs, which employed trajectory planning based on quintic polynomials. The simulation results demonstrated, compared to the pre-optimization baseline data, reductions of 6% in total operation time, 17.99% in energy consumption, and 27.4% in impact severity, thereby validating the method’s effectiveness and applicability in practical engineering scenarios. The comprehensive results demonstrate that the improved algorithm exhibits robust performance and excellent adaptability when addressing complex multi-objective optimization problems. Full article

We forecast short time series iteratively using a model based on stochastic differential equations. The recorded process is assumed to be consistent with an $\alpha$-stable Lévy motion. The generalized moments method provides the values of the scaling exponent and the parameter $\alpha$, which determine the form of the stochastic term at each iteration. Seven weekly recorded economic time series—the DAX, CAC, FTSE100, MIB, AEX, IBEX, and STOXX600—were examined for the period from 2020 to 2025. The parameter $\alpha$ is always 2 for the four of them, FTSE100, AEX, IBEX, and STOXX600, indicating quasi-Gaussian processes. For FTSE100, IBEX, and STOXX600, the processes are anti-persistent (H < 0.5).The rest of the examined markets show characteristics of uncorrelated processes whose values are drawn from either a log-normal or a log-Lévy distribution. Further, all processes are multifractal, as the non-zero value of the mean intermittency indicates. The model’s forecasts, with the time horizon always one-step-ahead, are compared to the forecasts of a properly chosen ARIMA model combined with Monte Carlo simulations. The low values of the absolute percentage error indicate that both models function well. The model’s outcomes are further compared to ARIMA forecasts by using the Diebold–Mariano test, which yields a better forecast ability for the proposed model since it has less average loss. The ability and accuracy of the model to forecast even small time series is further supported by the low value of the absolute percentage error; the value of 4 serves as an upper limit for the majority of the forecasts. Full article

To address the problems of local optima and insufficient convergence accuracy in parameter identification of primary frequency regulation (PFR) for steam turbines, this paper proposed a hybrid identification method that integrated an Improved Bayesian Optimization (IBO) algorithm and an Improved Whale Optimization Algorithm (IWOA). By initializing the Bayesian parameter population using Tent chaotic mapping and the reverse learning strategy, employing a radial basis kernel function hyperparameter training mechanism based on the Adam optimizer and optimizing the Expected Improvement (EI) function using the Limited-memory Broyden–Fletcher– Goldfarb–Shanno with Bounds (L-BFGS-B) method, IBO was proposed to obtain the optimal candidate set with the smallest objective function value. By introducing a nonlinear convergence factor and the adaptive Levy flight perturbation strategy, IWOA was proposed to obtain locally optimized optimal solutions. By using the reverse-guided optimization mechanism and employing a fitness-oriented selection strategy, the optimal solution was chosen to complete the closed-loop process of reverse learning feedback. Nine standard test functions and the Proportional Integral Derivative (PID) parameter identification of the electro-hydraulic servo system in a 330 MW steam turbine were presented as examples. Compared with Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Bayesian Optimization (BO) and Particle Swarm Optimization-Grey Wolf Optimizer (PSO-GWO), the Improved Bayesian Optimization-Whale Optimization Algorithm (IBO-WOA) proposed in this paper has been validated to effectively avoid the problem of getting stuck in local optima during complex optimization and has high parameter recognition accuracy. Meanwhile, an Out-Of-Distribution (OOD) Test based on noise injection had demonstrated that IBO-WOA had good robustness. The time constant identification of the steam turbine were carried out using IBO-WOA under two experimental conditions, and the identification results were input into the PFR model. The simulated power curve can track the experimental measured curve well, proving that the parameter identification results obtained by IBO-WOA have high accuracy and can be used for the modeling and response characteristic analysis of the steam turbine PFR. Full article

Using a Donsker-type construction, we prove the existence of a new class of processes, which we call the self-stabilizing processes. These processes have a particular property: the “local intensities of jumps” vary with the values. Moreover, we also show that the self-stabilizing processes have many other good properties, such as stochastic Hölder continuity and strong localizability. Such a self-stabilizing process is simultaneously a Markov process, a martingale (when the local index of stability is greater than 1), a self-scaling process and a self-regulating process. Full article

Accurate prediction of component content in the rare-earth extraction and separation process is crucial for control system design, product quality control, and optimization of energy consumption. To improve prediction accuracy and modeling efficiency, this paper proposes a model for predicting component content based on an Improved Black-winged Kite Algorithm-Optimized Stochastic Configuration Network (IBKA-SCN). First, we develop an Improved Black-winged Kite Algorithm (IBKA), incorporating good point set initialization and Lévy random-walk strategies to enhance global optimization capability. Theoretical convergence analysis is provided to ensure the stability and effectiveness of the algorithm. Second, to address the issue that constraint parameters and weight-scaling factors in Stochastic Configuration Network (SCN) rely on manual experience and struggle to balance accuracy and efficiency, IBKA is employed to adaptively search for the optimal hyperparameter combination. The applicability of IBKA-SCN is corroborated through four real-world regression tasks. Finally, the effectiveness of the proposed method is validated through an engineering case study on predicting component content. The results show that IBKA-SCN significantly outperforms existing mainstream methods in both prediction accuracy and modeling speed. Full article

With increasing urbanization and population growth, the volume of municipal solid waste (MSW) continues to rise. Efficient and environmentally responsible waste processing has become a core issue in sustainable development. Incineration plays a key role in reducing landfill usage and recovering energy from waste, contributing to circular economy initiatives. However, fluctuations in furnace temperature significantly affect combustion efficiency and emissions, undermining the environmental benefits of incineration. To address these challenges under dynamic operational conditions, this paper proposes a hybrid model combining an Improved Snow Ablation Optimizer (ISAO), Dual-Branch Convolutional Neural Network (DBCNN), and Bidirectional Long Short-Term Memory (BiLSTM). The model extracts dynamic features from control and condition variables and incorporates time series characteristics for accurate temperature prediction, thereby enhancing the overall efficiency of the incineration process. ISAO integrates Lévy flight, differential mutation, and elitism strategies to optimize parameters, contributing to better energy recovery and reduced emissions. Experimental results on real MSWI data demonstrate that the proposed method achieves high prediction accuracy and adaptability under varying operating conditions, showcasing its robustness and application potential in promoting sustainable waste management practices. By improving combustion efficiency and minimizing environmental impact, this model aligns with global sustainability goals, supporting a more efficient, eco-friendly waste-to-energy process. Full article

Each charging/discharging cycle leads to a gradual decrease in the battery’s capacity. The degradation of capacity in lithium-ion batteries represents a non-monotonous process with random jumps. Earlier studies claimed that the instantaneous degradation value of a lithium-ion battery is influenced by the historical dataset with long-range dependence. The existing methods ignore large jumps and long-range dependences in degradation processes. In order to capture long-range-dependent behavior with random jumps, we refer to the fractional Poisson process. We also outline the relationship between the long-range correlation and the Hurst index. The connection between random jumps in capacitance and long-range dependence of the fractional Poisson process is proven. In order to construct the fractional Poisson predictive model, we included fractional Brownian motion as the diffusion term and the fractional Poisson process as the jump term. The proposed approach is implemented on NASA’s dataset for Li-ion battery degradation. We believe that the error analysis for the fractional Poisson process is advantageous compared with that of the fractional Brownian motion, the fractional Levy stable motion, the Wiener model, and the long short-term memory model. Full article

As a crucial modeling tool for stochastic financial markets, the Lévy risk model effectively characterizes the evolution of risks during enterprise operations. Through dynamic evaluation and quantitative analysis of risk indicators under specific dividend- distribution strategies, this model can provide theoretical foundations for optimizing corporate capital allocation. Addressing the inadequate adaptability of traditional single-period threshold strategies in time-varying market environments, this paper proposes a dividend strategy based on multiperiod dynamic threshold adjustments. By implementing periodic modifications of threshold parameters, this strategy enhances the risk model’s dynamic responsiveness to market fluctuations and temporal variations. Within the framework of the spectrally negative Lévy risk model, this paper constructs a stochastic control model for multiperiod threshold dividend strategies. We derive the integro-differential equations for the expected present value of aggregate dividend payments before ruin and the Gerber–Shiu function, respectively. Combining the methodologies of the discounted increment density, the operator introduced by Dickson and Hipp, and the inverse Laplace transforms, we derive the explicit solutions to these integro-differential equations. Finally, numerical simulations of the related results are conducted using given examples, thereby demonstrating the feasibility of the analytical method proposed in this paper. Full article

The core structure of modern power systems reflects a fundamental symmetry between electricity supply and demand, and accurate load forecasting is essential for maintaining this dynamic balance. To improve the accuracy of short-term load forecasting in power systems, this paper proposes a novel model that combines a Multi-Strategy Improved Sand Cat Swarm Optimization algorithm (MSCSO) with a Self-Attention Temporal Convolutional Network (SA TCN). The model constructs efficient input features through data denoising, correlation filtering, and dimensionality reduction using UMAP. MSCSO integrates Uniform Tent Chaos Mapping, a sensitivity enhancement mechanism, and Lévy flight to optimize key parameters of the SA TCN, ensuring symmetrical exploration and stable convergence in the solution space. The self-attention mechanism exhibits structural symmetry when processing each position in the input sequence and does not rely on fixed positional order, enabling the model to more effectively capture long-term dependencies and preserve the symmetry of the sequence structure—demonstrating its advantage in symmetry-based modeling. Experimental results on historical load data from Panama show that the proposed model achieves excellent forecasting accuracy (RMSE = 24.7072, MAE = 17.5225, R² = 0.9830), highlighting its innovation and applicability in symmetrical system environments. Full article

To address the decline in measurement accuracy of magnetometers due to process errors and environmental interference, as well as the insufficient robustness of traditional calibration algorithms under strong interference conditions, this paper proposes an ellipsoid fitting algorithm based on Dynamic Adaptive Elite Particle Swarm Optimization (DAEPSO). The proposed algorithm integrates three enhancement mechanisms: dynamic stratified elite guidance, adaptive inertia weight adjustment, and inferior particle relearning via Lévy flight, aiming to improve convergence speed, solution accuracy, and noise resistance. First, a magnetometer calibration model is established. Second, the DAEPSO algorithm is employed to fit the ellipsoid parameters. Finally, error calibration is performed based on the optimized ellipsoid parameters. Our simulation experiments demonstrate that compared with the traditional Least Squares Method (LSM) the proposed method reduces the standard deviation of the total magnetic field intensity by 54.73%, effectively improving calibration precision in the presence of outliers. Furthermore, when compared to PSO, TSLPSO, MPSO, and AWPSO, the sum of the absolute distances from the simulation data to the fitted ellipsoidal surface decreases by 53.60%, 41.96%, 53.01%, and 27.40%, respectively. The results from 60 independent experiments show that DAEPSO achieves lower median errors and smaller interquartile ranges than comparative algorithms. In summary, the DAEPSO-based ellipsoid fitting algorithm exhibits high fitting accuracy and strong robustness in environments with intense interference noise, providing reliable theoretical support for practical engineering applications. Full article

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

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity. Full article

This paper establishes a new stochastic SIR epidemic model that incorporates telegraph noise and Lévy noise to simulate the complex environmental disturbances affecting disease transmission. Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller based on an integral sliding surface and an adaptive control law is proposed. This controller is capable of stabilizing the constructed model and effectively suppressing the spread of the disease. The main contributions of this paper include the following: establishing a comprehensive and realistic stochastic SIR model that accounts for the complex impacts of telegraph noise (symbolizing periodic environmental changes) and Lévy noise (representing sudden environmental shocks) on the dynamics of disease transmission; employing T-S fuzzy modeling, which considers the design of fuzzy rules and the symmetry of membership functions, to ensure linearization of the model; constructing an integral sliding surface and designing an adaptive sliding mode controller for the fuzzy-processed model. Finally, the effectiveness of the proposed control method is validated through numerical simulations. 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