Convergence Of Solutions Research Articles

Artificial neural network infused quasi oppositional learning partial reinforcement algorithm for structural design optimization of vehicle suspension components

Abstract This paper introduces and investigates an enhanced Partial Reinforcement Optimization Algorithm (E-PROA), a novel evolutionary algorithm inspired by partial reinforcement theory to efficiently solve complex engineering optimization problems. The proposed algorithm combines the Partial Reinforcement Optimization Algorithm (PROA) with a quasi-oppositional learning approach to improve the performance of the pure PROA. The E-PROA was applied to five distinct engineering design components: speed reducer design, step-cone pulley weight optimization, economic optimization of cantilever beams, coupling with bolted rim optimization, and vehicle suspension arm optimization problems. An artificial neural network as a metamodeling approach is used to obtain equations for shape optimization. Comparative analyses with other benchmark algorithms, such as the ship rescue optimization algorithm, mountain gazelle optimizer, and cheetah optimization algorithm, demonstrated the superior performance of E-PROA in terms of convergence rate, solution quality, and computational efficiency. The results indicate that E-PROA holds excellent promise as a technique for addressing complex engineering optimization problems.

Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential

The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier–Stokes–Cahn–Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results.

A Dini-Derivative-Aided Zeroing Neural Network for Time-Variant Quadratic Programming Involving Multi-Type Constraints With Robotic Applications.

Time-variant quadratic programming (QP) with multi-type constraints including equality, inequality, and bound constraints is ubiquitous in practice. In the literature, there exist a few zeroing neural networks (ZNNs) that are applicable to time-variant QPs with multi-type constraints. These ZNN solvers involve continuous and differentiable elements for handling inequality and/or bound constraints, and they possess their own drawbacks such as the failure in solving problems, the approximated optimal solutions, and the boring and sometimes difficult process of tuning parameters. Differing from the existing ZNN solvers, this article aims to propose a novel ZNN solver for time-variant QPs with multi-type constraints based on a continuous but not differentiable projection operator that is deemed unsuitable for designing ZNN solvers in the community, due to the lack of the required time derivative information. To achieve the aforementioned aim, the upper right-hand Dini derivative of the projection operator with respect to its input is introduced to serve as a mode switcher, leading to a novel ZNN solver, termed Dini-derivative-aided ZNN (Dini-ZNN). In theory, the convergent optimal solution of the Dini-ZNN solver is rigorously analyzed and proved. Comparative validations are performed, verifying the effectiveness of the Dini-ZNN solver that has merits such as guaranteed capability to solve problems, high solution accuracy, and no extra hyperparameter to be tuned. To illustrate potential applications, the Dini-ZNN solver is successfully applied to kinematic control of a joint-constrained robot with simulation and experimentation conducted.

Approximation of positive solutions of symmetric eigenvalue problems with nonlinear dependence on the spectral parameter

A symmetric partial differential eigenvalue problem with nonlinear dependence on the spectral parameter arising in plasma physics is studied. We propose and justify new conditions for the existence of a positive eigenvalue and the corresponding positive eigenfunction. A finite element approximation of the problem preserving the property of positivity of solutions is constructed. The existence and convergence of approximate solutions are established.

An efficient improved parrot optimizer for bladder cancer classification

Bladder Cancer (BC) is a common disease that comes with a high risk of morbidity, death, and expense. Primary risk factors for BC include exposure to carcinogens in the workplace or the environment, particularly tobacco. There are several difficulties, such as the requirement for a qualified expert in BC classification. The Parrot Optimizer (PO), is an optimization method inspired by key behaviors observed in trained Pyrrhura Molinae parrots, but the PO algorithm becomes stuck in sub-regions, has less accuracy, and a high error rate. So, an Improved variant of the PO (IPO) algorithm was developed using a combination of two strategies: (1) Mirror Reflection Learning (MRL) and (2) Bernoulli Maps (BMs). Both strategies improve optimization performance by avoiding local optimums and striking a compromise between convergence speed and solution diversity. The performance of the proposed IPO is evaluated against eight other competitor algorithms in terms of statistical convergence and other metrics according to Friedman’s test and Bonferroni–Dunn test on the IEEE Congress on Evolutionary Computation conducted in 2022 (CEC 2022) test suite functions and nine BC datasets from official repositories. The IPO algorithm ranked number one in best fitness and is more optimal than the other eight MH algorithms for CEC 2022 functions. The proposed IPO algorithm was integrated with the Support Vector Machine (SVM) classifier termed (IPO-SVM) approach for bladder cancer classification purposes. Nine BC datasets were then used to confirm the effectiveness of the proposed IPO algorithm. The experiments show that the IPO-SVM approach outperforms eight recently proposed MH algorithms. Using the nine BC datasets, IPO-SVM achieved an Accuracy (ACC) of 84.11%, Sensitivity (SE) of 98.10%, Precision (PPV) of 95.59%, Specificity (SP) of 95.98%, and F-score (F1) of 94.15%. This demonstrates how the proposed IPO approach can help to classify BCs effectively. The open-source codes are available at https://www.mathworks.com/matlabcentral/fileexchange/169846-an-efficient-improved-parrot-optimizer.

An improved chaotic GWO-LGBM hybrid algorithm for emotion recognition

To address the challenges associated with the unbalanced search abilities and low search accuracy of the Gray Wolf Optimization (GWO) algorithm, we propose an enhanced version termed the Improved Chaotic Gray Wolf Optimization Algorithm (ICGWO) based on cubic mapping. Initially, the population positions of gray wolves were perturbed to expedite the convergence speed. Subsequently, a nonlinear convergence factor was introduced to enhance both search ability and efficiency. Finally, within the algorithm, a dynamic inertia-weighting strategy was implemented to improve convergence speed and solution accuracy. Experimental simulations encompassing 23 classical test functions demonstrate that the ICGWO algorithm exhibits superior convergence speed, solution accuracy, and stability compared to other swarm intelligence optimization algorithms and certain enhanced GWO algorithms. In comparison to GWO, utilizing the ICGWO method for hyperparameter optimization within the Light Gradient Boosting Machine (LGBM) for emotional recognition led to notable enhancements in average accuracy and F1 score by 7.29 % and 3.92 % respectively for valence, and 4.33 % and 3.23 % respectively for arousal. Additionally, the standard deviation of the ICGWO-LGBM was less than one-tenth of the standard deviation of GWO-LGBM in both conditions. These results underscore the strong optimization capabilities and high stability of the ICGWO algorithm.

An efficient and accurate mapping method for elliptic equations in irregular annular domains

In this paper, we introduce a coordinate transformation, which transforms the irregular annular domain to a unit disk. We present its basic properties. As examples, we consider Poisson type equation and Cauchy–Navier elastic equations with variable coefficients in two-dimensional irregular annular domains, and prove the existence and uniqueness of weak solutions. We also construct the mixed Fourier–Legendre spectral schemes, and derive the optimal convergence of numerical solutions under the H1-norm. The numerical results indicate that the suggested method achieves high-order accuracy.

Modeling fluid flow in heterogeneous porous media with physics-informed neural networks: Weighting strategies for the mixed pressure head-velocity formulation

Physics-informed neural networks (PINNs) are receiving increased attention in modeling flow in porous media because they can surpass purely data-driven approaches. However, in heterogeneous domains, PINNs often face convergence challenges due to discontinuities in rock properties. A promising alternative is the mixed formulation of PINNs, which utilizes pressure head and velocity fields as primary variables. This formulation introduces a multi-term loss function whose terms must be carefully balanced to ensure effective convergence during training. The main goal of this work is to identify the most suitable weighting technique to overcome convergence issues and enhance the applicability of the mixed formulation of PINNs for modeling flow in heterogeneous porous media. Thus, we implement and adapt different global and local weighting techniques and evaluate their performance through multiple test scenarios, involving stochastic and block heterogeneity. The results reveal that the most appropriate weighting strategy is the max-average technique. In the case of stochastic heterogeneity, this technique allows for improving the convergence of the training algorithm. In the case of discontinuous heterogeneity, the max-average method is the only strategy that achieved convergence, highlighting its robustness. The results also show that under high heterogeneity, using an appropriate weighting technique becomes imperative because baseline PINN failed to converge. Implementing an optimal weighting strategy can improve convergence and yield accurate solutions with fewer learnable parameters, thereby enhancing overall model performance.

Mathematical modeling of allelopathic stimulatory phytoplankton species using fractal–fractional derivatives

In the current study, we employ the novel fractal–fractional operator in the Atangana–Baleanu sense to investigate the dynamics of an interacting phytoplankton species model. Initially, we utilize the Picard-Lindelöf theorem to validate the uniqueness and existence of solutions for the model. We then explore equilibrium points within the phytoplankton model and conduct Hyers–Ulam stability analysis. Additionally, we present a numerical scheme utilizing the Newton polynomial to validate our analytical findings. Numerical simulations illustrate the dynamical behavior of the model across various fractal and fractional parameter values, visualized through graphical representations. Our simulations reveal that the stability of equilibrium points is not significantly impacted with the long-term memory effect, which is characterized by fractal–fractional order values. However, an increase in fractal–fractional parameters accelerates the convergence of solutions to their intended equilibrium states.

Multi-UAV path planning using DMGWO ensuring 4D collision avoidance and simultaneous arrival

PurposeMulti-unmanned aerial vehicle (UAV) systems have succeeded in gaining the attention of researchers in diversified fields, especially in the past decade, owing to their capability to operate in complex scenarios in a coordinated manner. Path planning for UAV swarms is a challenging task depending upon the environmental conditions, the limitations of fixed-wing UAVs and the swarm constraints. Multiple optimization techniques have been studied for path-planning problems. However, there are local optimum and convergence rate problems. This study aims to propose a multi-UAV cooperative path planning (CoPP) scheme with four-dimensional collision avoidance and simultaneous arrival time.Design/methodology/approachA new two-step optimization algorithm is developed based on multiple populations (MP) of disturbance-based modified grey-wolf optimizer (DMGWO). The optimization is performed based on the objective function subject to multi constraints, including collision avoidance, same minimum time of flight and threat and obstacle avoidance in the terrain while meeting the UAV constraints. Comparative simulations using two different algorithms are performed to authenticate the proposed DMGWO.FindingsThe critical features of the proposed MP-DMGWO-based CoPP algorithm are local optimum avoidance and rapid convergence of the solution, i.e. fewer iterations as compared to the comparative algorithms. The efficiency of the proposed method is evident from the comparative simulation results.Originality/valueA new algorithm DMGWO is proposed for the CoPP problem of UAV swarm. The local best position of each wolf is used in addition to GWO. Besides, a disturbance is introduced in the best solutions for faster convergence and local optimum avoidance. The path optimization is performed based on a newly designed objective function that depends upon multiple constraints.

Perspectives for Improvements on Real-Time GNSS Positioning with the Use of New Observables

The research aims to analyze Global Navigation Satellite System (GNSS) positioning solutions using the Precise Point Positioning (PPP) method in kinematic mode, in which the position is obtained epoch by epoch through data from only one GNSS receiver, precise ephemerides, and satellite clock corrections, both with high accuracy. In this context, the adopted methodology employs the open-source software RTKLIB, which, through its data post-processing capability, enables the evaluation of kinematic PPP performance by incorporating new observables such as L5 and E5a bands, crucial for enhancing positional accuracy and mitigating multipath effects. Additionally, for survey simulations, data from the UFPR and POVE stations of the Brazilian Network for Continuous Monitoring of GNSS (RBMC) were utilized. The selected stations are located in the Northern and Southern regions of Brazil. The GNSS data were processed with the same tracking duration for a 45-minute cold-start, aimed at observing solution convergence. Subsequently, the estimated outputs in RTKLIB were obtained based on station origins using coordinates provided by SIRGAS-CON. Moreover, by utilizing precise ephemerides data, it was possible to conclude that the addition of new observables for triple-frequency positioning led to an improvement in the accuracy of the obtained coordinates, particularly in the Vertical component. In this regard, the increase in accuracy in experiments using only triple-frequency data with a 15° elevation mask was approximately 25% at the UFPR station and about ~37% at the POVE station. Furthermore, it was observed that reducing the elevation mask from 15° to 10° had a positive impact on dual-frequency positioning at the UFPR station, resulting in gains of over 3% in the East component and around ~21% in the North component compared to values obtained with the 15° mask. Similarly, during triple-frequency positioning at the POVE station, gains exceedingly approximately 16% in the North component and around ~22% in the Vertical component were observed.

Uniqueness and Convergence of Solution of Multi-Term Fractional Order Fredholm Integro-Differential Equation

Uniqueness and Convergence of Solution of Multi-Term Fractional Order Fredholm Integro-Differential Equation

Hierarchical optimization by spatial-temporal indictor in multi-scale decision pyramid for constrained large-scale multi-objective problems

Most existing constrained multi-objective evolutionary algorithms (CMOEAs) are not so efficient when handling constrained large-scale multi-objective problems (CLSMOPs). To overcome CLSMOPs, a hierarchical optimization, based on the spatial–temporal indictor in the decision pyramid (HOSTI-DP), is proposed to determine the dynamic trade-off between feasible and infeasible solutions in the effectively shrunken searching area. The decision pyramid consists of multiple decision spaces with a set of descending numbers of variables; it is initially constructed to speed up the solution convergence by the layer-by-layer dimensionality reduction and increase the population diversity based on the accumulation of these layers. The spatial–temporal indictor considers both the optimization stage (time) and the hierarchy structure of the decision pyramid (space) and it is designed to restrain the prematurely feasible solutions and find the promising infeasible solutions. Finally, the hierarchical optimization strategy, which applies the spatial–temporal indicator to the evolutionary algorithms in every layer of the decision pyramid and dynamically arranging the proportion among them, is designed for comprehensive balance of objectives, constraints, and computational complexity. Nine representative and state-of-the-art CMOEAs have been compared with the HOSTI-DP to demonstrate its effectiveness through comparative experiments on CLSMOPs with equality and inequality constraints and 1000 decision variables. Experimental results show that HOSTI-DP can significantly improve the performance of these CMOEAs.

Numerical analysis of the stochastic Stefan problem

The gradient discretisation method (GDM) – a generic framework encompassing many numerical methods – is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by compactness method using discrete functional analysis tools, Skorokhod theorem and the martingale representation theorem. The generic convergence results established in the GDM framework are applicable to a range of different numerical methods, including for example mass-lumped finite elements, but also some finite volume methods, mimetic methods, lowest-order virtual element methods, etc. Theoretical results are complemented by numerical tests based on two methods that fit in GDM framework.

MISAO: Ultra-Short-Term Photovoltaic Power Forecasting with Multi-Strategy Improved Snow Ablation Optimizer

The increase in installed PV capacity worldwide and the intermittent nature of solar resources highlight the importance of power prediction for grid integration of this technology. Therefore, there is an urgent need for an effective prediction model, but the choice of model hyperparameters greatly affects the prediction performance. In this paper, a multi-strategy improved snowmelt algorithm (MISAO) is proposed for optimizing intrinsic computing-expressive empirical mode decomposition with adaptive noise (ICEEMDAN) and weighted least squares support vector machine for PV power forecasting. Firstly, a cyclic chaotic mapping initialization strategy is used to generate a uniformly distributed high-quality population, which facilitates the algorithm to enter the appropriate search domain quickly. Secondly, the Gaussian diffusion strategy enhances the local exploration ability of the intelligences and extends their search in the solution space, effectively preventing them from falling into local optima. Finally, a stochastic follower search strategy is employed to reserve better candidate solutions for the next iteration, thus achieving a robust exploration–exploitation balance. With these strategies, the optimization performance of MISAO is comprehensively improved. In order to comprehensively evaluate the optimization performance of MISAO, a series of numerical optimization experiments were conducted using IEEE CEC2017 and test sets, and the effectiveness of each improvement strategy was verified. In terms of solution accuracy, convergence speed, robustness, and scalability, MISAO was compared with the basic SAO, various state-of-the-art optimizers, and some recently developed improved algorithms. The results showed that the overall optimization performance of MISAO is excellent, with Friedman average rankings of 1.80 and 1.82 in the two comparison experiments. In most of the test cases, MISAO delivered more accurate and reliable solutions than its competitors. In addition, the altered algorithm was applied to the selection of hyperparameters for the ICEEMDAN-WLSSVM PV prediction model, and seven neural network models, including WLSSVM, ICEEMDAN-WLSSVM, and MISAO-ICEEMDAN-WLSSVM, were used to predict the PV power under three different weather types. The results showed that the models have high prediction accuracy and stability. The MAPE, MAE and RMSE of the proposed model were reduced by at least 25.3%, 17.8% and 13.3%, respectively. This method is useful for predicting the output power, which is conducive to the economic dispatch of the grid and the stable operation of the power system.

Quintic and biquintic B-spline finite element solutions of clamped structures

Recent studies on the control of smart material partial differential equation systems point toward a need for considering higher-ordered polynomial splines in the formulation of bases for approximate solutions obtained via the Galerkin finite element method. However, basis modifications are not well documented in the literature, nor are they well understood by researchers who are often utilizing software packages in their basis and control designs. In this study, solutions are generated using modified bases with quintic and biquintic B-splines for three clamped structures: an ordinary differential equation cantilevered beam, a partial differential equation cantilevered beam, and an isotropic clamped plate. Convergent solutions are obtained and verified for all three models.

Distributed predefined-time economic dispatch based on event-triggered strategy for microgrids under directed graphs

The proliferation of new energy solutions and the enhanced accessibility of distributed power sources have significantly increased the complexity and variability of microgrid structures. Due to inherent limitations in its operational mode, the traditional centralized optimization method falls short in effectively addressing the economic dispatch problem in contemporary microgrids. In this paper, a distributed optimization method is devised to address the economic dispatch problem of microgrids under directed graphs by leveraging the consensus algorithm of multi-agent systems. We define the incremental cost of each microgrid unit as the consensus variable, achieving convergence through a pioneering combination of event-triggered strategy and predefined-time control theory. This approach not only optimizes resource use but also ensures timely and efficient solution convergence, addressing critical gaps in existing methodologies. This approach enables control over the upper bound of convergence time for optimal solutions by directly adjusting time parameters in the controller under the directed graph. Consequently, it achieves coordinated control of the power output in microgrids within a predefined time while reducing the communication resources between nodes with event-triggered mechanism. The effectiveness of the proposed algorithm is verified through simulation and analysis.

Impact of electric vehicles and wave energy systems on OPF of power networks using hybrid Osprey-PSO approach

In this article, a novel optimization algorithm named hybrid Osprey Optimization and Particle Swarm Optimization (OOPSO) is proposed to solve the Probabilistic Optimal Power Flow (POPF) problem in power systems with high penetration of renewable energy resources (RERs), such as photovoltaic, wind, and wave energy and integration of electric vehicles (EVs). The algorithm's results are compared with established optimization algorithms like Osprey Optimization Algorithm (OOA), Particle Swarm Optimization (PSO), and Heap Optimization. Applied to the 30 and 118-bus IEEE test systems, the OOPSO algorithm efficiently deals with the uncertainties produced by RERs generation. This research study includes EV charging profiles for weekdays and weekends. It considers home and work-level charging scenarios. The RERs and EVs penetration ensure system reliability while minimizing generation costs and satisfying power flow constraints. Compared to existing algorithms, the OOPSO algorithm achieves superior performance, faster convergence, and higher solution accuracy. The simulation results show the effectiveness of OOPSO. It appears to be a robust tool for POPF, integrating RERs in power systems with EVs. This work highlights the potential of OOPSO as a feasible approach for power system optimization in the context of RERs and EV integration, paving the way for further research into unconventional grid optimization techniques.

Nonlinear oscillators dynamics using optimal and modified homotopy perturbation method

This study investigates the several strongly nonlinear oscillators (Van der Pol, Duffing and Rayleigh) for which we have applied the most powerful and advanced optimal semi-analytical technique: optimal and modified homotopy perturbation method (OM-HPM) for the convergent semi-analytical series solution. The numerical simulation demonstrates the high accuracy of the OM-HPM, which is straightforward, does not require any domain decomposition, special transformation, or pade approximations to get the convergent series solution. The key features for the high accuracy of the OM-HPM lies on the best optimal auxiliary linear operator. Therefore, OM-HPM offering a valuable tool for engineers and researcher to analyze the complex nonlinear oscillator.

Joint Optimization of Relay Communication Rates in Clustered Drones under Interference Conditions

To address the issues of communication failure and inefficiency in clustered drone relay communication due to external malicious interference, this paper proposes a joint optimization method for relay communication rates under interference conditions for clustered drones. This method employs the following two-step processing framework: Firstly, the Discrete Soft Actor-Critic (DSAC) algorithm is used to train the relay drones for dynamic channel selection, effectively avoiding various types of interference. Simultaneously, the Bayesian optimization algorithm is applied to optimize the hyperparameters of the DSAC algorithm, further enhancing its performance. Subsequently, the modulation order, transmission power, trajectory of the relay drones, and power allocation factors of the clustered drones are jointly optimized. This complex problem is transformed into a convex subproblem for determining a solution, aiming to maximize the communication rate of the clustered drones. The simulation’s results demonstrate that the proposed algorithm exhibits excellent performances in terms of anti-interference capability, solution convergence, and stability. It effectively improves the mission efficiency of clustered drones under interference conditions and enhances their adaptability to dynamic environments.