Convergence Of Solutions Research Articles

MHO: A Modified Hippopotamus Optimization Algorithm for Global Optimization and Engineering Design Problems

The hippopotamus optimization algorithm (HO) is a novel metaheuristic algorithm that solves optimization problems by simulating the behavior of hippopotamuses. However, the traditional HO algorithm may encounter performance degradation and fall into local optima when dealing with complex global optimization and engineering design problems. In order to solve these problems, this paper proposes a modified hippopotamus optimization algorithm (MHO) to enhance the convergence speed and solution accuracy of the HO algorithm by introducing a sine chaotic map to initialize the population, changing the convergence factor in the growth mechanism, and incorporating the small-hole imaging reverse learning strategy. The MHO algorithm is tested on 23 benchmark functions and successfully solves three engineering design problems. According to the experimental data, the MHO algorithm obtains optimal performance on 13 of these functions and three design problems, exits the local optimum faster, and has better ordering and stability than the other nine metaheuristics. This study proposes the MHO algorithm, which offers fresh insights into practical engineering problems and parameter optimization.

Enhanced crayfish optimization algorithm: Orthogonal refracted opposition-based learning for robotic arm trajectory planning.

In high-dimensional scenarios, trajectory planning is a challenging and computationally complex optimization task that requires finding the optimal trajectory within a complex domain. Metaheuristic (MH) algorithms provide a practical approach to solving this problem. The Crayfish Optimization Algorithm (COA) is an MH algorithm inspired by the biological behavior of crayfish. However, COA has limitations, including insufficient global search capability and a tendency to converge to local optima. To address these challenges, an Enhanced Crayfish Optimization Algorithm (ECOA) is proposed for robotic arm trajectory planning. The proposed ECOA incorporates multiple novel strategies, including using a tent chaotic map for population initialization to enhance diversity and replacing the traditional step size adjustment with a nonlinear perturbation factor to improve global search capability. Furthermore, an orthogonal refracted opposition-based learning strategy enhances solution quality and search efficiency by leveraging the dominant dimensional information. Additionally, performance comparisons with eight advanced algorithms on the CEC2017 test set (30-dimensional, 50-dimensional, 100-dimensional) are conducted, and the ECOA's effectiveness is validated through Wilcoxon rank-sum and Friedman mean rank tests. In practical robotic arm trajectory planning experiments, ECOA demonstrated superior performance, reducing costs by 15% compared to the best competing algorithm and 10% over the original COA, with significantly lower variability. This demonstrates improved solution quality, robustness, and convergence stability. The study successfully introduces novel population initialization and search strategies for improvement, as well as practical verification in solving the robotic arm path problem. The results confirm the potential of ECOA to address optimization challenges in various engineering applications.

HawkFish Optimization Algorithm: A Gender-Bending Approach for Solving Complex Optimization Problems

Inspired by the gender transition behavior seen in hawkfish, this paper introduces the HawkFish optimization algorithm, a nature-inspired optimization technique modeled on the unique gender transition behavior of hawkfish. By leveraging this biological phenomenon, the proposed method addresses optimization problems through dual fitness functions, combining an original and inverse fitness function to drive search space exploration while avoiding local minima. The algorithm’s performance is rigorously evaluated against benchmark problems, including the CEC/GECCO 2019 suite, and applied to real-world engineering challenges like welded beam and tension/compression spring design. The proposed method consistently outperforms existing algorithms in terms of convergence rate, accuracy, and solution quality. The results underscore the algorithm’s efficiency in exploring unknown search spaces and solving complex optimization tasks, making it a promising tool for various domains requiring high precision and optimization efficiency.

Existence and convergence of approximate solutions for nonlinear measure driven differential systems

Existence and convergence of approximate solutions for nonlinear measure driven differential systems

A regional augmented PPP algorithm for offshore considering NWP

ABSTRACT In offshore areas with inhomogeneous distribution of reference stations, the low accuracy of regional augmented Zenith Tropospheric Delay (ZTD) products directly impacts regional augmented Precise Point Positioning (PPP) convergence time. Considering the availability of Numerical Weather Prediction (NWP) data at sea, we propose a regional augmented PPP algorithm that integrates tropospheric delays derived from NWP virtual grid points and the Continuously Operating Reference Station (CORS) network observations. Land and marine experiments are carried out to verify the effectiveness of this algorithm, evaluating ZTD interpolation accuracy and PPP positioning performance. The land experimental results show that this algorithm achieves similar ZTD accuracy and PPP results compared to traditional augmented PPP with perfect reference stations. The ZTD accuracy is 8.5 mm, and the average positioning accuracy is approximately 3.75 cm. The convergence time is less than 11 min where the data sampling interval is 30 s. Marine experiments indicate that the convergence time of this algorithm is 11–32% shorter than that of ionospheric-free PPP. The convergence time of this algorithm is reduced by 56–59%, and positioning accuracy in the E, N and U directions is augmented by 33.3%, 19.5% and 53.7%, respectively, compare to traditional augmented PPP at sea where the distribution of reference stations is inhomogeneous. Meanwhile, almost all stations can achieve a faster solution convergence by this algorithm. Furthermore, the algorithm is suitable not only for areas that lack reference stations at sea but also for the lack of reference stations on land.

Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation

Borehole trajectory optimization is a key issue in oil and gas drilling engineering. The traditional wellbore trajectory design method faces great challenges in optimizing the trajectory length and complexity, and it is difficult to meet the actual engineering requirements. In this paper, the three-stage wellbore trajectory optimization problem is studied, and a multi-objective optimization model including two objective functions of trajectory length and trajectory complexity is constructed. In this paper, an improved multi-objective particle swarm optimization algorithm is proposed, which combines the clustering strategy to improve the diversity of solutions, and enhances the local search ability and global convergence performance of the algorithm through the elite learning strategy. In order to verify the performance of the algorithm, comparative experiments were carried out using classical multi-objective benchmark functions. The results showed that the improved algorithm is superior to the traditional method in terms of diversity and convergence of solutions. Finally, the proposed algorithm was applied to the actual three-stage wellbore trajectory optimization problem. In summary, the research results of this paper provide theoretical support and engineering practice methods for wellbore trajectory optimization, and serve as an important reference for further improving the efficiency and quality of wellbore trajectory design.

Anti-interference Technology of Intelligent Communication Based on Improved GA and GWO

Chaotic mapping enhances anti-interference in frequency hopping communication by optimizing genetic algorithm population initialization. An intelligent decision engine model employs optimized grey wolf parameters and individual exchange mechanisms, enhancing grey wolf optimization convergence speed for constructing frequency hopping patterns. Experimental data reveals the improved genetic algorithm's efficiency with average run times of 0.312s and 0.057s for adaptive and enhanced versions, respectively. Achieving optimal solution convergence rates of 99.3% and 100%, the enhanced algorithm boosts decision-making accuracy and efficiency. The intelligent decision engine exhibits strong anti-interference capabilities, suitable for −2dB to 10dB signal-to-interference ratios with error rates below 10−6. The improved grey wolf optimization algorithm surpasses traditional approaches, yielding a 9.5% profit increment with a total value of 2310. This technology showcases adept learning and anti-interference capabilities, offering innovative solutions for communication systems and anti-interference technology advancements.

Compound Poisson particle approximation for McKean–Vlasov SDEs

Abstract We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha $-stable processes. Our approach utilizes compound Poisson particle approximations, allowing for simultaneous discretization of both the time and space variables in McKean–Vlasov SDEs. Notably, the approximation processes can be represented as a Markov chain with values on a lattice. Importantly, we demonstrate the propagation of chaos under relatively mild assumptions on the coefficients, including those with polynomial growth. This result establishes the convergence of the particle approximations towards the true solutions of the McKean–Vlasov SDEs. By only imposing moment conditions on the intensity measure of compound Poisson processes our approximation exhibits universality. In the case of ordinary differential equations (ODEs) we investigate scenarios where the drift term satisfies the one-sided Lipschitz assumption. We prove the optimal convergence rate for Filippov solutions in this setting. Additionally, we establish a functional central limit theorem for the approximation of ODEs and show the convergence of invariant measures for linear SDEs. As a practical application we construct a compound Poisson approximation for two-dimensional Navier–Stokes equations on the torus and demonstrate the optimal convergence rate.

DYNAMIC ANALYSIS OF A NANOBEAM UNDER THE INFLUENCE OF AN ELECTROMAGNETIC ACTUATOR AND A MECHANICAL IMPACT

The Optimal Auxiliary Functions Method (OAFM) is applied in the study of nonlinear vibration of a nanobeam, considering the curvature of the beam, the presence of an electromagnetic actuator and a mechanical impact. Our procedure is based on the existence of some auxiliary functions which assure a fast convergence of the approximate solution. The convergence-control parameters present in the auxiliary functions are evaluated by rigorous mathematical procedures.

Advances in Topological Methods for Solving Nonlinear Partial Differential Equations

Higher order nonlinear partial differential equations (PDEs) are very difficult to compare or analyze and therefore there is restriction towards analytical or numerical appraisal. The following research aims at solving the problem of the solutions of Nonlinear PDEs through the application of topological fixed-point theory and degree theory, as well as the application of variational methods towards improving the existence, uniqueness, and stability of solutions to PDEs under all possible boundary conditions. The purpose of the study is to investigate the effectiveness of these methods in multifaceted and multi-grained systems. We used both fixed-point analyses to check the convergence of solutions and degree-theoretic methods for checking multiplicity of solutions, and variational structure for critical points of solutions. Newton-Raphson and finite element techniques were used in solving solutions with much ease for increased efficiency. A selection of findings shows that topological techniques are an efficient means of handling nonlinearity in PDEs; degree theory uncovers the multiplicity of solutions while variational techniques unveil the stability characteristics. This research advances the field of nonlinear analysis beyond the prior art by broadening the scope of topology in new domains and providing enhanced methods of computation of PDEs where it matters most: where traditional linear methods fail to apply. In the context of physics, engineering, and environmental studies nonlinear modeling is vital and the practical implication highlighted herein is useful for all. Possible future work might apply these methods to more general boundary conditions as well as combined analytical-numerical approaches.

Numerical dynamics and optimal control for multi-strain age-structured epidemic model.

In this paper, a novel age-structured epidemiological model that simultaneously considers multiple viral strains is proposed. We develop a numerical framework for the study of the dynamics and optimal control by a linearly implicit Euler method, in which the biological meaning is unconditionally preserved. The first order convergence of numerical solutions in a finite time is derived from a uniform numerical boundedness. Moreover, the numerical dynamics are determined by a numerical basic reproduction number , which reflects the asymptotic stability of the equilibrium points. The abstract framework offers an effective and unified approach to study the long-time behaviour of multi-strain epidemic models that cover a wide variety of well-known models, which also provides a numerical optimal control strategy of the multi-strain age-structured SIR model. Finally, some numerical simulations illustrate the verification and the efficiency of our results.

A spherical vector-based adaptive evolutionary particle swarm optimization for UAV path planning under threat conditions

Unmanned aerial vehicle (UAV) path planning is a constrained multi-objective optimization problem. With the increasing scale of UAV applications, finding an efficient and safe path in complex real-world environments is crucial. However, existing particle swarm optimization (PSO) algorithms struggle with these problems as they fail to consider UAV dynamics, resulting in many infeasible solutions and poor convergence to optimal solutions. To address these challenges, we propose a spherical vector-based adaptive evolutionary particle swarm optimization (SAEPSO) algorithm. This algorithm, based on spherical vectors, directly incorporates UAV dynamic constraints and introduces improved tent map and reverse learning to enhance the diversity and distribution of initial solutions. Additionally, dynamic nonlinear and adaptive factors are integrated to balance exploration and exploitation capabilities. To avoid local optima in highly complex environments, we propose an adaptive acceleration strategy for poor particles, and an evolutionary programming strategy is incorporated to further improve the optimization capability. Finally, we conducted comparative studies and in six benchmark scenarios with varying threat levels, and the results demonstrated that the proposed algorithm outperforms others in the initial solution effectiveness, the final solution accuracy, convergence stability, and scalability.

Применение метода сквозного счета для моделирования несмешивающихся жидкостей c большим поверхностным натяжением

One of the most important advantages of the level set method is its ability to automatically handle topological changes. Instead of explicitly tracking the interface between the media, the level set method describes them as a zero isosurface of the level set function. This allows numerical modeling of the dynamics of a multiphase fluid as a single medium with varying parameters. It is known that a disadvantage of this approach is the possibility of non-physical oscillations of the velocity field near the interface, which occur at high surface forces due to the error in calculating the curvature of the interface and high gradients of other functions in the transition layer. Another disadvantage of the method is the problem of preserving the masses of liquids during the simulation. In this paper, several modifications of the level set method are described that allow reducing the mass loss of liquids, improving the convergence in the implicit solution of the transport equation, and reducing velocity oscillations near the interface in the case of high values of the surface tension coefficient. The proposed approaches were tested on a standard test problem of the dynamics of two immiscible liquids.

Осесимметричная задача фильтрации газа в пороупругой среде

The formulation and solution of the problem of burying carbon dioxide (carbon dioxide) in a poroelastic medium are considered. The model is based on the equations describing the filtration of liquids or gases in deformable porous media, which are a generalization of Muskett Leverett's models of poroelastic media. The assumption that the speed of movement of the solid skeleton of the medium is small made it possible to reduce the system of constitutive equations to two equations so that the effective pressure and porosity can be found. The gas filtration area refers to a rock formation in which an injection well is located at depth, and, on the sides, the formation is confined by impermeable rocks. The top of the formation coincides with the Earth surface and is permeable. The migration of carbon dioxide and its release to the surface occurs due to an increase in porosity at the top of the formation. Based on these assumptions, boundary conditions for the velocities of the gas and solid phases are set and then rewritten in terms of the desired function of the effective pressure of the medium. The resulting initial boundary value problem is solved numerically using a scheme of alternating directions and the fourth-order Runge-Kutta method. A difference scheme and an algorithm for solving the problem are given. The orders of uniform convergence in spatial and temporal variables were determined, and an approximate estimate for the rate of convergence of the numerical solution was obtained. Numerical modeling of several options for injecting carbon dioxide into the formation at different well depths and with different injection rates was carried out. Optimal gas injection conditions for its long-term geological storage were determined.

Personalized Indicator Based Evolutionary Algorithm for Uncertain Constrained Many‐Objective Optimization Problem With Interval Functions

ABSTRACTIn practical engineering problems, uncertainties due to prediction errors and fluctuations in equipment efficiency often lead to constrained many‐objective optimization problem with interval parameters (ICMaOPs). These problems pose significant challenges for evolutionary algorithms, particularly in balancing solution convergence, diversity, feasibility, and uncertainty. To address these challenges, a personalized indicator‐based evolutionary algorithm (PI‐ICMaOEA) specifically designed for ICMaOPs is proposed. The PI‐ICMaOEA integrates a comprehensive quality indicator that encapsulates convergence, diversity, uncertainty, and feasibility factors, converting multiple objectives in high‐dimensional search spaces into a single evaluative metric. Each factor's weight is personalized assigned based on individual performance, objective dimension, and the evolving conditions of the population. By prioritizing individuals with excellent indicator values for mating and environmental selection, PI‐ICMaOEA effectively enhances selection pressure in high‐dimensional spaces. Comparative simulations demonstrate that PI‐ICMaOEA is highly competitive, offering a robust solution for balancing convergence, diversity, uncertainty, and feasibility in ICMaOPs.

Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation

By deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution are obtained for singular p-Laplacian Caputo–Hadamard fractional differential equation with infinite-point boundary conditions. Nonlinearities involve derivative terms that make our analysis difficult in the course of this research, and we deal with the difficulty of derivative terms by making appropriate substitutions. An example is given to demonstrate the validity of our main results.

Yerba mate (Ilex paraguariensis) genome provides new insights into convergent evolution of caffeine biosynthesis.

Yerba mate (YM, Ilex paraguariensis) is an economically important crop marketed for the elaboration of mate, the third-most widely consumed caffeine-containing infusion worldwide. Here, we report the first genome assembly of this species, which has a total length of 1.06 Gb and contains 53,390 protein-coding genes. Comparative analyses revealed that the large YM genome size is partly due to a whole-genome duplication (Ip-α) during the early evolutionary history of Ilex, in addition to the hexaploidization event (γ) shared by core eudicots. Characterization of the genome allowed us to clone the genes encoding methyltransferase enzymes that catalyse multiple reactions required for caffeine production. To our surprise, this species has converged upon a different biochemical pathway compared to that of coffee and tea. In order to gain insight into the structural basis for the convergent enzyme activities, we obtained a crystal structure for the terminal enzyme in the pathway that forms caffeine. The structure reveals that convergent solutions have evolved for substrate positioning because different amino acid residues facilitate a different substrate orientation such that efficient methylation occurs in the independently evolved enzymes in YM and coffee. While our results show phylogenomic constraint limits the genes coopted for convergence of caffeine biosynthesis, the X-ray diffraction data suggest structural constraints are minimal for the convergent evolution of individual reactions.

A two-stage hybrid NSGA-III with BWO for path planning and task allocation in agricultural land preparation.

Automated large-scale farmland preparation operations face significant challenges related to path planning efficiency and uniformity in resource allocation. To improve agricultural production efficiency and reduce operational costs, an enhanced method for planning land preparation paths is proposed. In the initial stage, unmanned aerial vehicles (UAVs) are employed to collect data from the field, which is then used to construct accurate farm models. For single-field operations, a path planning approach is developed that minimizes energy consumption. The approach combines the selection of optimal operational angles with the implementation of efficient turning strategies, aiming to achieve full coverage. In addressing the issue of scheduling multiple machines across multiple fields, a two-stage optimization method, referred to as the BNSGA-III algorithm, is introduced. This algorithm integrates the NSGA-III algorithm with Beluga Whale Optimization (BWO), adaptive parameter adjustment, and Adaptive Inversion Crossover (AIC). The proposed method tackles the inherent complexity of agricultural environments, balancing operational efficiency and resource allocation through multi-objective optimization. Experimental results demonstrate that, compared to random operation directions, the proposed method reduces the path length by 1.9% to 3.1%, decreases the turning frequency by 19.5% to 24.0%, and improves coverage by 1.0% to 1.4%. In the context of multi-machine scheduling, the BNSGA-III algorithm outperforms the NSGA-II, NSGA-III, and MOEA/D algorithms, achieving improvements in total travel distance (12.3% to 34.4%), path balance (60.9% to 66.2%), and workload distribution (78.7% to 92.9%). Further evaluation shows that BNSGA-III excels in key metrics such as convergence (IGD), solution quality (HV), and diversity (Spread), thereby confirming its superiority in solution quality, convergence, and diversity. The findings of this study provide strong support for the advancement of intelligent agriculture.

Mean field limits of particle-based stochastic reaction-drift-diffusion models*

Abstract We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued stochastic processes (MVSPs), which describe the evolution of the singular, stochastic concentration fields of each chemical species. The mean field large population limit of such models is derived and proven, giving coarse-grained deterministic partial integro-differential equations (PIDEs) for the limiting deterministic concentration fields’ dynamics. We generalize previous studies on the mean field limit of models involving only diffusive motion, with care to formulating the MVSP representation to ensure detailed balance of reversible reactions in the presence of potentials. Our work illustrates the more general set of PIDEs that arise in the mean field limit, demonstrating that the limiting macroscopic reactive interaction terms for reversible reactions obtain additional nonlinear concentration-dependent coefficients compared to the purely diffusive case. Numerical studies are presented which illustrate that two-body repulsive potential interactions can have a significant impact on the reaction dynamics, and also demonstrate the empirical numerical convergence of solutions to the PBSRDD model to the derived mean field PIDEs as the population size increases.

An innovative complex-valued encoding black-winged kite algorithm for global optimization

The black-winged kite algorithm (BKA) constructed on the black-winged kites’ migratory and predatory instincts is a revolutionary swarm intelligence method that integrates the Leader tactic with the Cauchy variation procedure to retrieve the expansive appropriate convergence solution. The essential BKA exhibits marginalized resolution efficiency, inferior assessment precision, and stagnant sensitive anticipation. To foster aggregate discovery intensity and advance widespread computational efficacy, an innovative complex-valued encoding BKA (CBKA) is presented to resolve the global optimization. The complex-valued encoding manipulates the dual-diploid configuration to encode the black-winged kite, and the actual and fictitious portions are inserted into the BKA, which transforms dual-dimensional encoding into a single-dimensional manifestation. With the inherent parallelism and consistency, the actual and fictitious portions are renewed separately for each search agent, which reinforces population pluralism, restricts discovery stagnation, extends identification area, promotes estimation excellence, advances information resources, and fosters collaboration efficiency. The CBKA not only showcases abundant flexibility and compatibility to accomplish supplementary advantages and sharpen resolution precision but also incorporates localized exploitation and universal exploration to forestall exaggerated convergence and cultivate desirable solutions. The function evaluations, engineering layouts, and adaptive infinite impulse response system identification are executed to certify the suitability and affordability of the CBKA. The experimental results manifest that the computational accomplishment and convergence productivity of the CBKA are superior to those of other comparison algorithms, the CBKA delivers noteworthy stabilization and resilience to explore superior assessment precision and swifter convergence efficiency.