Cauchy Operator Research Articles

Improved multi-strategy artificial rabbits optimization for solving global optimization problems

Artificial rabbits optimization (ARO) is a metaheuristic algorithm based on the survival strategy of rabbits proposed in 2022. ARO has favorable optimization performance, but it still has some shortcomings, such as weak exploitation capacity, easy to fall into local optima, and serious decline of population diversity at the later stage. In order to solve these problems, we propose an improved multi-strategy artificial rabbits optimization, called IMARO, based on ARO algorithm. In this paper, a roulette fitness distance balanced hiding strategy is proposed so that rabbits can find better locations to hide more reasonably. Meanwhile, in order to improve the deficiency of ARO which is easy to fall into local optimum, an improved non-monopoly search strategy based on Gaussian and Cauchy operators is designed to improve the ability of the algorithm to obtain the global optimal solution. Finally, a covariance restart strategy is designed to improve population diversity when the exploitation is stagnant and to improve the convergence accuracy and convergence speed of ARO. The performance of IMARO is verified by comparing original ARO algorithm with six basic algorithms and seven improved algorithms. The results of CEC2014, CEC2017, CEC2022 show that IMARO has a good exploitation and exploration ability and can effectively get rid of local optimum. Moreover, IMARO produces optimal results on six real-world engineering problems, further demonstrating its efficiency in solving real-world optimization challenges.

Optimization of PV module ash accumulation prediction based on an improved vulture algorithm

Abstract In this research, an ash accumulation prediction model based on the Improved Bald Eagle Algorithm (IBES) optimization is proposed, and a least-squares support vector machine (LSSVM) is used to investigate the correlation between climatic parameters and the quantity of ash deposition on PV panel surfaces. Ash deposit affects PV panel output power over time and is influenced by meteorological factors. Following a thorough selection procedure, meteorological variables like wind speed and rainfall are used in the model to forecast the amount of ash that will accumulate on the slab. The original condor method was prone to local optimum convergence and had a slow convergence rate. These weaknesses are addressed by the optimal selection of the next iteration, which introduces the Cauchy variation operator to mutate the population’s optimal individuals. The optimization parameters of the revised algorithm are incorporated into the model and results are compared to models of other optimization algorithms. The outcomes demonstrate that the IBES-LSSVM ash accumulation prediction model has a higher degree of fit and a reduced prediction error.

HHPSO: A Heuristic Hybrid Particle Swarm Optimization Path Planner for Quadcopters

Path planning for quadcopters has been proven to be one kind of NP-hard problem with huge search space and tiny feasible solution range. Metaheuristic algorithms are widely used in such types of problems for their flexibility and effectiveness. Nevertheless, most of them cannot meet the needs in terms of efficiency and suffer from the limitations of premature convergence and local minima. This paper proposes a novel algorithm named Heuristic Hybrid Particle Swarm Optimization (HHPSO) to address the path planning problem. On the heuristic side, we use the control points of cubic b-splines as variables instead of waypoints and establish some heuristic rules during algorithm initialization to generate higher-quality particles. On the hybrid side, we introduce an iteration-varying penalty term to shrink the search range gradually, a Cauchy mutation operator to improve the exploration ability, and an injection operator to prevent population homogenization. Numerical simulations, physical model-based simulations, and a real-world experiment demonstrate the proposed algorithm’s superiority, effectiveness and robustness.

DEMFFA: a multi-strategy modified Fennec Fox algorithm with mixed improved differential evolutionary variation strategies

The Fennec Fox algorithm (FFA) is a new meta-heuristic algorithm that is primarily inspired by the Fennec fox's ability to dig and escape from wild predators. Compared with other classical algorithms, FFA shows strong competitiveness. The “No free lunch” theorem shows that an algorithm has different effects in the face of different problems, such as: when solving high-dimensional or more complex applications, there are challenges such as easily falling into local optimal and slow convergence speed. To solve this problem with FFA, in this paper, an improved Fenna fox algorithm DEMFFA is proposed by adding sin chaotic mapping, formula factor adjustment, Cauchy operator mutation, and differential evolution mutation strategies. Firstly, a sin chaotic mapping strategy is added in the initialization stage to make the population distribution more uniform, thus speeding up the algorithm convergence speed. Secondly, in order to expedite the convergence speed of the algorithm, adjustments are made to the factors of the formula whose position is updated in the first stage, resulting in faster convergence. Finally, in order to prevent the algorithm from getting into the local optimal too early and expand the search space of the population, the Cauchy operator mutation strategy and differential evolution mutation strategy are added after the first and second stages of the original algorithm update. In order to verify the performance of the proposed DEMFFA, qualitative analysis is carried out on different test sets, and the proposed algorithm is tested with the original FFA, other classical algorithms, improved algorithms, and newly proposed algorithms on three different test sets. And we also carried out a qualitative analysis of the CEC2020. In addition, DEMFFA is applied to 10 practical engineering design problems and a complex 24-bar truss topology optimization problem, and the results show that the DEMFFA algorithm has the potential to solve complex problems.

Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain

Spectral Asymptotics of the Cauchy Operator and its Product with Bergman’s Projection on a Doubly Connected Domain

Robust Q‐learning‐based multi‐objective sheep flock optimizer with a Cauchy operator for effective path planning in unmanned aerial vehicles

SummaryUnmanned aerial vehicle (UAV) path planning can be treated as a nondeterministic polynomial (NP) hard concern or an optimization problem. The conventional approaches are unable to effectively handle these issues due to discontinuity, non‐linearity, multi‐modality, and inseparability. On the other hand, meta‐heuristic algorithms are effective at tackling these issues because they are simple, adaptable, and derivation free. To enhance the performance in a variety of challenging circumstances, this paper proposes a novel Q‐learning‐based multi‐objective sheep flock optimizer with a Cauchy operator (Q‐MOSFO‐CA) to solve the constrained UAV path planning issues. The multi‐objective functions considered here are costs and constraints (threat, terrain, turning, climbing, and gliding constraints) to determine the feasible and optimal path. To avoid the probability of falling into the local optimum and to address the shortcoming of unbalanced convergence and also to maintain the exploitation and exploration capability, the Cauchy operator (CA) is integrated with the sheep flock optimization (SFO) algorithm. The Q‐learning model is introduced to balance both the global and local searches. Here, the exploration model performs the global search whereas the exploitation model performs the local search to attain an optimal solution. In the simulation scenario, the statistical analysis is conducted under two scenarios, and some essential measures such as the number of iterations at convergence (NIC), evaluation time (ET), energy consumption, and convergence analysis are determined. The proposed method obtains NIC of 1305 and 1436, ET of 12.8 and 15.2 s, and energy consumption of 20,600 and 21,465 J for both Scenarios 1 and 2, respectively.

Prediction of thermal comfort indoors and cooling loads based on reasonable zoning using the improved HHO with multi-strategy fusion-FENN algorithm

A comfortable indoor thermal environment helps occupants work healthily and efficiently, and the air-conditioning system, as the most energy-consuming system in building operation, accurate energy modeling while balancing thermal comfort can provide effective control strategies for managers. Metaheuristic algorithms are widely optimized for various types of machine learning models for the study of data-driven. However, the majority of them currently use the default hyperparameter or random and grid search, which are prone to obtaining inaccurate prediction results. In this paper, a sizable commercial building in Shaanxi Province is used as a research sample. The regional per floor firstly is divided with business model distribution, the cross-validation of random forest and correlation analysis is used to extract features, and the input factors of the prediction model are decided, and then the fully elman neural network is optimized using a segmental fusion strategy combining Cauchy operator and reverse learning to promote harris hawks optimization algorithm, and the prediction model the IMFHHO-FENN (improved Harris Hawks Optimization with multi-strategy fusion-Fully Elman Neural Network) is trained and constructed, which is finally used for predicting thermal comfort and cooling load. According to verification results, it can be proved that the IMFHHO-FENN model has excellent performance compared to mainstream single and combined models and can provide accurate results of predicted models in the design phase of building energy efficiency and later operation management, reducing energy consumption waste while satisfying personnel thermal comfort as much as possible and supply marked theoretical and decision reference for building equipment management.

Numerical Computation of Distributions in Finite-State Inhomogeneous Continuous Time Markov Chains, Based on Ergodicity Bounds and Piecewise Constant Approximation

In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturbation theory, its time-dependent probability characteristics can be approximately obtained from another Markov chain, having piecewise constant intensities and the same state space. The approximation error (the taxicab distance between the state probability distributions) is provided. It is shown how the Cauchy operator and the state probability distribution for an arbitrary initial condition can be calculated. The findings are illustrated with the numerical examples.

Energy optimization routing for hierarchical cluster based WSN using artificial bee colony

Technology advancement in Wireless sensor network (WSNs) has attracted much attention in smart computing and potential usage across numerous applications fields. WSN composed of tiny and self-configured sensor nodes with battery operated. Sensors are restricted to limited energy and resources. Unbalanced nodes energy results in more energy consumption and affects network lifetime. Achieving energy efficiency remains a challenging issue in designing WSN routing. Approaches for minimising node energy usage through clustering techniques have offered optimal solutions. However, the existing clustering scheme fails to balance nodes energy without considering energy parameters, low energy node being chosen as cluster head, node density, and scalability. Existing scheme limits to global exploration possibilities and restricted to only specific search regions. In this paper, we propose an energy optimization routing using improved artificial bee colony (EOR-iABC) for cluster based WSN. The proposed EOR-iABC routing scheme intends to achieve energy optimization and prolong network's lifetime. The EOR-iABC adapts distinctive search policy using improved artificial bee colony algorithm for selection of energy efficient cluster heads (CH) in periodic time intervals through integration of crossover and mutation. The delay convergence is eliminated by associating employee and onlooker-bee stages, which helps to reform local search strategies. An optimal path from CH to base station (BS) is discovered through energy-efficient fitness node to improve network data collection efficiency. Grenade explosion method (GEM) and Cauchy operator are employed to extend search policies dynamically from one region to another for large-scale WSN. Simulation results show EOR-iABC outperforms in terms of energy efficiency by 27% compared to OCABC scheme and by 16% compared to IABCOCT scheme.

Intelligent contributions of the artificial orca algorithm for continuous problems and real-time emergency medical services.

The Artificial Orca Algorithm (AOA) is an existing swarm intelligence algorithm, empowered in this paper by two well-known mutation operators and opposition-based learning, yielding the novel methods Deep Self-Learning Artificial Orca Algorithm (DSLAOA), Opposition Deep Self-Learning Artificial Orca Algorithm (ODSLAOA), and Opposition Artificial Orca Learning Algorithm. The DSLAOA and ODSLAOA are based on the Cauchy and Gauss mutation operators. Their effectiveness is evaluated on both continuous and discrete problems. The suggested algorithms are tested and compared to seven recent state-of-the-art metaheuristics in the continuous context. The results demonstrate that, when compared to the other algorithms, DSLAOA based on the Cauchy operator is the most effective technique. After that, a specific real-world scenario involving emergency medical services in a dire situation is tackled. The Ambulance Dispatching and Emergency Calls Covering Problem is the addressed problem, and a mathematical formulation is made to model this issue. AOA, DSLAOAC, and DSLAOAG are tested and contrasted with a successful recent heuristic in this field. The experiments are run on real data, and the results show that the swarm approaches are effective and helpful in determining the resources required in this kind of emergency.

A New Method for Multi-UAV Cooperative Mission Planning Under Fault

Aiming at the many-to-one mission planning problem in the case of UAV fault, a self-organizing solving method is designed. This method organically combines the situation assessment of single UAV with the collaborative optimization of multiple UAV. On the one hand, the situation assessment of single UAV is carried out based on Bayesian network, and the striking probability of each UAV is obtained. On the other hand, in order to solve the problem of multiple UAV cooperation, the improved discrete particle swarm optimization based mixed strategy (MSDPSO) is proposed. The algorithm has been improved in the following four aspects. Firstly, Sobol sequence is used to initialize the population to improve the coverage of solution space. Then, a nonlinear time-varying strategy is proposed to accelerate the convergence of the algorithm. Cauchy operator is also introduced to enhance the search space of discrete particle swarm optimization. At the same time, an adaptive cross learning strategy is proposed to enrich the diversity of the population, thereby improving the global optimization ability of the algorithm. In addition, the cubic spline interpolation is used to plan trajectory of UAV. Finally, improved discrete particle swarm optimization is used in three-dimensional space for simulation and comparison with both healthy and faulty UAV involved. Results show that the designed algorithm has significant improvement on solution optimality and convergence rate, which provides a theoretical basis for the application of multiple UAV collaborative task planning.

Generating functions of the Cauchy operator of a hamiltonian system

The article is related to the mathematical apparatus for describing the phase trajectories of a hamiltonian system. An approach related to the construction of generating functions for the Cauchy operator is proposed. It is shown that one-parameter families of generating functions satisfy the Hamilton—Jacobi equation or its modifications. Using the example of small oscillations of a mathematical pendulum, it is shown that the description of the Cauchy operator for sufficiently long periods of time requires the use of generating functions of various types. With the help of generating functions, a variational principle similar to the principle of least action is formulated. The efficiency of using generating functions in the development of conservative methods of numerical integration is also noted.

A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$

A mixed boundary value problem with arbitrary continuous, not necessarily satisfying boundary conditions, functions in initial conditions and inhomogeneities of the equation is solved. A method is proposed for finding a generalized solution by a modification of the interpolation operators of functions constructed from solutions of Cauchy problems with second-order differential expression. Methods of finding the Fourier coefficients of auxiliary functions using the Stieltjes integral or the resolvent of the third-order Cauchy differential operator are proposed.

A hybrid Artificial Immune optimization for high-dimensional feature selection

For high-dimensional data, the traditional feature selection method is slightly inadequate. At present, most of the existing hybrid search methods have problems of high computational cost and unsatisfactory feature reduction rate. In this paper, a hybrid feature selection method based on artificial immune algorithm optimization (HFSIA) is proposed to solve the feature reduction problem of high-dimensional data. This method combines the filter method with the metaheuristic-based search strategy more effectively. Inspired by biological research results, the method introduces a lethal mutation mechanism and a Cauchy mutation operator with adaptive adjustment factors to improve the search performance of the algorithm. In addition, this method introduces an adaptive adjustment factor in the population update stage to improve the problem of insufficient diversity of the original algorithm. The effective combination of these mechanisms enables the algorithm to obtain better search capability at a lower computational cost. Experimental comparisons with 23 state-of-the-art feature selection methods are conducted on 22 high-dimensional benchmark datasets. The results show that the computational cost of HFSIA is comparable to 5 classical feature selection methods known for their speed. Moreover, it achieves a higher average classification accuracy than 18 hybrid feature selection methods reported in the latest literature with the best feature reduction rate.

An Efficient Hybrid Feature Selection Method Using the Artificial Immune Algorithm for High-Dimensional Data.

Feature selection provides the optimal subset of features for data mining models. However, current feature selection methods for high-dimensional data also require a better balance between feature subset quality and computational cost. In this paper, an efficient hybrid feature selection method (HFIA) based on artificial immune algorithm optimization is proposed to solve the feature selection problem of high-dimensional data. The algorithm combines filter algorithms and improves clone selection algorithms to explore the feature space of high-dimensional data. According to the target requirements of feature selection, combined with biological research results, this method introduces the lethal mutation mechanism and the Cauchy operator to improve the search performance of the algorithm. Moreover, the adaptive adjustment factor is introduced in the mutation and update phases of the algorithm. The effective combination of these mechanisms enables the algorithm to obtain a better search ability and lower computational costs. Experimental comparisons with 19 state-of-the-art feature selection methods are conducted on 25 high-dimensional benchmark datasets. The results show that the feature reduction rate for all datasets is above 99%, and the performance improvement for the classifier is between 5% and 48.33%. Compared with the five classical filtering feature selection methods, the computational cost of HFIA is lower than the two of them, and it is far better than these five algorithms in terms of the feature reduction rate and classification accuracy improvement. Compared with the 14 hybrid feature selection methods reported in the latest literature, the average winning rates in terms of classification accuracy, feature reduction rate, and computational cost are 85.83%, 88.33%, and 96.67%, respectively.

Inverse time overcurrent optimization of distribution network with DG based on improved gray wolf algorithm

Inverse time overcurrent protection can be applied to distribution networks with distributed power sources because of its superior protection characteristics, but its time limit coordination and value setting are complicated, which limits its large-scale engineering application. Therefore, this paper proposes an inverse time overcurrent protection setting strategy for distribution network(DN) based on improved gray wolf optimizer (GWO) algorithm. Firstly, the current setting optimization model and the protection operation characteristics are established considering the reliability, rapidity and selectivity. Secondly, the GWO algorithm is improved by introducing the population initialization strategy based on elite backward learning, adaptive weights and variation strategy based on the Cauchy operator for the characteristics of the traditional GWO algorithm which is easy to trap in local optimum and low convergence accuracy. The improved algorithm does not introduce new parameters and achieves a balance between global and local. Finally, the case study results represent that the improved GWO algorithm has high accuracy and stability in both two-phase short-circuit and three-phase short-circuit scenarios, and has good practical applicability.

Closed-form solutions for several classes of singular integral equations with convolution and Cauchy operator

The main goal of this paper is to study the existence of solutions for several new classes of singular convolution integral equations containing the Cauchy operator in the normal type case. To investigate the solutions of such equations, we establish the Noethericity theory of solvability. By means of the properties of complex Fourier transforms, we transform these equations into Riemann boundary value problems with nodes. The analytic solutions and conditions of solvability are obtained via using Riemann–Hilbert approach. Moreover, we also discuss the asymptotic property of solutions near nodes. Thus, this paper generalizes the theories of complex analysis, functional analysis, integral equations and the classical Riemann boundary value problems.

Amalgamated Evolutionary Approach for Optimized Routing in Time Varying Ultra Dense Heterogeneous Networks

Routing mechanisms in Ultra-Dense Network (UDNs) are expected to be flexible, scalable, and robust in nature and the establishment of the shortest path between the source and destination pairs will always be a critical challenge. Through this projected work, the optimized shortest route of different source-destination pairs is found using a class of evolutionary optimization algorithms namely PSO, GA, and our proposed hybrid PSO–Genetic Mutation (PSO-GM) algorithm which searches for an optimized solution by representing it as a Shortest Path Routing (SPR) problem. The key attribute of the PSO-GM approach is related to the application of an amalgamated strategy with Gaussian, Cauchy, Levy, Single-point, and Chaos mutation operators. Simulation results and application of the above-mentioned algorithms to the SPR problem in UDNs reveal that the hybrid PSO-GM algorithm provides a comparatively enhanced optimized solution. In the case of the rate of convergence to the theoretical limit, the hybrid PSO-GM gives us 20% better results compared to the PSO and GA.

Quantum OPTICS and deep self-learning on swarm intelligence algorithms for Covid-19 emergency transportation.

In this paper, the quantum technology is exploited to empower the OPTICS unsupervised learning algorithm, which is a density-based clustering algorithm with numerous applications in the real world. We design an algorithm called Quantum Ordering Points To Identify the Clustering Structure (QOPTICS) and demonstrate that its computational complexity outperforms that of its classical counterpart. On the other hand, we propose a Deep self-learning approach for modeling the improvement of two Swarm Intelligence Algorithms, namely Artificial Orca Algorithm (AOA) and Elephant Herding Optimization (EHO) in order to improve their effectiveness. The deep self-learning approach is based on two well-known dynamic mutation operators, namely Cauchy mutation operator and Gaussian mutation operator. And in order to improve the efficiency of these algorithms, they are hybridized with QOPTICS and executed on just one cluster it yields. This way, both effectiveness and efficiency are handled. To evaluate the proposed approaches, an intelligent application is developed to manage the dispatching of emergency vehicles in a large geographic region and in the context of Covid-19 crisis in order to avoid an important loss in human lives. A theoretical model is designed to describe the issue mathematically. Extensive experiments are then performed to validate the mathematical model and evaluate the performance of the proposed deep self-learning algorithms. Comparison with a state-of-the-art technique shows a significant positive impact of hybridizing Quantum Machine Learning (QML) with Deep Self Learning (DSL) on solving the Covid-19 EMS transportation.

Scattering and inverse scattering for the AKNS system: A rational function approach

AbstractWe consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS (Ablowitz–Kaup–Newell–Segur) system. The proposed numerical forward scattering transform computes the solution of the AKNS system that is valid on the entire real axis and thereby computes a reflection coefficient at a point by solving a single linear system. The proposed numerical inverse scattering transform makes use of a novel improvement in the rational function approach to the oscillatory Cauchy operator, enabling the efficient solution of certain Riemann–Hilbert problems without contour deformations. The latter development enables access to high‐precision computations and this is demonstrated on the inverse scattering transform for the one‐dimensional Schrödinger operator with a potential.