Chaotic Optimization Algorithm Research Articles

Enhancing stochastic optimization: investigating fixed points of chaotic maps for global optimization

<p>Chaotic maps, despite their deterministic nature, can introduce controlled randomness into optimization algorithms. This chaotic map behaviour helps overcome the lack of mathematical validation in traditional stochastic methods. The chaotic optimization algorithm (COA) uses chaotic maps that help it achieve faster convergence and escape local optima. The effective use of these maps to find the global optimum would be possible only with a complete understanding of them, especially their fixed points. In chaotic maps, fixed points repeat indefinitely, disrupting the map's characteristic unpredictability. While using chaotic maps for global optimization, it is crucial to avoid starting the search at fixed points and implement corrective measures if they arise in between the sequence. This paper outlines strategies for addressing fixed points and provides a numerical evaluation (using Newton's method) of the fixed points for 20 widely used chaotic maps. By appropriately handling fixed points, researchers and practitioners across diverse fields can avoid costly failures, improve accuracy, and enhance the reliability of their systems.</p>

A Hindmarsh–Rose neuron model with electromagnetic radiation control for the mechanical optimization design

This paper proposes a Hindmarsh–Rose(HR) neuron model controlled by electromagnetic radiation to solve the mechanical optimization design problem. A novel memristor for simulating electromagnetic radiation is established to control the dynamical behavior of HR neuron models. By analyzing the HR model and using the numerical analysis methods of phase portrait, bifurcation diagram, Lyapunov exponent and spectral entropy (SE) complexity, the HR model is shown to have a hidden attractor and rich chaotic dynamics. Then, a chaotic optimization algorithm based on HR neuron model is designed to solve the mechanical optimization design of tension/compression coil springs and pressure vessels. The chaotic sequence of this algorithm which has high-quality pseudo-random number, has stronger global search ability. Simulation of two mechanical optimization design problems in comparison with some well-known optimization algorithms demonstrates the superiority of the HR in the solution quality.

A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

CAVOA: A chaotic optimization algorithm for optimal power flow with facts devices and stochastic wind power generation

AbstractThe study proposes a modified version of African Vultures Optimization Algorithm (AVOA) to address the optimal power flow (OPF) issue. The developed optimizer is called Chaotic AVOA (CAVOA). Prior to applying CAVOA to the problem at hand, its accuracy is evaluated using 23 benchmark functions. The production powers of WTs that are interrupted are predicted using Weibull probability density functions (PDFs). Two additional costs, namely penalty cost and reserve cost, are incorporated into the goal function of the OPF. The simulation results of CAVOA are compared with those of the original AVOA to solve the OPF. The proposed OPF technique and its solution methodology are verified on the IEEE 30‐bus test system, taking into account the flexible alternating current transmission systems (FACTS) devices, which have several benefits such as reducing active power transmission loss, regulating power flow, and improving voltage stability/profile. The research's simulation results demonstrate that CAVOA is more effective in identifying the OPF's optimal solution by reducing the overall power cost and power losses. The results indicate that the CAVOA algorithm outperforms AVOA as a metaheuristic optimization algorithm due to its superior capability in addressing challenging OPF problems with a minimal convergence rate. For example, when comparing the two algorithms, CAVOA achieved a significant improvement. It successfully reduced the cost function by approximately 0.023% in Case I and 0.035% in Case II, while also decreasing power loss by 2.57% in Case II and 0.57% in Case I. Additionally, CAVOA exhibited a remarkable reduction of 5.36% in voltage deviation compared to AVOA in Case I. Furthermore, in Case III, CAVOA demonstrated a decrease of 0.64% in gross cost when compared to AVOA.

Assessment of water resources carrying capacity using chaotic particle swarm genetic algorithm

AbstractWater resources carrying capacity (WRCC) has been evaluated repeatedly to guide sustainable regional development, with the increasing conflicts over water resources between society and nature. Urban underlying surfaces are constantly changing under the rapid development of urbanization, which has changed the WRCC. The chaotic particle swarm genetic algorithm (CPSGA) is proposed in this study to evaluate the WRCC. It combines the genetic algorithm (GA), chaotic optimization algorithm (COA), and particle swarm optimization (PSO), as well as introduces the chaotic mapping of COA and the velocity position update strategy of PSO into the GA framework to strengthen the population quality and improve the algorithm's efficiency. The effectiveness of CPSGA was demonstrated using three typical functions. Nanjing, China, was used as the study area to evaluate the WRCC from 2015 to 2018. The results showed that the comprehensive evaluation scores of the WRCC of Nanjing from 2015 to 2018 were up to 0.83. In addition, the CPSGA had better astringency and stability than GA, COA, and PSO. The application indicated that the proposed methodology is feasible, providing a reference for conducting WRCC research elsewhere.

Survey of Recent Applications of the Chaotic Lozi Map

Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure and applied its properties in many fields (e.g., improvement of physical devices, electrical components such as memristors, cryptography, optimization, evolutionary algorithms, synchronization, control, secure communications, AI with swarm intelligence, chimeras, solitary states, etc.) through algorithms such as the COLM algorithm (Chaotic Optimization algorithm based on Lozi Map), Particle Swarm Optimization (PSO), and Differential Evolution (DE). In this article, we present a survey based on dozens of articles on the use of this map in algorithms aimed at real applications or applications exploring new directions of dynamical systems such as chimeras and solitary states.

Satisfaction-Based Multiobjective Optimization of the Design of a 65 GHz Millimeter-Wave Connector

It is difficult to simultaneously ensure the radio frequency (RF) performance and mechanical strength of 65 GHz millimeter-wave connectors. To address this, satisfaction-based multiobjective method for connector design optimization is proposed. An optimization model is developed for the structural dimensions of 65 GHz millimeter-wave connectors to minimize the voltage standing wave ratio, insertion loss, and deflection and maximum stress of the center conductor. The proposed optimization model concurrently satisfies the design requirements in terms of characteristic impedance, transmission frequency, and dielectric withstanding voltage. The model is optimized by innovatively using the multiobjective chaotic optimization algorithm in microwave finite-element simulations. The resulting optimal structure satisfies all performance requirements, thereby proving the rationality and feasibility of the proposed method. Moreover, this study establishes a novel design for other microwave devices to solve the problem of multiple performance index restrictions.

Analysis of Chaotic Maps for Global Optimization and a Hybrid Chaotic Pattern Search Algorithm for Optimizing the Reliability of a Bank

Optimization is an imperative feature in almost all fields of Engineering, Economics, and Sciences. Due to the advent of high-end computers and the gradual increase in the complexity of optimization problems, algorithms for numerical optimization have been developed. Numerous existing numerical optimization algorithms suffer from premature convergence, poor local/global search abilities, and high computational complexity. A chaotic optimization algorithm and a chaotic map could help overcome most of these setbacks. This paper offers a detailed study and analysis of five chaotic maps used for global Optimization, namely Chebyshev, Cubic, ICMIC, Neuron, and Sine maps. This work also proposes a pioneering global optimization method, Hybrid Chaotic Pattern Search Algorithm (HCPSA), for finding the global minimum for multivariable unconstrained optimization problems. Numerical results over 12 benchmark functions and comparative results (comparison of accuracy and computational time) with some popular algorithms evidence the effectiveness of the proposed algorithm for higher dimensional non-linear functions. The efficient usage of chaotic maps has helped reduce the computational time to evaluate the optimum for higher dimensional non-linear functions. To showcase the use of HCPSA in a real-world problem, we have taken the problem of analyzing financial ratios for predicting bankruptcy. Banks predict bankruptcy from the start of their businesses to determine their financial stability. In this work, we initially perform Logistic Regression (LR) on the data obtained from the banks to get the reliability function with financial ratios as decision variables. After this, the function is maximized using HCPSA and a Chebyshev map. This methodology is beneficial for decision-makers within a bank to maximize the reliability of the financial ratios and, most essential, to protect the bank from disasters. Comparative results of reliability prediction using HCPSA and PSO and a non-parametric statistical test proves that the proposed algorithm is better in terms of accuracy.

Research on Human Resource Management Performance Evaluation Method Based on Chaos Optimization Algorithm

All enterprise components and business activities are centered on the customer. Whether human resource management is reasonable and effective not only is a matter of human resource management, but also directly influences whether other resources can be used reasonably and effectively, and determines the efficiency of business operations. In human resource management, perfect performance evaluation criteria are developed based on the actual situation in order to evaluate employee productivity and work ethic. Nonetheless, in the process of actual enterprise HR management performance evaluation work, there are not only imperfect performance evaluation standards, but also relatively objective evaluation standards, and HR cannot conduct a comprehensive analysis of each position, which has a negative impact on the quality of enterprise HR management work. This paper improves the performance evaluation model for the original data mining and proposes a human resource management performance evaluation method based on chaotic optimization algorithm, which generates the initial values of evaluation data through chaotic logistic mapping, bringing the initial data closer to the optimal value, reducing the impact of random initialization on the algorithm’s performance, and when the model is trained, it can make the algorithm’s performance more stable. Capability thereby addresses the flaws in the original evaluation method. Experiments demonstrate that our method significantly improves the precision of model training and prediction.

A Prediction Method for Floor Water Inrush Based on Chaotic Fruit Fly Optimization Algorithm–Generalized Regression Neural Network

The research was aimed at predicting floor water-inrush risk in coal mines and forewarn of such accidents to guide safe production of coal mines in practice. To this end, a prediction method for floor water inrush combining the chaotic fruit fly optimization algorithm (CFOA) and the generalized regression neural network (GRNN) is proposed. Floor water inrush is predicted by virtue of the robust nonlinear mapping capability of the GRNN. However, because the prediction effect of the GRNN is influenced by the smoothing factor, the CFOA is adopted to optimize this factor. In this way, influences of human factors during parameter determination of the GRNN prediction model are decreased, and the prediction accuracy and applicability of the model are improved. Results show that the CFOA–GRNN prediction model has an accuracy of 93.2% for whether floor water inrush will occur or not. Compared with the BPNN, RNN, and GRU network prediction model, the CFOA–GRNN model is superior in the prediction accuracy and generalization, and it can more accurately predict floor water inrush.

Chaotic whale-atom search optimization-based deep stacked auto encoder for crowd behaviour recognition

ABSTRACT The activity recognition gained immense popularity due to increasing number of surveillance cameras. The purpose of activity recognition is to detect the actions from the series of examination by varying the environmental condition. In this paper, Chaotic Whale Atom Search Optimisation (CWASO)-based Deep stacked autoencoder (CWASO-Deep SAE) is proposed for crowd behaviour recognition. The key frames are subjected to the descriptor of feature to extort the features, which bring out the classifier input vector. In this model, the statistical features, optical flow features and visual features are conducted to extract important features. Furthermore, the significant features are shown in the deep stacked auto-encoder (Deep SAE) for activity recognition, as the guidance of deep SAE is performed byCWASO, that is planned is designed by adjoining Atom search optimisation (ASO) algorithm and Chaotic Whale optimisation algorithm (CWOA). The proposed systems’ performance is analysed using two datasets. By considering the training data, the projected method attains performance that is high for dataset-1 with maximum precision, sensitivity, and with specific value of 96.826%, 96.790%, and 99.395%, respectively. Similarly, by considering the K-Fold, this method attains the maximum precision of 96.897%, sensitivity of 96.885%, and with specific values of 97.245% for the dataset-1.

Optimising an output of a slip line field using a chaotic swamp optimisation algorithm

In solving earth pressure problems, many input parameters are needed to account for more realistic soil properties and complex boundary conditions. Finding an optimal output while considering many inputs can be costly and time consuming. The input parameters themselves may be significantly uncertain due to lack of laboratory test data and variations in design and construction stages. Adopting an optimisation technique can be useful in such a problem. In this study, a chaotic particle swamp optimisation algorithm is applied to three different earth pressure problems – that is, a retaining wall problem, a plane strain tunnel problem and a suffosion sinkhole problem, to determine their global optimal outputs and corresponding input parameters. The problems are solved using a slip line theory satisfying static equilibrium and the Mohr–Coulomb failure criterion. This improved particle swamp optimisation algorithm is found to show better performances, in accuracy and computational effort, compared to conventional Monte Carlo simulations.

Decentralized Coordination Dispatch Model Based on Chaotic Mutation Harris Hawks Optimization Algorithm

Aiming at the economic dispatch problem for an interconnected system with wind power integration, and in order to realize the goals of system economy and improvement of the cross-regional consumption level of wind energy, a decentralized coordination dispatch model is established in this paper. In this model, a DC tie-line is cut by the branch cutting method and used as a coupling variable. A virtual upper-level dispatch center is established, and the economic dispatch problem to be solved is decomposed into a master optimization problem for the upper-level dispatch center and subsidiary optimization problems for the lower-level dispatch centers. For solving this model, an improved Harris hawks optimization (HHO) algorithm called the chaotic mutation Harris hawks optimization (CMHHO) algorithm is proposed. In the CMHHO algorithm, tent mapping and the “DE/pbad-to-pbest/1” strategy are introduced, and a new nonlinear escape energy factor adjustment is proposed. Through an algorithm comparison experiment and a simulation experiment with two examples, the superiority of the CMHHO algorithm, the effectiveness of the proposed model and the applicability of the CMHHO algorithm to the proposed model are verified. The model proposed is of great significance for solving the economic dispatch problem for an interconnected system with wind power integration.

Image Encryption Algorithm Based on Artificial Bee Colony Algorithm and Chaotic System

This article proposes an image encryption algorithm based on a chaotic bit-plane decomposition and optimization algorithm of a crossover operator artificial bee colony algorithm. Firstly, use the SHA-256 hash algorithm to calculate the plaintext image’s hash value as the starting value of the fractional Lorenz hyperchaotic system after operation. Utilize the chaotic sequence to permutate plaintext image in a bit plane to obtain the scrambled image. Secondly, block the scrambled image into four subimages of equal size, and count the hash value of each row of each block by the SHA-256 hash algorithm as the starting value of the Sine-Tent-Logistic chaotic system. Use the obtained chaotic sequence to substitute the images. Then, stitch the four sub-block images to get the final encrypted image, and the population is obtained. Finally, use the information entropy of ciphertext image as the fitness function of the artificial bee colony algorithm based on a crossover operator. Select the ciphertext image with the best information entropy from the population as the optimal encrypted image, and then, return the position value of the best honey source meanwhile. The experimental simulation and security analysis indicate that the scheme has an excellent encryption effect and ability to oppose various general attacks.

TUNING OF TWO-DEGREE-OF-FREEDOM IMC BASED ON A STRANGE NONCHAOTIC OPTIMIZATION APPROACH FOR LARGE TIME-DELAY PROCESSES

The internal model control (IMC) has a good control effect for large time-delay systems, but the parameter tuning of the controller is a challenge for researchers. As a typical fractal (strange) attractor, a strange nonchaotic attractor has the dynamic characteristics of randomness and ergodicity. Based on these characteristics, an optimization method is proposed to tune the parameters of an internal model controller for a large time-delay process, which is named a strange nonchaotic optimization algorithm (SNOA). SNOA has the advantages of easy implementation, short execution time and having robust mechanisms to avoid local optimization. It can find the optimal parameters of the internal model controller in large time-delay systems. The results show that SNOA can effectively improve the dynamic stability of the large time-delay systems. It has also proved to be superior to chaotic optimization (CO) algorithm and particle swarm optimization (PSO) algorithm.

Particle Swarm Optimization Algorithm-Tuned Fuzzy Cascade Fractional Order PI-Fractional Order PD for Frequency Regulation of Dual-Area Power System

This study proposes a virgin structure of Fuzzy Logic Control (FLC) for Load Frequency Control (LFC) in a dual-area interconnected electrical power system. This configuration benefits from the advantages of fuzzy control and the merits of Fractional Order theory in traditional PID control. The proposed design is based on Fuzzy Cascade Fractional Order Proportional-Integral and Fractional Order Proportional-Derivative (FC FOPI-FOPD). It includes two controllers, namely FOPI and FOPD connected in cascade in addition to the fuzzy controller and its input scaling factor gains. To boost the performance of this controller, a simple and powerful optimization method called the Particle Swarm Optimization (PSO) algorithm is employed to attain the best possible values of the suggested controller’s parameters. This task is accomplished by reducing the Integral Time Absolute Error (ITAE) of the deviation in frequency and tie line power. Furthermore, to authenticate the excellence of the proposed FC FOPI-FOPD, a comparative study is carried out based on the obtained results and those from previously published works based on classical PID tuned by the Losi Map-Based Chaotic Optimization Algorithm (LCOA), Fuzzy PID Optimized by Teaching Learning-Based Optimization (TLBO) algorithm and Fuzzy PID with a filtered derivative mode tuned by PSO, which is employed in the same interconnected power system. The robustness of the suggested fuzzy structure is investigated against the parametric uncertainties of the testbed system. The simulation results revealed that the proposed FC FOPI-FOPD is robust, and it outperformed the other investigated controllers. For example, the drops in the frequency in area one and area two were improved by 89.785% and 97.590%, respectively, based on employing the proposed fuzzy configuration compared with the results obtained from the traditional PID.

Design and Implementation of University Students Scientific Research Ability Evaluation System Based on Neural Network

At present, many colleges attach more and more importance to the cultivation of scientific research ability of college students. However, there is no unified standard to effectively measure the cultivation effect. The current performance inference method cannot comprehensively evaluate the scientific research ability of college students. Few scholars have directly analyzed the college students’ scientific research ability from the internal and external influencing factors. Therefore, this paper tries to design and implement a neural network analysis system for scientific research ability evaluation of college students. After surveying the status quo of scientific research ability evaluation of college students in northern China’s Hebei Province, a hierarchical evaluation index system was constructed for college students’ scientific research ability, referring to the existing evaluation index systems, and the weights were designed for the evaluation indices. Next, the backpropagation (BP) neural network was optimized by chaotic sine-cosine grasshopper optimization algorithm (CSCGOA) and used to establish a neural network analysis system for scientific research ability evaluation of college students. The proposed system was proved effective through experiments. The relevant results effectively enhance the scientific level and accuracy of the evaluation of college students’ scientific research ability, improve the cultivation of college students, and provide a scientific basis for colleges to understand the scientific research ability of their students.

The Bees Algorithm Tuned Sliding Mode Control for Load Frequency Control in Two-Area Power System

This paper proposes a design of Sliding Mode Control (SMC) for Load Frequency Control (LFC) in a two-area electrical power system. The mathematical model design of the SMC is derived based on the parameters of the investigated system. In order to achieve the optimal use of the proposed controller, an optimisation tool called the Bees Algorithm (BA) is suggested in this work to tune the parameters of the SMC. The dynamic performance of the power system with SMC employed for LFC is studied by applying a load disturbance of 0.2 pu in area one. To validate the supremacy of the proposed controller, the results are compared with those of recently published works based on Fuzzy Logic Control (FLC) tuned by Teaching–Learning-Based Optimisation (TLBO) algorithm and the traditional PID optimised by Lozi map-based Chaotic Optimisation Algorithm (LCOA). Furthermore, the robustness of SMC-based BA is examined against parametric uncertainties of the electrical power system by simultaneous changes in certain parameters of the testbed system with 40% of their nominal values. Simulation results prove the superiority and the robustness of the proposed SMC as an LFC system for the investigated power system.

Multiobjective Optimization of Turbine Coolant Collection/Distribution Plenum Based on the Surrogate Model

The turbine coolant collection/distribution chamber, as an important component of the secondary air system, undertakes the task of collecting and distributing coolant for guide vanes. To improve the outflow uniformity and reduce the flow loss, a multiobjective optimization method is developed for geometric parameters of turbine chamber. Numerical experiments were designed by Latin hypercube sampling and solved by the CFD method. Based on these data sampling, least square support vector machine (LS-SVM) was used for the surrogate model, and a kind of chaotic optimization algorithms was used for searching for the Pareto solution set. The results show that the streamline change in the optimized chamber is smoother, and the jet impingement effect of the coolant from the inlet tube was significantly weakened. At the condition that each goal has the weight of 0.5, the optimized discharge coefficient increases by 26%, and the outflow nonuniformity decreases by 79% compared with reference structure.

Rider Chaotic Biography Optimization-driven Deep Stacked Auto-encoder for Big Data Classification Using Spark Architecture

The novelty in big data is rising day-by-day in such a way that the existing software tools face difficulty in supervision of big data. Furthermore, the rate of the imbalanced data in the huge datasets is a key constraint to the research industry. Thus, this paper proposes a novel technique for handling the big data using Spark framework. The proposed technique undergoes two steps for classifying the big data, which involves feature selection and classification, which is performed in the initial nodes of Spark architecture. The proposed optimization algorithm is named rider chaotic biography optimization (RCBO) algorithm, which is the integration of the rider optimization algorithm (ROA) and the standard chaotic biogeography-based optimisation (CBBO). The proposed RCBO deep-stacked auto-encoder using Spark framework effectively handles the big data for attaining effective big data classification. Here, the proposed RCBO is employed for selecting suitable features from the massive dataset.