Chaotic Particle Swarm Optimization Research Articles

A multiple fault diagnosis approach for transformer based on double antenna RFID sensor and PSA-optimized LSTM

This work aims to realize multiple mechanical fault diagnosis for transformers in the incubation period. A double antenna radio frequency identification (RFID) sensor is used to obtain vibration signals generated by a transformer. The measured raw vibration signals have prominent nonlinear characteristics; besides, they are mixed with vast noises, such as electromagnetic interference, measurement disturbance and so on, making it challenging to identify distinguishable features from the measured data. The long short-term memory (LSTM), which exhibits satisfactory performance in dealing with large-scale nonlinear time-series signals, is adopted to extract features from high-dimensional raw signals. Because the parameters of the LSTM cell and support vector machine significantly determine the accuracy of diagnosis, these parameters are determined using the chaotic quantum particle swarm optimization algorithm. Moreover, the sparse periodical attention (PSA) mechanism is used to enhance the LSTM model’s performance by focusing on global feature learning and determining the input data length. The experimental results verify that the exploited RFID sensor realizes reliable data wireless transmission within 17.5 m. Moreover, the PSA-optimized LSTM approach achieves satisfactory trade-off between diagnosis accuracy and computation complexity while dealing with multiple mechanical fault diagnosis of a transformer in early stages.

A Novel Prediction Model for Seawall Deformation Based on CPSO-WNN-LSTM

Admittedly, deformation prediction plays a vital role in ensuring the safety of seawall during its operation period. However, there still is a lack of systematic study of the seawall deformation prediction model currently. Moreover, the absence of the major influencing factor selection is generally widespread in the existing model. To overcome this problem, the Chaotic Particle Swarm Optimization (CPSO) algorithm is introduced to optimize the wavelet neural network (WNN) model, and the CPSO-WNN model is utilized to determine the major influencing factors of seawall deformation. Afterward, on the basis of major influencing factor determination results, the CPSO algorithm is applied to optimize the parameters of Long Short-Term Memory (LSTM). Subsequently, the monitoring datasets are divided into training samples and test samples to construct the prediction model and validate the effectiveness, respectively. Ultimately, the CPSO-WNN-LSTM model is employed to fit and predict the long-term settlement monitoring data series of an actual seawall located in China. The prediction performances of LSTM and BPNN prediction models were introduced to be comparisons to verify the merits of the proposed model. The analysis results indicate that the proposed model takes advantage of practicality, high efficiency, stable capability, and high precision in seawall deformation prediction.

Chaotic heterogeneous comprehensive learning PSO method for size and shape optimization of structures

This paper proposes a novel chaotic heterogeneous comprehensive learning particle swarm optimization (CLPSO) method for the simultaneous size and shape design of structures. The heterogeneous CLPSO divides the particles into two explorative and exploitative subpopulations. The exploration performs the global searches for the set of best particles experienced solely within its own subpopulation, whilst the exploitation refines the deep searches learnt from the global best particle over an entire population. In essence, the proposed method maintains a good balance between the global explorative and local exploitative optimization schemes. The global searches within the explorative subpopulation are independent to the exploitative simulations even if the latter scheme prematurely converges to the local swarm position. For both subpopulations, the comprehensive learning approach constructs the particles through a cross-positioning process on the individual variable space and avoids the local optimal pitfall. Moreover, the chaotic logistic map within the exploitative optimization tests the global best particle through the set of diversely generated samples and hence enhances the local search ability. Various enriching techniques, including automatic adaptive (inertial weight and acceleration) parameters with dynamic space reduction, are incorporated to improve the likelihood of finding the optimal solution of practical-scale problems at modest computing efforts. The accuracy and robustness of the proposed method are illustrated through a number of planar and spatial truss design benchmarks subjected to the challenging nonconvex and/or nonsmooth programs.

Effective Workflow Scheduling in Cloud using Constriction Factor based Inertia Weight Particle Swarm Optimization

Cloud computing allows rapid provision of resources based on the need. This enables users to execute the independent tasks and dependent tasks called workflows on the cloud system. Workflow scheduling is a crucial problem that is NP Hard and is still a challenging problem. Particle Swarm Optimization (PSO) is one of the commonly used metaheuristic algorithms for solving task scheduling problems, but it has issues with premature convergence and lack of diversity. In recent years, chaotic maps have been employed in PSO to enhance its performance. This study proposes a Constriction factor-based inertia weight in PSO for workflow scheduling (CFPSO). The proposed algorithm utilizes a constriction factor for updating the inertia weight, which enhances the exploration ability of the algorithm thereby avoid local optima. The algorithm considers a fitness function with an aim to minimize makespan, service cost, and maximize load balance. The proposed algorithm is evaluated using a set of benchmark workflows, and the obtained results are compared with the standard PSO algorithm, Grey Wolf Optimizer (GWO) algorithm and Chaotic PSO algorithm. The extensive experimentation performed show that the proposed algorithm outperforms the other algorithms in terms of makespan, service cost, and load balance. The proposed CFPSO shows reduction of 20% of makespan, 2% of the service cost and 18% load balance rate compared to the conventional algorithms on Montage workflow with 1000 tasks. The use of constriction factor enhances the performance of the algorithm and makes it suitable for solving complex problems with multiple objectives. The proposed algorithm can be used in real-world applications to optimize workflow scheduling in cloud computing environments.

Offloading approach for mobile edge computing based on chaotic quantum particle swarm optimization strategy

Offloading approach for mobile edge computing based on chaotic quantum particle swarm optimization strategy

Overcoming Nonlinear Dynamics in Diabetic Retinopathy Classification: A Robust AI-Based Model with Chaotic Swarm Intelligence Optimization and Recurrent Long Short-Term Memory

Diabetic retinopathy (DR), which is seen in approximately one-third of diabetes patients worldwide, leads to irreversible vision loss and even blindness if not diagnosed and treated in time. It is vital to limit the progression of DR disease in order to prevent the loss of vision in diabetic patients. It is therefore essential that DR disease is diagnosed at an early phase. Thanks to retinal screening at least twice a year, DR disease can be diagnosed in its early phases. However, due to the variations and complexity of DR, it is really difficult to determine the phase of DR disease in current clinical diagnoses. This paper presents a robust artificial intelligence (AI)-based model that can overcome nonlinear dynamics with low computational complexity and high classification accuracy using fundus images to determine the phase of DR disease. The proposed model consists of four stages, excluding the preprocessing stage. In the preprocessing stage, fractal analysis is performed to reveal the presence of chaos in the dataset consisting of 12,500 color fundus images. In the first stage, two-dimensional stationary wavelet transform (2D-SWT) is applied to the dataset consisting of color fundus images in order to prevent information loss in the images and to reveal their characteristic features. In the second stage, 96 features are extracted by applying statistical- and entropy-based feature functions to approximate, horizontal, vertical, and diagonal matrices of 2D-SWT. In the third stage, the features that keep the classifier performance high are selected by a chaotic-based wrapper approach consisting of the k-nearest neighbor (kNN) and chaotic particle swarm optimization algorithms (CPSO) to cope with both chaoticity and computational complexity in the fundus images. At the last stage, an AI-based classification model is created with the recurrent neural network-long short-term memory (RNN-LSTM) architecture by selecting the lowest number of feature sets that can keep the classification performance high. The performance of the DR disease classification model was tested on 2500 color fundus image data, which included five classes: no DR, mild non-proliferative DR (NPDR), moderate NPDR, severe NPDR, and proliferative DR (PDR). The robustness of the DR disease classification model was confirmed by the 10-fold cross-validation. In addition, the classification performance of the proposed model is compared with the support vector machine (SVM), which is one of the machine learning techniques. The results obtained show that the proposed model can overcome nonlinear dynamics in color fundus images with low computational complexity and is very effective and successful in precisely diagnosing all phases of DR disease.

An improved long short term memory network for intrusion detection.

Over the years, intrusion detection system has played a crucial role in network security by discovering attacks from network traffics and generating an alarm signal to be sent to the security team. Machine learning methods, e.g., Support Vector Machine, K Nearest Neighbour, have been used in building intrusion detection systems but such systems still suffer from low accuracy and high false alarm rate. Deep learning models (e.g., Long Short-Term Memory, LSTM) have been employed in designing intrusion detection systems to address this issue. However, LSTM needs a high number of iterations to achieve high performance. In this paper, a novel, and improved version of the Long Short-Term Memory (ILSTM) algorithm was proposed. The ILSTM is based on the novel integration of the chaotic butterfly optimization algorithm (CBOA) and particle swarm optimization (PSO) to improve the accuracy of the LSTM algorithm. The ILSTM was then used to build an efficient intrusion detection system for binary and multi-class classification cases. The proposed algorithm has two phases: phase one involves training a conventional LSTM network to get initial weights, and phase two involves using the hybrid swarm algorithms, CBOA and PSO, to optimize the weights of LSTM to improve the accuracy. The performance of ILSTM and the intrusion detection system were evaluated using two public datasets (NSL-KDD dataset and LITNET-2020) under nine performance metrics. The results showed that the proposed ILSTM algorithm outperformed the original LSTM and other related deep-learning algorithms regarding accuracy and precision. The ILSTM achieved an accuracy of 93.09% and a precision of 96.86% while LSTM gave an accuracy of 82.74% and a precision of 76.49%. Also, the ILSTM performed better than LSTM in both datasets. In addition, the statistical analysis showed that ILSTM is more statistically significant than LSTM. Further, the proposed ISTLM gave better results of multiclassification of intrusion types such as DoS, Prob, and U2R attacks.

Cooperative control of multiple intersections combining agent and chaotic particle swarm optimization

The regional intersection can be regarded as an agent model, that should be controlled and optimized. The traditional particle swarm optimization algorithm has been enhanced through optimization techniques and the inclusion of chaos algorithms and agent interactive and cooperative control technology, resulting in the development of a chaotic particle swarm optimization algorithm. Multi-agent is applied to the collaborative control of intersections to realize the collaborative decision-making of multi-intersections. The state and action of intersection signal control agent are defined to reduce the dimension of state-action space and speed up the convergence rate. The proposed method takes vehicle delay, vehicle queue length and regional access ratio as optimization objectives, implements regional traffic signal control strategy and improves overall traffic efficiency. By constructing a simulation environment based on Paramics software, the effectiveness of the regional traffic signal control method based on chaotic particle swarm optimization algorithm is verified, and the convergence efficiency and signal timing optimization have interactive effects.

Digital Twin 3D System for Power Maintenance Vehicles Based on UWB and Deep Learning

To address the issue of the insufficient safety monitoring of power maintenance vehicles during power operations, this study proposes a vehicle monitoring scheme based on ultra wideband (UWB) and deep learning. The UWB localization algorithm employs Chaotic Particle Swarm Optimization (CSPO) to optimize the Time Difference of Arrival (TDOA)/Angle of Arrival (AOA) locating scheme in order to overcome the adverse effects of the non-visual distance and multipath effects in substations and significantly improve the positioning accuracy of vehicles. To solve the problem of the a large aspect ratio and the angle in the process of power maintenance vehicle operation situational awareness in the mechanical arm of the maintenance vehicle, the arm recognition network is based on the You Only Look Once version 5 (YOLOv5) and modified by Convolutional Block Attention Module (CBAM). The long-edge definition method with circular smoothing label, SIoU loss function, and HardSwish activation function enhance the precision and processing speed for the arm state. The experimental results show that the proposed CPSO-TDOA/AOA outperforms other algorithms in localization accuracy and effectively attenuates the non-visual distance and multipath effects. The recognition accuracy of the YOLOv5-CSL-CBAM network is substantially improved; the mAP value of the vehicles arm reaches 85.04%. The detection speed meets the real-time requirement, and the digital twin of the maintenance vehicle is effectively realized in the 3D substation model.

A Novel Parameter Estimation Method for PMSM by Using Chaotic Particle Swarm Optimization With Dynamic Self-Optimization

In this study, a novel parameter estimation method for permanent magnet synchronous motor (PMSM) of chaotic particle swarm optimization with dynamic self-optimization (DSCPSO) is proposed, where the voltage source inverter (VSI) nonlinearity is estimated simultaneously with the parameters to achieve real-time compensation of VSI nonlinearity. In DSCPSO, the tent chaos theory is introduced into the updating of particle swarm algorithm (PSO) populations, inertia weights and learning factors to enhance its ability to explore potentially better regions. Moreover, a memory tempering annealing (MTA) strategy is employed to guarantee particle pluralistic learning, which combines the superior robustness of the simulated annealing algorithm (SA) while enhancing population diversity. Furthermore, to achieve a reasonable tradeoff between exploration and exploitation, a dynamic lens imaging opposition-based learning (DLIOBL) and domain optimization strategy based on evolutionary information is designed, i.e., DLIOBL in the pre-evolutionary stage guarantees the depth of the exploration learning, while the domain optimization strategy is performed in the post-evolutionary stage accelerates the exploitation operation and avoids the problem of slow convergence in the late stages of PSO. The proposed method is applied to the parameter estimation of PMSM and the experimental results show that, the proposed method can track the VSI nonlinearity and variable parameter better than the conventional method under different working conditions.

Multi-index dominant grouping of rock mass discontinuities based on the combined weighting method: A case study for the Huayang tunnel

The properties of discontinuities are determined by their occurrence, trace length, aperture, roughness, and the degree of particle fill; therefore, a multi-index dominant grouping method for rock mass discontinuities based on the combined weighting method was proposed. Firstly, the combined weighting method was used to calculate the weighted value of each index participating in the similarity measurement, and a reasonable elimination of outlier discontinuities is achieved based on the principle of possibility clustering. The adaptive chaotic annealing particle swarm optimization algorithm was then used to search the global optimal initial clustering centers of the fuzzy C-means clustering algorithm. The objective function was established by minimizing the weighted sum of the distance between the discontinuities to be grouped, and the clustering centers to complete the multi-index dominant grouping of rock mass discontinuities. 230 artificial discontinuities with outliers were grouped and compared with other methods, which indicated that this method has higher grouping accuracy. The proposed method was applied to group the measured discontinuities of the Huayang tunnel in Chongqing City, China. Based on the grouping results, a discrete element model for tunnel excavation was established, and the construction was guided according to the calculated results from the model. The engineering applicability of the method was further verified.

Multi-objective route optimization of urban cold chain distribution using electric and diesel powered vehicles

Increasingly serious urban road congestion and environmental pollution have led some cities to impose restrictions such as limiting certain types of vehicles and the areas in which they can operate and introducing subsidies and other incentives for electric refrigerated vehicles. As a result, both internal combustion engine (ICE) refrigerated vehicles and electric refrigerated vehicles will be used together in urban cold chain distribution for a long time into the future. Most current studies are concerned with mixed vehicle type allocation or mixed vehicle routing problems. Although there are some studies that combine the two, there has been little research into the effects of low carbon emission and multiple objective optimization on distribution and routing for a mixture of vehicle types. This paper describes the creation of an optimized decision-making cold chain distribution model that includes different types of distribution vehicles and different route optimization criteria that represent the three enterprise objectives of minimal cost, minimum carbon emissions and minimum distance. The decision criteria are influenced by conflicting benefits offered by ICE and electric refrigerated vehicles as well as government subsidies for electric refrigerated vehicles and carbon emission trading by logistics enterprises. A chaotic particle swarm optimization algorithm was used to analyze a cold chain distribution system in Wuhan, Hubei Province, China. The results show that: (1) The choice of enterprise distribution models and the vehicles and routes determined are closely related to enterprise goals. To minimize total cost, ICE refrigerated trucks with less load capacity and electric refrigerated trucks with greater load capacity are preferred. To minimize carbon emissions, ICE refrigerated trucks and electric refrigerated trucks with less load capacity are preferred. To minimize total distance, ICE refrigerated trucks and electric refrigerated trucks with greater load capacity are preferred. (2) As the value of government subsidies increases, the total load capacity of electric refrigerated vehicles also increases, the distribution routes change, and total carbon emissions and total distribution costs decrease. (3) When carbon emission trading prices increase, the number of electric refrigerated vehicles gradually increases, the distribution path changes, the total distribution costs increase, and total carbon emissions decrease. Some suggestions are made for government to determine subsidies for electric refrigerated vehicles and carbon emission trading policies that will guide the choice of distribution vehicles and affect the criteria used for route optimization by cold chain logistics enterprises.

Internet of Things Energy Consumption Optimization in Buildings: A Step toward Sustainability

The internal components of a smart building interact through a compatible fabric and logic. A smart building integrates systems, structure, services, management, and their interrelationships to create a dynamic and cost-efficient environment. Smart buildings reduce the amount of cooling and heating load required to cool and heat spaces, thereby lowering operating costs and energy consumption without sacrificing occupant comfort. Smart structures are an Internet of Things (IoT) concern. The Internet of Things is a global network that virtualizes commonplace objects. The Internet of Things infuses non-technical objects with technology. IoT development has led to the creation of new protocols based on architectures for wireless sensor networks. Energy conservation extends the life and improves the performance of these networks, while overcoming the limitations of IoT node batteries. This research seeks to develop a data transmission model for routing IoT data in smart buildings. Utilization of intelligent object clustering and particle swarm optimization (PSO), chaotic particle swarm optimization (CPSO), and fractional chaotic order particle swarm optimization (FCPSO) optimization methods. Using the proposed algorithm to minimize energy consumption in the IoT is possible due to the algorithm’s ability to mitigate the problem by considering the number of parameters that can have a significant impact on performance, which is the goal of many optimization approaches.

Forecasting by Combining Chaotic PSO and Automated LSSVR

An automatic least square support vector regression (LSSVR) optimization method that uses mixed kernel chaotic particle swarm optimization (CPSO) to handle regression issues has been provided. The LSSVR model is composed of three components. The position of the particles (solution) in a chaotic sequence with good randomness and ergodicity of the initial characteristics is taken into consideration in the first section. The binary particle swarm optimization (PSO) used to choose potential input characteristic combinations makes up the second section. The final step involves using a chaotic search to narrow down the set of potential input characteristics before combining the PSO-optimized parameters to create CP-LSSVR. The CP-LSSVR is used to forecast the impressive datasets testing targets obtained from the UCI dataset for purposes of illustration and evaluation. The results suggest CP-LSSVR has a good predictive capability discussed in this paper and can build a projected model utilizing a limited number of characteristics.

Frequency control scheme based on the CDM-PID controller for the hybrid microgrid system with stochastic renewable generators

In this paper, we introduce a Coefficient Diagram Method (CDM) to design a conventional PID controller. This controller is used to decrease the frequency fluctuations of a microgrid system composed of two renewable energy sources (WTG and STPG) and four controlled elements (UC, FESS, BESS and DEG). The method compares two characteristic polynomials of the same order:, the coefficients of the first polynomial are a function of microgrid parameters and the unknown gains of the PID controller. The second is called the target polynomial; its coefficients are calculated by choosing the stability indices and the equivalent time constant to satisfy the desired performances of the closed-loop system. Mathematically, the order of the polynomial controller determines the type of linear system of equations to solve: undetermined or overdetermined. In our application, the least squares method is used to find an approximate solution to the overdetermined system resulting from this comparison. Digital simulation is performed to test the performance of the microgrid controlled by the CDM-PID controller. The obtained results are compared with two recently published works where the parameters of the PID controllers are tuned by DE and chaotic PSO algorithms. The results show that the CDM-PID controller gives better performance.

Adaptive slope and CPSO-based energy management strategy of hybrid energy storage system for electric logistics vehicles

Energy management strategy play a crucial role in the optimal control of energy in pure electric logistics vehicles with hybrid energy storage system (HESS). Aiming at the problem that the energy management strategy of HESS cannot be reasonably allocated according to different slope conditions, this paper adds the road slope coefficient to the input of fuzzy control and designs a fuzzy controller that automatically adjusts the output power of ultracapacitor based on different road slope coefficients. Then, a chaotic particle swarm optimization (CPSO) method is used to optimize the designed fuzzy controller. Finally, the simulation test is carried out under urban dynamometer driving schedule (UDDS) urban road driving cycle by using Matlab/Simulink. The results show that the improved control strategy can increase the energy utilization by 3.63\% and reduce the battery power consumption by 3.97%. Furthermore, the proposed strategy can improve 30.66% energy utilization and 18.70% ultracapacitor power storage at the downhill situation, and can reduce the energy consumption of the whole vehicle by 5.23%, the average current by 6.19%, and the lithium-ion battery power consumption by 2.20% under the actual urban road gradient.

A novel cyber intrusion detection model based on improved hybrid sampling

The class imbalance of samples of network traffic will cause the poor classification performance of intrusion detection models based on machine learning. To solve this problem, this paper researches sampling algorithm and deep learning for intrusion detection in imbalanced network traffic. This paper proposes a deep recurrent neural network (delayed long short-term memory (DLSTM)) intrusion detection model based on the balanced samples. First, an improved hybrid sampling (IHS) method based on chaotic particle swarm optimization (CPSO) algorithm is proposed as the sampling algorithm to balance the imbalanced samples. Next, a DLSTM with long short-term memory (LSTM) function is proposed to realize high-precision classification of intrusion behaviours. Finally, the method is validated on the standard network traffic dataset. The experimental results show that the DLSTM intrusion detection model based on the IHS method outperforms other comparative models at accuracy. The model is available to the computer network information security defence system.

Remaining useful life prediction of lithium-ion battery based on chaotic particle swarm optimization and particle filter

The remaining useful life (RUL) prediction of lithium-ion batteries is crucial to ensure the safety and reliability of electric vehicles. Due to the complexity of the battery aging mechanism, the accurate prediction of RUL by traditional methods is difficult to guarantee. To improve the prediction performance of the particle filter (PF), an improved particle filter based on the chaotic particle swarm optimization algorithm (CPSO-PF) is presented. Then it is applied to predict the RUL of lithium-ion batteries. First, for a better posterior estimate in the PF, CPSO is used to drive the prior distribution of the particles toward a high likelihood probability to obtain a better-proposed distribution, which helps overcome the problem of degeneracy and impoverishment of particles. Then, Three models were employed to track the degradation trajectory of the batteries, including PF、the extended Kalman particle filter (EKPF), and CPSO-PF. Finally, the RUL of lithium-ion batteries was predicted with the three models. The experimental results demonstrate that CPSO-PF has higher prediction accuracy and strong robustness.

Design and hardware in loop testing of an intelligent controller for power quality improvement in a complex micro grid

The wide-ranging use of renewable energy sources (RES) in the modern era leads to the association of distributed non-conventional energy resources in contrary to large-scale and localized conventional non-renewable sources. The prevalent use of distributed sources produces various Power-Quality issues. A thorough review of the literature provides numerous approaches for Power Quality (PQ) improvements; however, most techniques can improve only a few PQ problems. The new technical challenges like power loss, stability, reliability and power quality (PQ) issues are observed in present micro grid scenario. In this regard, this research work is an attempt to address PQ improvement in a three-phase realistic complex micro grid (integration of three simple micro grids to the point of common coupling. Improvement of various PQ factors for example sag/swell, unbalancing, power factor (Pf), total harmonic distortion (THD), communication delay and addition of impedance has been addressed in this research work. In this research article, a Kernel based Deep Auto Regressive Exogenous Output Neural Network (KDNARX) controller has been proposed and applied to improve power quality issues in a complex or realistic three phase complex micro grid (RTPCMG) in grid connected mode of operation. The RTPCMG is a combination of three simple grids with individual ratings of (4 kW, 4 kW and 6 kW). Photo voltaic cell, wind generator (WG), fuel cell (FC) and battery energy storage system (BESS) are the constituent distributed generators (DGs) for the proposed micro grid. The PQ improvement by application of proposed KDNARX controller to the DG inverter switching, has been overly tested in 12 different power quality issues under various operating conditions. The Kernel parameters are optimized by a new optimization technique called Cosine Chaotic PSO (CCPSO) algorithm. The results proved the strength of the new control technique ensuring PQ improvement and stability study of a three phase AC micro grid. Also, the potentiality of the new control scheme is compared with ANN and NARX and its superiority has been proved. Further, some case studies are validated through hardware in loop (HIL) environment thus justifying its real time implementation.

CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

(Background) To solve the cluster analysis better, we propose a new method based on the chaotic particle swarm optimization (CPSO) algorithm.
 (Methods) In order to enhance the performance in clustering, we propose a novel method based on CPSO. We first evaluate the clustering performance of this model using the Variance Ratio Criterion (VRC) as the evaluation metric. The effectiveness of the CPSO algorithm is compared with that of the traditional Particle Swarm Optimization (PSO) algorithm. The CPSO aims to improve the VRC value while avoiding local optimal solutions. The simulated dataset is set at three levels of overlapping: non-overlapping, partial overlapping, and severe overlapping. Finally, we compare CPSO with two other methods.
 (Results) By observing the comparative results, our proposed CPSO method performs outstandingly. In the conditions of non-overlapping, partial overlapping, and severe overlapping, our method has the best variance ratio criterion values of 1683.2, 620.5, and 275.6, respectively. The mean VRC values in these three cases are 1683.2, 617.8, and 222.6.
 (Conclusion) The CPSO performed better than other SOTA methods for cluster analysis problems. CPSO is effective for cluster analysis.