Synergistic Swarm Optimization Algorithm

This research paper presents a novel optimization method called the Synergistic Swarm Optimization Algorithm(SSOA).The SSOA combines the principles of swarmintelligence and synergistic cooperation to search for optimal solutions efficiently.A synergistic cooperation mechanism is employed,where particles exchange information and learn from each other to improve their search behaviors.This cooperation enhances the exploitation of promising regions in the search space while maintaining exploration capabilities.Furthermore,adaptive mechanisms,such as dynamic parameter adjustment and diversification strategies,are incorporated to balance exploration and exploitation.By leveraging the collaborative nature of swarm intelligence and integrating synergistic cooperation,the SSOAmethod aims to achieve superior convergence speed and solution quality performance compared to other optimization algorithms.The effectiveness of the proposed SSOA is investigated in solving the 23 benchmark functions and various engineering design problems.The experimental results highlight the effectiveness and potential of the SSOA method in addressing challenging optimization problems,making it a promising tool for a wide range of applications in engineering and beyond.Matlab codes of SSOA are available at:https://www.mathworks.com/matlabcentral/fileexchange/153466-synergistic-swarm-optimization-algorithm.

Hybrid Hierarchical Particle Swarm Optimization with Evolutionary Artificial Bee Colony Algorithm for Task Scheduling in Cloud Computing

Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.

Optimal Configuration of Fault Location Measurement Points in DC Distribution Networks Based on Improved Particle Swarm Optimization Algorithm

The escalating deployment of distributed power sources and random loads in DC distribution networks hasamplified the potential consequences of faults if left uncontrolled. To expedite the process of achieving an optimalconfiguration of measurement points, this paper presents an optimal configuration scheme for fault locationmeasurement points in DC distribution networks based on an improved particle swarm optimization algorithm.Initially, a measurement point distribution optimization model is formulated, leveraging compressive sensing.The model aims to achieve the minimum number of measurement points while attaining the best compressivesensing reconstruction effect. It incorporates constraints from the compressive sensing algorithm and networkwide viewability. Subsequently, the traditional particle swarm algorithm is enhanced by utilizing the Haltonsequence for population initialization, generating uniformly distributed individuals. This enhancement reducesindividual search blindness and overlap probability, thereby promoting population diversity. Furthermore, anadaptive t-distribution perturbation strategy is introduced during the particle update process to enhance the globalsearch capability and search speed. The established model for the optimal configuration of measurement points issolved, and the results demonstrate the efficacy and practicality of the proposed method. The optimal configurationreduces the number of measurement points, enhances localization accuracy, and improves the convergence speedof the algorithm. These findings validate the effectiveness and utility of the proposed approach.

A Proposed Feature Selection Particle Swarm Optimization Adaptation for Intelligent Logistics--A Supply Chain Backlog Elimination Framework

The diversity of data sources resulted in seeking effective manipulation and dissemination.The challenge that arises from the increasing dimensionality has a negative effect on the computation performance,efficiency,and stability of computing.One of the most successful optimization algorithms is Particle Swarm Optimization(PSO)which has proved its effectiveness in exploring the highest influencing features in the search space based on its fast convergence and the ability to utilize a small set of parameters in the search task.This research proposes an effective enhancement of PSO that tackles the challenge of randomness search which directly enhances PSO performance.On the other hand,this research proposes a generic intelligent framework for early prediction of orders delay and eliminate orders backlogs which could be considered as an efficient potential solution for raising the supply chain performance.The proposed adapted algorithm has been applied to a supply chain dataset which minimized the features set from twenty-one features to ten significant features.To confirm the proposed algorithm results,the updated data has been examined by eight of the well-known classification algorithms which reached a minimum accuracy percentage equal to 94.3%for random forest and a maximum of 99.0 for Naïve Bayes.Moreover,the proposed algorithm adaptation has been compared with other proposed adaptations of PSO from the literature over different datasets.The proposed PSO adaptation reached a higher accuracy compared with the literature ranging from 97.8 to 99.36 which also proved the advancement of the current research.

An Opposition-Based Learning-Based Search Mechanism for Flying Foxes Optimization Algorithm

The flying foxes optimization(FFO)algorithm,as a newly introduced metaheuristic algorithm,is inspired by the survival tactics of flying foxes in heat wave environments.FFO preferentially selects the best-performing individuals.This tendency will cause the newly generated solution to remain closely tied to the candidate optimal in the search area.To address this issue,the paper introduces an opposition-based learning-based search mechanism for FFO algorithm(IFFO).Firstly,this paper introduces niching techniques to improve the survival list method,which not only focuses on the adaptability of individuals but also considers the population’s crowding degree to enhance the global search capability.Secondly,an initialization strategy of opposition-based learning is used to perturb the initial population and elevate its quality.Finally,to verify the superiority of the improved search mechanism,IFFO,FFO and the cutting-edge metaheuristic algorithms are compared and analyzed using a set of test functions.The results prove that compared with other algorithms,IFFO is characterized by its rapid convergence,precise results and robust stability.

Research on Flexible Job Shop Scheduling Based on Improved Two-Layer Optimization Algorithm

To improve the productivity,the resource utilization and reduce the production cost of flexible job shops,this paper designs an improved two-layer optimization algorithm for the dual-resource scheduling optimization problem of flexible job shop considering workpiece batching.Firstly,a mathematical model is established to minimize the maximum completion time.Secondly,an improved two-layer optimization algorithm is designed:the outer layer algorithm uses an improved PSO(Particle Swarm Optimization)to solve the workpiece batching problem,and the inner layer algorithm uses an improved GA(Genetic Algorithm)to solve the dual-resource scheduling problem.Then,a rescheduling method is designed to solve the task disturbance problem,represented by machine failures,occurring in the workshop production process.Finally,the superiority and effectiveness of the improved two-layer optimization algorithm are verified by two typical cases.The case results show that the improved two-layer optimization algorithm increases the average productivity by 7.44% compared to the ordinary two-layer optimization algorithm.By setting the different numbers of AGVs(Automated Guided Vehicles)and analyzing the impact on the production cycle of the whole order,this paper uses two indicators,the maximum completion time decreasing rate and the average AGV load time,to obtain the optimal number of AGVs,which saves the cost of production while ensuring the production efficiency.This research combines the solved problem with the real production process,which improves the productivity and reduces the production cost of the flexible job shop,and provides new ideas for the subsequent research.

A Two-Layer Encoding Learning Swarm Optimizer Based on Frequent Itemsets for Sparse Large-Scale Multi-Objective Optimization

Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.

Fitness Sharing Chaotic Particle Swarm Optimization (FSCPSO): A Metaheuristic Approach for Allocating Dynamic Virtual Machine (VM) in Fog Computing Architecture

In recent decades,fog computing has played a vital role in executing parallel computational tasks,specifically,scientific workflow tasks.In cloud data centers,fog computing takes more time to run workflow applications.Therefore,it is essential to develop effective models for Virtual Machine(VM)allocation and task scheduling in fog computing environments.Effective task scheduling,VM migration,and allocation,altogether optimize the use of computational resources across different fog nodes.This process ensures that the tasks are executed with minimal energy consumption,which reduces the chances of resource bottlenecks.In this manuscript,the proposed framework comprises two phases:(i)effective task scheduling using a fractional selectivity approach and(ii)VM allocation by proposing an algorithm by the name of Fitness Sharing Chaotic Particle Swarm Optimization(FSCPSO).The proposed FSCPSO algorithm integrates the concepts of chaos theory and fitness sharing that effectively balance both global exploration and local exploitation.This balance enables the use of a wide range of solutions that leads to minimal total cost and makespan,in comparison to other traditional optimization algorithms.The FSCPSO algorithm’s performance is analyzed using six evaluation measures namely,Load Balancing Level(LBL),Average Resource Utilization(ARU),total cost,makespan,energy consumption,and response time.In relation to the conventional optimization algorithms,the FSCPSO algorithm achieves a higher LBL of 39.12%,ARU of 58.15%,a minimal total cost of 1175,and a makespan of 85.87 ms,particularly when evaluated for 50 tasks.

Improved Particle Swarm Optimization for Parameter Identification of Permanent Magnet Synchronous Motor

In the process of identifying parameters for a permanent magnet synchronous motor,the particle swarm optimization method is prone to being stuck in local optima in the later stages of iteration,resulting in low parameter accuracy.This work proposes a fuzzy particle swarm optimization approach based on the transformation function and the filled function.This approach addresses the topic of particle swarmoptimization in parameter identification from two perspectives.Firstly,the algorithm uses a transformation function to change the form of the fitness function without changing the position of the extreme point of the fitness function,making the extreme point of the fitness function more prominent and improving the algorithm’s search ability while reducing the algorithm’s computational burden.Secondly,on the basis of themulti-loop fuzzy control systembased onmultiplemembership functions,it is merged with the filled function to improve the algorithm’s capacity to skip out of the local optimal solution.This approach can be used to identify the parameters of permanent magnet synchronous motors by sampling only the stator current,voltage,and speed data.The simulation results show that the method can effectively identify the electrical parameters of a permanent magnet synchronous motor,and it has superior global convergence performance and robustness.

Optimization Algorithms for Sidelobes SSL Reduction: A Comparative Study

The development of new technologies in smart cities is often hailed as it becomes a necessity to solve many problems like energy consumption and transportation. Wireless networks are part of these technologies but implementation of several antennas, using different frequency bandwidths for many applications might introduce a negative effect on human health security. In wireless networks, most antennas generate sidelobes SSL. SSL causes interference and can be an additional resource for RF power that can affect human being health. This paper aims to study algorithms that can reduce SSL. The study concerns typical uniform linear antenna arrays. Different optimum side lobe level reduction algorithms are presented. Genetic algorithm GA, Chebyshev, and Particle Swarm Optimization algorithm are used in the optimization process. A comparative study between the indicated algorithms in terms of stability, precision, and running time is shown. Results show that using these algorithms in optimizing antenna parameters can reduce SSL. A comparison of these algorithms is carried out and results show the difference between them in terms of running time and SSL reduction Level.

Quantitative algorithm for airborne gamma spectrum of large sample based on improved shuffled frog leaping-particle swarm optimization convolutional neural network

In airborne gamma ray spectrum processing,different analysis methods,technical requirements,analysis models,and calculation methods need to be established.To meet the engineering practice requirements of airborne gamma-ray measurements and improve computational efficiency,an improved shuffled frog leaping algorithm-particle swarm optimization convolutional neural network(SFLA-PSO CNN)for large-sample quantitative analysis of airborne gamma-ray spectra is proposed herein.This method was used to train the weight of the neural network,optimize the structure of the network,delete redundant connections,and enable the neural network to acquire the capability of quantitative spectrum processing.In full-spectrum data processing,this method can perform the functions of energy spectrum peak searching and peak area calculations.After network training,the mean SNR and RMSE of the spectral lines were 31.27 and 2.75,respectively,satisfying the demand for noise reduction.To test the processing ability of the algorithm in large samples of airborne gamma spectra,this study considered the measured data from the Saihangaobi survey area as an example to conduct data spectral analysis.The results show that calculation of the single-peak area takes only 0.13~0.15 ms,and the average relative errors of the peak area in the U,Th,and K spectra are 3.11,9.50,and 6.18%,indicating the high processing efficiency and accuracy of this algorithm.The performance of the model can be further improved by optimizing related parameters,but it can already meet the requirements of practical engineering measurement.This study provides a new idea for the full-spectrum processing of airborne gamma rays.

Data-driven production optimization using particle swarm algorithm based on the ensemble-learning proxy model

Production optimization is of significance for carbonate reservoirs,directly affecting the sustainability and profitability of reservoir development.Traditional physics-based numerical simulations suffer from insufficient calculation accuracy and excessive time consumption when performing production optimization.We establish an ensemble proxy-model-assisted optimization framework combining the Bayesian random forest(BRF)with the particle swarm optimization algorithm(PSO).The BRF method is implemented to construct a proxy model of the injectioneproduction system that can accurately predict the dynamic parameters of producers based on injection data and production measures.With the help of proxy model,PSO is applied to search the optimal injection pattern integrating Pareto front analysis.After experimental testing,the proxy model not only boasts higher prediction accuracy compared to deep learning,but it also requires 8 times less time for training.In addition,the injection mode adjusted by the PSO algorithm can effectively reduce the gaseoil ratio and increase the oil production by more than 10% for carbonate reservoirs.The proposed proxy-model-assisted optimization protocol brings new perspectives on the multi-objective optimization problems in the petroleum industry,which can provide more options for the project decision-makers to balance the oil production and the gaseoil ratio considering physical and operational constraints.

Angular insensitive nonreciprocal ultrawide band absorption in plasma-embedded photonic crystals designed with improved particle swarm optimization algorithm

Using an improved particle swarm optimization algorithm(IPSO)to drive a transfer matrix method,a nonreciprocal absorber with an ultrawide absorption bandwidth and angular insensitivity is realized in plasma-embedded photonic crystals arranged in a structure composed of periodic and quasi-periodic sequences on a normalized scale.The effective dielectric function,which determines the absorption of the plasma,is subject to the basic parameters of the plasma,causing the absorption of the proposed absorber to be easily modulated by these parameters.Compared with other quasi-periodic sequences,the Octonacci sequence is superior both in relative bandwidth and absolute bandwidth.Under further optimization using IPSO with 14 parameters set to be optimized,the absorption characteristics of the proposed structure with different numbers of layers of the smallest structure unit N are shown and discussed.IPSO is also used to address angular insensitive nonreciprocal ultrawide bandwidth absorption,and the optimized result shows excellent unidirectional absorbability and angular insensitivity of the proposed structure.The impacts of the sequence number of quasi-periodic sequence M and collision frequency of plasma1ν1 to absorption in the angle domain and frequency domain are investigated.Additionally,the impedance match theory and the interference field theory are introduced to express the findings of the algorithm.

Product quality prediction based on RBF optimized by firefly algorithm

With the development of information technology,a large number of product quality data in the entire manufacturing process is accumulated,but it is not explored and used effectively.The traditional product quality prediction models have many disadvantages,such as high complexity and low accuracy.To overcome the above problems,we propose an optimized data equalization method to pre-process dataset and design a simple but effective product quality prediction model:radial basis function model optimized by the firefly algorithm with Levy flight mechanism(RBFFALM).First,the new data equalization method is introduced to pre-process the dataset,which reduces the dimension of the data,removes redundant features,and improves the data distribution.Then the RBFFALFM is used to predict product quality.Comprehensive expe riments conducted on real-world product quality datasets validate that the new model RBFFALFM combining with the new data pre-processing method outperforms other previous me thods on predicting product quality.

An Improved Lung Cancer Segmentation Based on Nature-Inspired Optimization Approaches

The distinction and precise identification of tumor nodules are crucial for timely lung cancer diagnosis andplanning intervention. This research work addresses the major issues pertaining to the field of medical imageprocessing while focusing on lung cancer Computed Tomography (CT) images. In this context, the paper proposesan improved lung cancer segmentation technique based on the strengths of nature-inspired approaches. Thebetter resolution of CT is exploited to distinguish healthy subjects from those who have lung cancer. In thisprocess, the visual challenges of the K-means are addressed with the integration of four nature-inspired swarmintelligent techniques. The techniques experimented in this paper are K-means with Artificial Bee Colony (ABC),K-means with Cuckoo Search Algorithm (CSA), K-means with Particle Swarm Optimization (PSO), and Kmeanswith Firefly Algorithm (FFA). The testing and evaluation are performed on Early Lung Cancer ActionProgram (ELCAP) database. The simulation analysis is performed using lung cancer images set against metrics:precision, sensitivity, specificity, f-measure, accuracy,Matthews Correlation Coefficient (MCC), Jaccard, and Dice.The detailed evaluation shows that the K-means with Cuckoo Search Algorithm (CSA) significantly improved thequality of lung cancer segmentation in comparison to the other optimization approaches utilized for lung cancerimages. The results exhibit that the proposed approach (K-means with CSA) achieves precision, sensitivity, and Fmeasureof 0.942, 0.964, and 0.953, respectively, and an average accuracy of 93%. The experimental results prove thatK-meanswithABC,K-meanswith PSO,K-meanswith FFA, andK-meanswithCSAhave achieved an improvementof 10.8%, 13.38%, 13.93%, and 15.7%, respectively, for accuracy measure in comparison to K-means segmentationfor lung cancer images. Further, it is highlighted that the proposed K-means with CSA have achieved a significantimprovement in accuracy, hence can be utilized by researchers for improved segmentation processes of medicalimage datasets for identifying the targeted region of interest.

Hybrid Global Optimization Algorithm for Feature Selection

This paper proposes Parallelized Linear Time-Variant Acceleration Coefficients and Inertial Weight of Particle Swarm Optimization algorithm(PLTVACIW-PSO).Its designed has introduced the benefits of Parallel computing into the combined power of TVAC(Time-Variant Acceleration Coefficients)and IW(Inertial Weight).Proposed algorithm has been tested against linear,non-linear,traditional,andmultiswarmbased optimization algorithms.An experimental study is performed in two stages to assess the proposed PLTVACIW-PSO.Phase I uses 12 recognized Standard Benchmarks methods to evaluate the comparative performance of the proposed PLTVACIWPSO vs.IW based Particle Swarm Optimization(PSO)algorithms,TVAC based PSO algorithms,traditional PSO,Genetic algorithms(GA),Differential evolution(DE),and,finally,Flower Pollination(FP)algorithms.In phase II,the proposed PLTVACIW-PSO uses the same 12 known Benchmark functions to test its performance against the BAT(BA)and Multi-Swarm BAT algorithms.In phase III,the proposed PLTVACIW-PSO is employed to augment the feature selection problem formedical datasets.This experimental study shows that the planned PLTVACIW-PSO outpaces the performances of other comparable algorithms.Outcomes from the experiments shows that the PLTVACIW-PSO is capable of outlining a feature subset that is capable of enhancing the classification efficiency and gives the minimal subset of the core features.

Closed-loop scheduling optimization strategy based on particle swarm optimization with niche technology and soft sensor method of attributes-applied to gasoline blending process

Gasoline blending scheduling optimization can bring significant economic and efficient benefits to refineries.However,the optimization model is complex and difficult to build,which is a typical mixed integer nonlinear programming(MINLP)problem.Considering the large scale of the MINLP model,in order to improve the efficiency of the solution,the mixed integer linear programming-nonlinear programming(MILP-NLP)strategy is used to solve the problem.This paper uses the linear blending rules plus the blending effect correction to build the gasoline blending model,and a relaxed MILP model is constructed on this basis.The particle swarm optimization algorithm with niche technology(NPSO)is proposed to optimize the solution,and the high-precision soft-sensor method is used to calculate the deviation of gasoline attributes,the blending effect is dynamically corrected to ensure the accuracy of the blending effect and optimization results,thus forming a prediction-verification-reprediction closed-loop scheduling optimization strategy suitable for engineering applications.The optimization result of the MILP model provides a good initial point.By fixing the integer variables to the MILPoptimal value,the approximate MINLP optimal solution can be obtained through a NLP solution.The above solution strategy has been successfully applied to the actual gasoline production case of a refinery(3.5 million tons per year),and the results show that the strategy is effective and feasible.The optimization results based on the closed-loop scheduling optimization strategy have higher reliability.Compared with the standard particle swarm optimization algorithm,NPSO algorithm improves the optimization ability and efficiency to a certain extent,effectively reduces the blending cost while ensuring the convergence speed.

Optimization of CNC Turning Machining Parameters Based on Bp-DWMOPSO Algorithm

Cutting parameters have a significant impact on the machining effect.In order to reduce the machining time and improve the machining quality,this paper proposes an optimization algorithm based on Bp neural networkImproved Multi-Objective Particle Swarm(Bp-DWMOPSO).Firstly,this paper analyzes the existing problems in the traditional multi-objective particle swarm algorithm.Secondly,the Bp neural network model and the dynamic weight multi-objective particle swarm algorithm model are established.Finally,the Bp-DWMOPSO algorithm is designed based on the established models.In order to verify the effectiveness of the algorithm,this paper obtains the required data through equal probability orthogonal experiments on a typical Computer Numerical Control(CNC)turning machining case and uses the Bp-DWMOPSO algorithm for optimization.The experimental results show that the Cutting speed is 69.4 mm/min,the Feed speed is 0.05 mm/r,and the Depth of cut is 0.5 mm.The results show that the Bp-DWMOPSO algorithm can find the cutting parameters with a higher material removal rate and lower spindle load while ensuring the machining quality.This method provides a new idea for the optimization of turning machining parameters.

An Energy-Efficient Multi-swarm Optimization in Wireless Sensor Networks

Wireless Sensor Networks are a group of sensors with inadequate power sources that are installed in a particular region to gather information from the surroundings.Designing energy-efficient data gathering methods in large-scale Wireless Sensor Networks(WSN)is one of the most difficult areas of study.As every sensor node has afinite amount of energy.Battery power is the most significant source in the WSN.Clustering is a well-known technique for enhan-cing the power feature in WSN.In the proposed method multi-Swarm optimiza-tion based on a Genetic Algorithm and Adaptive Hierarchical clustering-based routing protocol are used for enhancing the network’s lifespan and routing opti-mization.By using distributed data transmission modification,an adaptive hier-archical clustering-based routing algorithm for power consumption is presented to ensure continuous coverage of the entire area.To begin,a hierarchical cluster-ing-based routing protocol is presented in terms of balancing node energy con-sumption.The Multi-Swarm optimization(MSO)based Genetic Algorithms are proposed to select an efficient Cluster Head(CH).It also improves the network’s longevity and optimizes the routing.As a result of the study’sfindings,the pro-posed MSO-Genetic Algorithm with Hill climbing(GAHC)is effective,as it increases the number of clusters created,average energy expended,lifespan com-putation reduces average packet loss,and end-to-end delay.

Neural network hyperparameter optimization based on improved particle swarm optimization

Hyperparameter optimization is considered as one of the most challenges in deep learning and dominates the precision of model in a certain.Recent proposals tried to solve this issue through the particle swarm optimization(PSO),but its native defect may result in the local optima trapped and convergence difficulty.In this paper,the genetic operations are introduced to the PSO,which makes the best hyperparameter combination scheme for specific network architecture be located easier.Spe-cifically,to prevent the troubles caused by the different data types and value scopes,a mixed coding method is used to ensure the effectiveness of particles.Moreover,the crossover and mutation opera-tions are added to the process of particles updating,to increase the diversity of particles and avoid local optima in searching.Verified with three benchmark datasets,MNIST,Fashion-MNIST,and CIFAR10,it is demonstrated that the proposed scheme can achieve accuracies of 99.58%,93.39%,and 78.96%,respectively,improving the accuracy by about 0.1%,0.5%,and 2%,respectively,compared with that of the PSO.