Particle Swarm Optimization Algorithm Algorithm Research Articles

A Combined Marine Predators and Particle Swarm Optimization for Task Offloading in Vehicular Edge Computing Network

With the rapid advancement in technology, numerous advanced vehicular applications have emerged that generate large volumes of data that need to be processed on the fly. The vehicles' computing resources are limited and constrained in processing the huge amount of data generated by these applications. Cloud data centers, which are large and capable of processing the generated data, tend to be far away from the vehicles. The long distance between the cloud and the vehicles results in large transmission delays, making the cloud less suitable for executing such data. To address the long-standing issue of huge transmission delays in the cloud, edge computing, which deploys computing servers at the edge of the network, was introduced. The edge computing network shortens the communication distance between the vehicles and the processing resources and also provides more powerful computation compared to the vehicles' computing resources. The advantages offered by the vehicular edge network can only be fully realized with robust and efficient resource allocation. Poor allocation of these resources can lead to a worse situation than the cloud. In this paper, a hybrid Marine Predatory and Particle Swarm Optimization Algorithm (MPA–PSO) is proposed for optimal resource allocation. The MPA–PSO algorithm takes advantage of the effectiveness and reliability of the global and local search abilities of the Particle Swarm Optimization Algorithm (PSO) to improve the suboptimal global search ability of the MPA. This enhances the other steps in the MPA to ensure an optimal solution. The proposed MPA–PSO algorithm was implemented using MATLAB alongside the conventional PSO and MPA, and the proposed MPA–PSO recorded a significant improvement over the PSO and MPA.

Friction compensation control method for a typical excavator system based on the accurate friction model

Traditional identification methods make it difficult to accurately determine the parameters of the friction model. Based on the LuGre friction model, a hybrid optimization algorithm (HO) is presented to address such aspects. This algorithm combines the genetic algorithm (GA) and particle swarm optimization algorithm (PSO) to obtain the globally optimal solutions. It incorporates three main improvements: introducing selection and crossover operations into the PSO algorithm, utilizing a variable inertia weight coefficient, and applying variable learning coefficients for enhanced performance. Compared to the static optimal solutions of the GA and PSO algorithms, the HO algorithm can improve the optimal solution by 40.68 % and 35.89 % respectively. The HO algorithm can achieve the highest model accuracy: the maximum identified friction error with the HO algorithm is only 1.70 kN, compared to 3.69 kN with the GA method and 8.52 kN with the PSO algorithm. Furthermore, a novel adaptive friction compensation controller (AC) is introduced based on the identification results to improve the stability and accuracy of the electro-hydraulic proportional systems of a 23-ton robotic excavator. Comparisons with existing proportional integral differential (PID) and feedforward compensation controllers (FC) highlight the superiority of the proposed adaptive controller in terms of trajectory accuracy and robustness. In sinusoidal trajectory tracking experiments, the AC method can achieve the highest tracking performance among the three controllers, and the maximum tracking error is only 11.56 mm. Compared to the FC controller, the control accuracy with the AC controller can be improved by 43.38 %. Experiments and simulations have shown that the friction compensation controller can effectively mitigate friction and other disturbances. As a result, the phenomena of crawling and flat peak phenomena can be eliminated.

Study on agricultural drought disaster risk assessment in Heilongjiang reclamation area based on SSAPSO optimization projection pursuit model.

Heilongjiang reclamation area serves as a crucial hub for commodity grain production and strategic reserves in China, playing a vital role in maintaining national food security. Investigating the assessment of agricultural drought risk in this region can yield valuable insights into spatial and temporal variations in drought risk. Such insights can aid in formulating effective strategies for disaster prevention and mitigation, thereby minimizing food losses caused by drought disasters. This study employs a comprehensive indicator system comprising 17 indicators categorized into hazard, exposure, vulnerability, and resistance capacity. The projection pursuit model is applied to evaluate regional drought risk, while the PSO algorithm, optimized by the SSA algorithm, addresses the limitations of low local search ability and search accuracy during the large-scale search process of the PSO optimization algorithm. This study examines and compares the optimization and convergence capabilities of three algorithms: real number encoding-based genetic algorithm (RAGA), particle swarm optimization algorithm (PSO), and sparrow algorithm-based improved particle swarm optimization algorithm (SSAPSO). The analysis demonstrates that SSAPSO exhibits superior optimization performance and convergence properties, establishing it as a highly effective algorithm for optimization tasks. The findings reveal the following trends: over time, agricultural drought risk in Heilongjiang reclamation area has generally declined, with fluctuations observed in hazard and vulnerability, an increase in exposure, and a continuous enhancement of resistance capacity. Spatially, the western region exhibits significantly higher agricultural drought risk compared to the eastern region, primarily due to elevated hazard and vulnerability, coupled with lower resistance capacity. As the agricultural economy grows and agricultural expertise accumulates, the risk of agricultural drought decreases. However, variations in economic growth among different regions lead to diverse spatial distributions of risk.

Fuel consumption estimation for jet aircraft: a mathematical model development

PurposeReducing aircraft fuel consumption has become a paramount research area, focusing on optimizing operational parameters like speed and altitude during the cruise phase. However, the existing methods for fuel reduction often rely on complex experimental calculations and data extraction from embedded systems, making practical implementation challenging. To address this, this study aims to devise a simple and accessible approach using available information.Design/methodology/approachIn this paper, a novel analytic method to estimate and optimize fuel consumption for aircraft equipped with jet engines is proposed, with a particular emphasis on speed and altitude parameters. The dynamic variations in weight caused by fuel consumption during flight are also accounted for. The derived fuel consumption equation was rigorously validated by applying it to the Boeing 737–700 and comparing the results against the fuel consumption reference tables provided in the Boeing manual. Remarkably, the equation yielded closely aligned outcomes across various altitudes studied. In the second part of this paper, a pioneering approach is introduced by leveraging the particle swarm optimization algorithm (PSO). This novel application of PSO allows us to explore the equation’s potential in finding the optimal altitude and speed for an actual flight from Algiers to Brussels.FindingsThe results demonstrate that using the main findings of this study, including the innovative equation and the application of PSO, significantly simplifies and expedites the process of determining the ideal parameters, showcasing the practical applicability of the approach.Research limitations/implicationsThe suggested methodology stands out for its simplicity and practicality, particularly when compared to alternative approaches, owing to the ready availability of data for utilization. Nevertheless, its applicability is limited in scenarios where zero wind effects are a prevailing factor.Originality/valueThe research opens up new possibilities for fuel-efficient aviation, with a particular focus on the development of a unique fuel consumption equation and the pioneering use of the PSO algorithm for optimizing flight parameters. This study’s accessible approach can pave the way for more environmentally conscious and economical flight operations.

Adaptive multi-strategy particle swarm optimization for solving NP-hard optimization problems

Particle Swarm Optimization algorithm (PSO) has been widely utilized for addressing optimization problems due to its straightforward implementation and efficiency in tackling various test functions and engineering optimization problems. Nevertheless, PSO encounters issues like premature convergence and a lack of diversity, particularly when confronted with complex high-dimensional optimization tasks. In this study, we propose an enhanced version of the Island Model Particle Swarm Optimization (IMPSO), where island models are integrated into the PSO algorithm based on several migration strategies. The first contribution consists in applying a new selection and replacement strategies based on tabu search technique, while the second contribution consists in proposing a dynamic migration rate relying on the Biogeography-Based Optimization technique. To assess and validate the effectiveness of the proposed method, several unconstrained benchmark functions are applied. The obtained results confirm that the approach yield better performance than the old version of IMPSO for solving NP-hard optimization problems. Compared to the performance of other well-known evolutionary algorithms, the proposed approach is more efficient and effective.

A non-intrusive load recognition method combining adaptive PSO algorithm and CNN model

Real-time monitoring of electricity usage details through load monitoring techniques is a crucial aspect of smart power grid management and monitoring, allowing for the acquisition of information on the electricity usage of individual appliances for power users. Accurate detection of electricity load is essential for refined load management and monitoring of power supply quality, facilitating the improvement of power management at the user side and enhancing power operation efficiency. Non-intrusive load monitoring (NILM) techniques require only the analysis of total load data to achieve load monitoring of electricity usage details, and offer advantages such as low cost, easy implementation, high reliability, and user acceptance. However, with the increasing number of distributed new load devices on the user side and the diversification of device development, simple load recognition algorithms are insufficient to meet the identification needs of multiple devices and achieve high recognition accuracy. To address this issue, a non-intrusive load recognition (NILR) model that combines an adaptive particle swarm optimization algorithm (PSO) and convolutional neural network (CNN) has been proposed. In this model, pixelated images of different electrical V-I trajectories are used as inputs for the CNN, and the optimal network layer and convolutional kernel size are determined by the adaptive PSO optimization algorithm during the CNN training process. The proposed model has been validated on the public dataset PLAID, and experimental results demonstrate that it has achieved a overall recognition accuracy of 97.26% and F-1 score of 96.92%, significantly better than other comparison models. The proposed model effectively reduces the confusion between various devices, exhibiting good recognition and generalization capabilities.

Particle Swarm Optimization for Penalize cox models in long-term prediction of breast cancer data

The particle swarm optimization algorithm (PSO) was applied to penalize the Cox model for predicting long-term outcomes of breast cancer patients. This study makes use of data on 198 patients' breast cancer survival, including their age, estrogen receptor status, tumor size, and grade, as well as the expression levels of 76 genes. The objective was to identify a subset of features that could accurately predict patient survival while controlling for overfitting and model complexity. PSO was used to search for optimal model parameters. The algorithm was designed to minimize a penalized partial likelihood function, which balances the tradeoff between an accurate model and model complexity. The values of the objective function were compared with other feature selection techniques, including the Least Absolute Shrinkage and Selection Operator (LASSO) and Elastic regression, and were found to perform better in relation to predictive accuracy and feature selection. The study results showed that PSO-based Cox models with cross-validation to regularization parameters had higher prediction accuracy than models trained with other feature selection methods. The PSO algorithm identified a subset of features that were consistently selected across multiple iterations, indicating their importance in predicting patient survival. Overall, the study demonstrates the potential of PSO-based feature selection in improving the accuracy and interpretability of Cox regression models for predicting long-term outcomes in breast cancer patients.

Loss minimization in Quadratic Boost Converter Multilevel Inverter fed induction motor system by Tuning of FOPID controller using PSO

Particle swarm optimization algorithm (PSO) is suggested to discover fractional order PID (FOPID) controller optimal variables for a better performance of induction motor. This PSO algorithm is designed to handle multiple optimization issues, due to its ease of application. A Closed Loop Quadratic Boost Converter Multilevel Inverter Fed Induction Motor (QBCMLIIM) system is simulated to earn reduced switching losses and reduced THD by incorporating particle swarm optimization(PSO) tuned Fractional Order PID controller. PSO stands to be one of the popular Artificial Intelligence (AI) method. The PSO algorithm starts its process from the initial particles by allotting initial velocities to the particles. At each location the objective function and the corresponding best values are evaluated. The double loop feedback system enhances the performance and robustness by suppressing the oscillations and overshoots.

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 injection–production 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 gas–oil 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 gas–oil ratio considering physical and operational constraints.

Inversion Analysis of the In Situ Stress Field around Underground Caverns Based on Particle Swarm Optimization Optimized Back Propagation Neural Network

The in situ stress distribution is one of the driving factors for the design and construction of underground engineering. Numerical analysis methods based on artificial neural networks are the most common and effective methods for in situ stress inversion. However, conventional algorithms often have some drawbacks, such as slow convergence, overfitting, and the local minimum problem, which will directly affect the inversion results. An intelligent inverse method optimizing the back-propagation (BP) neural network with the particle swarm optimization algorithm (PSO) is applied to the back analysis of in situ stress. The PSO algorithm is used to optimize the initial parameters of the BP neural network, improving the stability and accuracy of the inversion results. The numerical simulation is utilized to calculate the stress field and generate training samples. In the application of the Shuangjiangkou Hydropower Station underground powerhouse, the average relative error decreases by about 3.45% by using the proposed method compared with the BP method. Subsequently, the in situ stress distribution shows the significant tectonic movement of the surrounding rock, with the first principal stress value of 20 to 26 MPa. The fault and the lamprophyre significantly influence the in situ stress, with 15–30% localized stress reduction in the rock mass within 10 m. The research results demonstrate the reliability and improvement of the proposed method and provide a reference for similar underground engineering.

Analysis of various algorithms for optimizing the wave energy converters associated with a sloped wall-type breakwater

The optimal arrangement of multiple wave energy converters (WECs) is an important topic that can greatly affect the efficiency of ocean energy extraction. This study used various algorithms to optimize multiple heaving-buoy-type hemispherical WEC associated with a sloped wall-type breakwater. To this end, a calculation framework linking a three-dimensional frequency-domain numerical wave tank (FR-NWT) based on the Rankin panel method and an optimization algorithm was established. The fitness function for optimization was set to the power efficiency of WEC. The algorithms used were a genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm (PSO), and advanced PSO algorithm. Under irregular wave conditions, optimization of the spacing between each WEC, the distance between the WEC and the breakwater, the diameter and draft of the WEC, the bottom length and slope angle of the breakwater were performed. The results of the advanced PSO algorithm were consistent and did not converge to local maxima. The excellence of the advanced PSO algorithm in this study was demonstrated.

A novel hybrid PSO based on levy flight and wavelet mutation for global optimization.

The concise concept and good optimization performance are the advantages of particle swarm optimization algorithm (PSO), which makes it widely used in many fields. However, when solving complex multimodal optimization problems, it is easy to fall into early convergence. The rapid loss of population diversity is one of the important reasons why the PSO algorithm falls into early convergence. For this reason, this paper attempts to combine the PSO algorithm with wavelet theory and levy flight theory to propose a new hybrid algorithm called PSOLFWM. It applies the random wandering of levy flight and the mutation operation of wavelet theory to enhance the population diversity and seeking performance of the PSO to make it search more efficiently in the solution space to obtain higher quality solutions. A series of classical test functions and 19 optimization algorithms proposed in recent years are used to evaluate the optimization performance accuracy of the proposed method. The experimental results show that the proposed algorithm is superior to the comparison method in terms of convergence speed and convergence accuracy. The success of the high-dimensional function test and dynamic shift performance test further verifies that the proposed algorithm has higher search stability and anti-interference performance than the comparison algorithm. More importantly, both t-Test and Wilcoxon's rank sum test statistical analyses were carried out. The results show that there are significant differences between the proposed algorithm and other comparison algorithms at the significance level α = 0.05, and the performance is better than other comparison algorithms.

Application of dynamic baseline adjustment based on swarm intelligence optimization in the signal processing of fiber SPR sensor

In view of the difficulty in determining the appropriate parameters in traditional centroid method, which is used to detect the resonance point of SPR reflection spectrum, a dynamic baseline adjustment method based on the particle swarm optimization algorithm (PSO) is proposed. The method regards the parameter of spectral width (β), number of measurement points below the baseline (m), and the area ratio (λ) as the foundation for selecting the best dynamic baseline. Based on the condition of two-level fitness function, PSO algorithm is adopted to track the dynamic baseline with the best combination of parameters. To verify the effectiveness of the algorithm, on the one hand, design the simulation experiments which prove that the new algorithm is superior to other algorithms in tracking ability and anti-noise ability. On the other hand, design the application experiment under the condition of light source fluctuation, by measuring the spectral data of standard sucrose solutions with 8 different concentrations by the fiber SPR sensor, the calculation effects of resonance point by four centroid methods are compared. The experimental results show that the improved method has the best predictive ability in measuring the concentrations of measured sucrose solutions, its fitting degree between the calculated resonance wavelength and the concentration of measured liquid is 0.9963, the root mean squares error (RMSE) is 1.78. In addition, the dominant positions of three parameters are investigated, the results show that the fixed m method has the best effect which can provide a basis for the selection of appropriate centroid parameters. Finally, to prove the feasibility of PSO in determining the parameters of optimal baseline, PSO and other metaheuristic algorithms are implemented for comparison. The experimental results show PSO algorithm has great application potential in terms of measurement effect and optimization speed for the studied problem. Therefore, the improved method can effectively extract the centroid parameters and eliminate the influence of light source fluctuation, which verifies the feasibility of the proposed method in the signal processing of fiber SPR sensor.

An Online Data-Driven Evolutionary Algorithm–Based Optimal Design of Urban Stormwater-Drainage Systems

To reduce flood risk in urban areas, an optimal design of drainage networks for urban areas is essential for flooding control and drainage management of the urban stormwater drainage system (USDS). A conventional design is generally used for drainage networks, resulting in high computational costs and limited flooding reduction effect. In this study, based on an on-line data-driven evolutionary algorithm coupled with the storm water management model (SWMM), a novel approach for USDS drainage network optimization design was developed. A case in Xi’an City, China, was then selected for practical implementation, where the performances of the local planning scheme, the particle swarm optimization algorithm (PSO) and the proposed approach were compared. Results confirmed that our proposed methodological approach is feasibility and highly efficiency, leading to a 32% reduction in total flooding from that resulting from the local planning scheme. In addition, the average computational time was reduced by 57%, while the flooding control effect was better, compared to PSO algorithm optimization. These results suggest that our optimization design approach is reliable and applicable, and can benefit and assist designers in practice.

Modeling and optimization approach for phytoremediation of formaldehyde from polluted indoor air by Nephrolepis obliterata plant.

This study aimed to model the removal of formaldehyde as an indoor air pollutant by Nephrolepis obliterata (R.Br.) J.Sm. plant using response surface methodology (RSM) and artificial neural network (ANN) models, and optimization of the models by particle swarm optimization algorithm (PSO). The data obtained in pilot-scale experiments under a controlled environment were used in this study. The effects of parameters on the removal efficiency such as formaldehyde concentration, relative humidity, light intensity, and leaf surface area were empirically investigated and considered as model parameters. The results of the RSM model, with power transformation, were in meaningful compromise with the experiments. A multilayer perceptron (MLP) neural network was also designed, and the mean of squared error (MSE), mean absolute error (MAE), and R2 were used to evaluate the network. Several training algorithms were assessed and the best one, the Levenberg Marquardt (LM), was selected. The PSO algorithm proved that the highest removal efficiency of formaldehyde was obtained in the presence of light, maximum leaf surface area and relative humidity, and at the lowest inlet concentration. The empirical system breakthrough occurred at 15mg/m3 of formaldehyde, and the maximum elimination capacity was about 0.96mg per m2 of leaves. The findings indicated that the ANN model predicted the removal efficiency more accurately compared to the RSM model.

Particle swarm optimization of the spectral and energy efficiency of an SCMA‐based heterogeneous cellular network

AbstractBackgroundThe effect of stochastic small base station (SBS) deployment on the energy efficiency (EE) and spectral efficiency (SE) of sparse code multiple access (SCMA)‐based heterogeneous cellular networks (HCNs) is still mostly unknown.AimThis research study seeks to provide insight into the interaction between SE and EE in SBS sleep‐mode enabled SCMA‐based HCNs.MethodologyA model that characterizes the energy‐spectral‐efficiency (ESE) of a two‐tier SBS sleep‐mode enabled SCMA‐based HCN was derived. A multiobjective optimization problem was formulated to maximize the SE and EE of the SCMA‐based HCN simultaneously. The multiobjective optimization problem was solved using a proposed weighted sum modified particle swarm optimization algorithm (PSO). A comparison was made between the performance of the proposed weighted sum modified PSO algorithm and the genetic algorithm (GA) and the case where the SCMA‐based HCN is unoptimized.ResultsThe Pareto‐optimal front generated showed a simultaneous maximization of the SE and EE of the SCMA‐based HCN at high traffic levels and a convex front that allows network operators to select the SE‐EE tradeoff at low traffic levels flexibly. The proposed PSO algorithm offers a higher SBS density, and a higher SBS transmit power at high traffic levels than at low traffic levels. The unoptimized SCMA‐based HCN achieves an 80% lower SE and a 51% lower EE than the proposed PSO optimized SCMA‐based HCN. The optimum SE and EE achieved by the SCMA‐based HCN using the proposed PSO algorithm or the GA are comparable, but the proposed PSO uses a 51.85% lower SBS density and a 35.96% lower SBS transmit power to achieve the optimal SE and EE at moderate traffic levels.ConclusionIn sleep‐mode enabled SCMA‐based HCNs, network engineers have to decide the balance of SBS density and SBS transmit power that helps achieve the desired SE and EE.

Comparison of cascade P-PI controller tuning methods for PMDC motor based on intelligence techniques

In this paper, there are two contributions: The first contribution is to design a robust cascade P-PI controller to control the speed and position of the permanent magnet DC motor (PMDC). The second contribution is to use three methods to tuning the parameter values for this cascade controller by making a comparison between them to obtain the best results to ensure accurate tracking trajectory on the axis to reach the desired position. These methods are the classical method (CM) and it requires some assumptions, the genetic algorithm (GA), and the particle swarm optimization algorithm (PSO). The simulation results show the system becomes unstable after applying the load when using the classical method because it assumes cancellation of the load effect. Also, an overshoot of about 3.763% is observed, and a deviation from the desired position of about 12.03 degrees is observed when using the GA algorithm, while no deviation or overshoot is observed when using the PSO algorithm. Therefore, the PSO algorithm has superiority as compared to the other two methods in improving the performance of the PMDC motor by extracting the best parameters for the cascade P-PI controller to reach the desired position at a regular speed.

Hyperspectral remote sensing image classification based on spectral-spatial feature fusion and PSO algorithm

Hyperspectral images(HSI) have rich spectral information and spatial information. In the classification of hyperspectral images, the combination of spectral information and spatial information has become an effective means to obtain good classification results. Specifically, firstly, PCA algorithm is introduced to extract the spectral information of the image. Secondly, a bilateral filter is introduced for each band to extract the spatial information of the image. Thirdly, the image is classified by using SVM to get the final classification result. Considering that the performance of SVM depends on the choice of parameters, particle swarm optimization algorithm (PSO) is combined with the proposed method to find the optimal penalty parameters and kernel parameters. We find that the classification accuracy is effectively improved by using PCA, bilateral filtering and optimizing SVM-PSO parameters on this basis. Experimental results based on one real hyperspectral dataset show that the proposed algorithm can achieve higher classification accuracy in a shorter time than other algorithms.

A modified PSO Algorithm based on Cloud Theory for optimizing the Fuzzy PID controller

To obtain a more efficient intelligent controller, this paper presents a modified cloud theory-based particle swarm optimization (CTPSO) algorithm to improve fuzzy PID controller. Cloud evolution and mutation methods based on cloud theory are introduced to tune inertia weight of particle swarm optimization algorithm (PSO), which can improve the optimization accuracy and speed of PSO. The comparative experiments indicate that CTPSO performs better than PSO and other optimization algorithm recently proposed by other researchers. The CTPSO is used to set the initial PID control parameters and optimize control rules of fuzzy PID controller. According to an engineering case of the 180°C-die heater’s temperature control, the novel optimized fuzzy PID controller can suppress the oscillation and overshoot significantly. It also owns smaller adjustment time, static error and better comprehensive performance compared with the initial controller.

Performance analysis of selected metaheuristic optimization algorithms applied in the solution of an unconstrained task

PurposeThe purpose of this paper is to execute the efficiency analysis of the selected metaheuristic algorithms (MAs) based on the investigation of analytical functions and investigation optimization processes for permanent magnet motor.Design/methodology/approachA comparative performance analysis was conducted for selected MAs. Optimization calculations were performed for as follows: genetic algorithm (GA), particle swarm optimization algorithm (PSO), bat algorithm, cuckoo search algorithm (CS) and only best individual algorithm (OBI). All of the optimization algorithms were developed as computer scripts. Next, all optimization procedures were applied to search the optimal of the line-start permanent magnet synchronous by the use of the multi-objective objective function.FindingsThe research results show, that the best statistical efficiency (mean objective function and standard deviation [SD]) is obtained for PSO and CS algorithms. While the best results for several runs are obtained for PSO and GA. The type of the optimization algorithm should be selected taking into account the duration of the single optimization process. In the case of time-consuming processes, algorithms with low SD should be used.Originality/valueThe new proposed simple nondeterministic algorithm can be also applied for simple optimization calculations. On the basis of the presented simulation results, it is possible to determine the quality of the compared MAs.