Algorithm Called Particle Swarm Optimization Research Articles

Nature-inspired Metaheuristics for finding Optimal Designs for the Continuation-Ratio Models

The continuation-ratio (CR) model is frequently used in dose response studies to model a three-category outcome as the dose levels vary. Design issues for a CR model defined on an unrestricted dose interval have been discussed for estimating model parameters or a selected function of the model parameters. This paper uses metaheuristics to address design issues for a CR model defined on any compact dose interval when there are one or more objectives in the study and some are more important than others. Specifically, we use an exemplary nature-inspired metaheuristic algorithm called particle swarm optimization (PSO) to find locally optimal designs for estimating a few interesting functions of the model parameters, such as the most effective dose ($MED$), the maximum tolerated dose ($MTD$) and for estimating all parameters in a CR model. We demonstrate that PSO can efficiently find locally multiple-objective optimal designs for a CR model on various dose intervals and a small simulation study shows it tends to outperform the popular deterministic cocktail algorithm (CA) and another competitive metaheuristic algorithm called differential evolutionary (DE). We also discuss hybrid algorithms and their flexible applications to design early Phase 2 trials or tackle biomedical problems, such as different strategies for handling the recent pandemic.

A Machine Learning Approach for Walking Classification in Elderly People with Gait Disorders.

Walking ability of elderly individuals, who suffer from walking difficulties, is limited, which restricts their mobility independence. The physical health and well-being of the elderly population are affected by their level of physical activity. Therefore, monitoring daily activities can help improve the quality of life. This becomes especially a huge challenge for those, who suffer from dementia and Alzheimer's disease. Thus, it is of great importance for personnel in care homes/rehabilitation centers to monitor their daily activities and progress. Unlike normal subjects, it is required to place the sensor on the back of this group of patients, which makes it even more challenging to detect walking from other activities. With the latest advancements in the field of health sensing and sensor technology, a huge amount of accelerometer data can be easily collected. In this study, a Machine Learning (ML) based algorithm was developed to analyze the accelerometer data collected from patients with walking difficulties, who live in one of the municipalities in Denmark. The ML algorithm is capable of accurately classifying the walking activity of these individuals with different walking abnormalities. Various statistical, temporal, and spectral features were extracted from the time series data collected using an accelerometer sensor placed on the back of the participants. The back sensor placement is desirable in patients with dementia and Alzheimer's disease since they may remove visible sensors to them due to the nature of their diseases. Then, an evolutionary optimization algorithm called Particle Swarm Optimization (PSO) was used to select a subset of features to be used in the classification step. Four different ML classifiers such as k-Nearest Neighbors (kNN), Random Forest (RF), Stacking Classifier (Stack), and Extreme Gradient Boosting (XGB) were trained and compared on an accelerometry dataset consisting of 20 participants. These models were evaluated using the leave-one-group-out cross-validation (LOGO-CV) technique. The Stack model achieved the best performance with average sensitivity, positive predictive values (precision), F1-score, and accuracy of 86.85%, 93.25%, 88.81%, and 93.32%, respectively, to classify walking episodes. In general, the empirical results confirmed that the proposed models are capable of classifying the walking episodes despite the challenging sensor placement on the back of the patients, who suffer from walking disabilities.

PSO-DBNet for Peak-to-Average Power Ratio Reduction Using Deep Belief Network

Data transmission through a wireless network has faced various signal problems in the past decades. The orthogonal frequency division multiplexing (OFDM) technique is widely accepted in multiple data transfer patterns at various frequency bands. A recent wireless communication network uses OFDM in long-term evolution (LTE) and 5G, among others. The main problem faced by 5G wireless OFDM is distortion of transmission signals in the network. This transmission loss is called peak-to-average power ratio (PAPR). This wireless signal distortion can be reduced using various techniques. This study uses machine learning-based algorithm to solve the problem of PAPR in 5G wireless communication. Partial transmit sequence (PTS) helps in the fast transfer of data in wireless LTE. PTS is merged with deep belief neural network (DBNet) for the efficient processing of signals in wireless 5G networks. Result indicates that the proposed system outperforms other existing techniques. Therefore, PAPR reduction in OFDM by DBNet is optimized with the help of an evolutionary algorithm called particle swarm optimization. Hence, the specified design supports in improving the proposed PAPR reduction architecture.

Sizing Optimization Algorithm for Vehicle-to-Grid System Considering Cost and Reliability Based on Rule-Based Scheme

The most widely two Renewable Energy Sources (RESs) used are solar and wind as naturally found sources due to the provided merits as clean, free of charge, and environmentally friendly. However, they are facing limitations in intermittency. This article aims to utilize natural resources integrated with the utility grid and Electric Vehicle (EV) to provide a hybrid system with a minimum of two objectives namely Cost of Electricity (COE) and reliability using the Losses Power Supply Probability (LPSP) method. The two mentioned objectives are considered to satisfy the residential load demand with EV in terms of Vehicle-to-Grid (V2G) as this article considered. The mentioned objective has been addressed by the Improved Antlion Optimization Algorithm (IALO) and coupled with a high supervisory control method called Rule-Based Energy Management Strategy (RB-EMS) to guarantee to spread the power among the system component. Optimization results show the hybrid integration of the utilized RESs with the Battery (BT) gives the most economic and reliable system for the study area integrated with the EV battery. The gained result was validated with a natural-inspired metaheuristic algorithm called Particle Swarm Optimization (PSO). This article assesses the effect on the RESs generators to achieve an economic and reliable system.

Infrared Image Enhancement Based on Optimally Weighted Multi-Scale Laplacian of Gaussian and Local Statistics Using Particle Swarm Optimization

Infrared imagery is extensively used in defense, remote sensing and medical applications. While the infrared images have many advantages over RGB images, the details in these images are usually blurred which in turn leads to some difficulties for human operators. In this paper, a new method based on Laplacian of Gaussian scale-space and local variance is presented to improve the visual quality of the infrared images. At the first step, the Gaussian scale-space is constructed by convolving the original image with different Gaussian kernels. Then, the two-dimensional Laplacian kernels are convolved with the Gaussian scale-space to achieve details with both positive as well as negative contrasts. The weighted details are added to the original image to deblur the dim areas. At the final step, to increase the dynamic range of the image and have better visual quality, the local variance of the image is also added to the output of the previous step. Since finding optimum weighting coefficients is a difficult task empirically, here, we use a population-based meta-heuristic optimization algorithm called particle swarm optimization (PSO) to find the optimum values for weighting coefficient values. Beside qualitative comparison, Structural Similarity (SSIM) and second-derivative-like measure of enhancement (SDME) are used to quantitatively investigate the images quality. The proposed method outperforms the baseline algorithms in both qualitative and quantitative perspectives.

Introduction of a novel evolutionary neural network for evaluating the compressive strength of concretes: A case of Rice Husk Ash concrete

The construction industry is facing challenges from the hazardous nature of Ordinary Portland Cement (OPC) production as one of the main contributors to global warming and CO2 emission. Given its increasing demand, the need to replace OPC with sustainable alternatives for green concrete production is essential. The promising results of using Rice Husk Ash (RHA) in concrete mixtures as a supplementary cementitious material (SCM) have attracted great attention. However, conventional laboratory procedures for the analysis of concrete properties like Compressive Strength (CS) are laborious and expensive. Therefore, developing a reliable and accurate model for its prediction can save time and reduce operational costs. In this study, the Artificial Neural Network (ANN) technique was hybridized with a robust optimization technique called Particle Swarm Optimization algorithm with Two Differential mutations (PSOTD) to predict the CS of RHA concrete. To compare the results of the PSOTD over classical optimization techniques, three other algorithms, including the best reported conventional Back-Propagation algorithm (i.e., Levenberg-Marquardt (LM)), Differential Evolution (DE), and Particle Swarm Optimization (PSO), were employed. For the training dataset, the coefficients of determination obtained for the ANN-LM, ANN-DE, ANN-PSO, and ANN-PSOTD were 0.9797, 0.9389, 0.9462, and 0.9803, while for the testing dataset, the values were 0.9682, 0.9198, 0.9223, and 0.9697, respectively. Overall, the error measures show the superiority of the ANN-PSOTD in predicting the CS of RHA concretes. To further enhance the prediction accuracy and reliability, the hybrid model of ANN-LM and ANN-PSOTD (i.e., ANN-PSOTD-LM) was also proposed. However, there is a trade-off between the computational time and the accuracy of models when the ANN-PSOTD-LM technique is chosen.

An improved classification of mineralized zones using particle swarm optimization: A case study from Dagh-Dali Zn[sbnd]Pb (±Au) prospect, Northwest Iran

Classification of mineralized areas into different geochemical classes in terms of prospectivity is crucial in the optimal management of exploration risk and costs. Machine learning (ML) algorithms can be served as appropriate alternatives for separating ore-related anomalies due to avoiding the assumptions of statistical distribution and compatibility with the multivariate nature of geochemical features. By hybridizing the ML with a metaheuristic algorithm called particle swarm optimization (PSO), this contribution aims to provide an innovative approach to optimize the classification of geochemical anomalies within the study area. The algorithm, PSO, is inspired by simulating the social behavior of flocks of birds in search of food. The Dagh-Dali ZnPb (±Au) mineral prospect in northwest Iran was subjected as a case study to examine the integrity of the proposed method. Mineralization-related features were extracted by applying principal component analysis (PCA) on metallogenic elements analyzed in soil samples as PC1 and PC2 with elemental assemblages of AgAuPbZn and PbZn, respectively. The silhouette index was employed to estimate the number of underlying geochemical clusters within the adopted feature space. To constitute a comparative analysis, two k-means clustering and PSO-based learning (PSO-L) algorithms were implemented to classify the gridded data of PC1 and PC2 within the study area. The results indicated that the use of PSO has improved the cost function of the clustering problem (up to 4%). Adapting the mineralization classes with the metallogenic evidence demonstrated by boreholes drilled in the study area indicated that PSO-L was superior to the traditional k-means method, improving the accurate estimation of subsurface mineralization classes by 7%. By overcoming the drawbacks of conventional methods for trapping at the local optima, PSO-based learning possesses the potential to highlight weak mineralization signals that are numerically located in boundary conditions. The results show that the proposed approach can serve as an effective medium for optimal modeling of geochemical classes and management of detailed exploration operations.

Optimizing process of Healthcare Assistance at Road Side using Particle Swarm optimization and Person Accident Behaviour

In the worldwide road accidents are very common and happened throughout the day. It is not restricted to time, density of population, geographical location, tropical geography, etc. Due to rapid increase in population and many other factors like driving and safety rules, driving pattern, etc., the worldwide rate of roadside accidents are also increasing. The African countries is having highest road accident inhabitants along with highest number of fatalities, whereas the Asian countries are the second rank in the world incurred rate of accidents with more fatalities during the road accidents. Hence, In order to handle these road accidents the major concern is to provide quick and fast emergency and health-care services like deployment of quick response team(QrT), first-aid, immediate hospitalization, and various assistance services that helps in reducing the fatalities during the road accidents. Now there is a need to develop effective and less parameterized approach which will helps in reducing the road accidents and provide quick response assistance to the needy. In order to develop the effective and comprehensive solution to the above mentioned problem, optimization is the key ingredient, which results in the evolvement of one of the most popular and effective algorithm called particle swarm optimization. In this paper we are going to evaluate, analyse and simulate particle swarm optimization (PSO) algorithm in order to design and develop novel solution to the above mentioned problem based on accident pattern and the behaviour of a person who met with the road accident.

Optimized color image watermarking through watermark strength optimization using particle swarm optimization technique

Digital Watermarking is a technique in which some presume content like image or data is embedded in any cover content in a way such that the quality of the digital content should not be degraded and it should not be visible to human eyes. In this paper a secure watermarking scheme has been proposed for color images and is optimized using one of the nature inspired algorithm called Particle swarm optimization. Here for embedding color watermark is used and is embedded in all three planes (R,G,B) of color host image using 2 D DCT and entropy encoding scheme. The value of embedding strength is optimized using PSO algorithm to provide balance between robustness and imperceptibility characteristics of watermarking. The proposed algorithm is tested by performing various types of attacks on watermarked image and good PSNR and NC values are received which proves the imperceptibility and robustness of the scheme.

Optimization of street canyon outdoor channel deployment geometry for mmWave 5G communication

Millimeter Wave (mmWave) channel study is important in 5G communication to assess novel technological solutions in realistic environments. Thus, it is vital to develop reliable channel models integrating the effects of mmWave atmospheric absorption, foliage loss, and the directionality of high gain antenna systems used in mmWave links. In this paper, a design is presented that combines mmWave channel modeling with machine learning for the efficient management of environment geometry and channel specification in a 5G urban microcell (UMi) street canyon (SC) outdoor channel. Accordingly, we first investigate the channel characteristics of mmWave line of sight (LOS) and non-line of sight (NLOS) directional outdoor links in various reference cases. The analysis is conducted for the backhaul and cellular access cases using a low complexity custom channel model based on ray tracing. Additional modeling components such as antenna directionality, oxygen absorption, and foliage loss modeling are also included to enhance accuracy and generality. It is observed that the estimated channel path loss is largely dependent on SC deployment parameters due to the antenna directionality combined with the small wavelength of mmWaves, and the use of correct values for them is essential to obtain optimal channel performance. Hence, we apply a metaheuristic algorithm called particle swarm optimization (PSO) for the optimal placement of position and deployment parameters of SC channel in a mmWave communication system to yield the best channel path loss.

Channel model for simultaneous backhaul and access for mmWave 5G outdoor street canyon channel

Millimeter waves (mmWaves) with very wide frequency bands are proposed for 5G new radio to deliver higher data-speed and capacity. Transmission using mmWaves suffers significant path loss and can be compensated by employing directional antennas. The narrow-beam directional antennas act as spatial filters that filter out multipaths falling outside their beam area. This, together with the insignificance of diffraction and diffused scattering in urban outdoors causes mmWave outdoor channel multipath to be spatially sparse with few specular reflections, posing unique requirements on channel modeling. In this paper, we have derived a low complexity mmWave directional channel model based on ray tracing for the urban microcell street canyon environment. A comprehensive characterization of outdoor links in various realistic scenarios including, line of sight (LOS)/non-LOS, beam aligned/unaligned and road canyon with/without crossroads is presented. The model captures azimuth and elevation directions of propagation in 3D plane by using a highly directional horn antenna design. Atmospheric absorption loss of mmWave is also modeled to enhance the model’s accuracy and generality. The model is validated against measurements reported in the literature. Furthermore, the channel is studied for varying propagation conditions, antenna beamwidths and polarizations, transmitter/receiver heights and positions, and street deployment parameters. Additionally, we propose a metaheuristic algorithm called particle swarm optimization to simultaneously optimize the deployment parameters that minimize path loss as the objective function. The proposed model helps in mmWave system evaluation without the necessity for any costly measurement setup or complex off-the-shelf ray tracing model.

PAPR and BER Reduction on Improving Performance for Filtered-OFDM using MSM and PSO

Filtered-Orthogonal Division Multiplexing (F-OFDM) is one of the capable alternative candidate modulation methods for 5G communication systems. F-OFDM utilizes the allocated spectrum by having lower side-lobes, which leads to higher spectral efficiency. However, it experiences an elevated peak-to-average power ratio (PAPR). This influences the radio frequency components’ operation mode, such as the power amplifier and the digital-to-analog converter. Also, high PAPR builds the amplifiers to exertion in non-linear regions and enhance the Bit Error Rate (BER). Moreover, Large PAPR guides to spectral spreading and band distortion. Selective Mapping (SLM) provides enhanced PAPR reduction without the data rate loss and also exclusive of the signal distortion. Though, SLM has elevated computational complexity additionally. Numerous procedures have been suggested in the research for OFDM. In this thesis, a modified-SLM using Discrete Sine Transform (DST) is recommended to lessen the PAPR of filtered-OFDM. The idea of a Discrete Sine Transform is de-correlating the data in a sequence by compressed a large amount of signal energy into a few transform coefficients; consequently it provides an improved diminution in PAPR. Furthermore, the BER performance of the system has been enhanced by applying an optimization algorithm called Particle Swarm Optimization (PSO). This proposed model results illustrate that the proposed Modified Selective mapping using Discrete Sine Transform (MSLM-DST) technique can provide a PAPR reduction of about 4.4 dB. Moreover, the PSO improved the system performance as it significantly reduces the BER of the system.

Development of an expression for the output voltage ripple of the DC-DC boost converter circuits by using particle swarm optimization algorithm

In this study, a mathematical expression is derived to calculate the ripple value of the output voltage of 2-phase interleaved cascaded boost converter (ICBC) circuits. In this context, the total number of 432 data of ICBC circuit including four parameters (switching frequency, duty ratio, coupling coefficient and the output voltage ripple) are acquired using Ansys-Electronics software. The expression of the output voltage ripple enclosing ICBC circuit parameters related to optimization variables is developed. Afterwards, the coefficients of the expression are acquired by using an algorithm called Particle Swarm Optimization (PSO). While the mean absolute error (MAE) of 420 data is obtained as 1.5055, the MAE of 12 test data not used in the optimization process is found to be 1.4608. These results show that, the output voltage ripple of ICBC can be easily calculated closing their actual values with the proposed basic mathematical expression instead of long-term and complex simulations. In addition, the accuracy of the developed mathematical expression is verified with the co-simulation of Maxwell 3D and Twin Builder interfaces within the Ansys-Electronics software.

Proposing a novel predictive technique using M5Rules-PSO model estimating cooling load in energy-efficient building system

In this study, we employed the most suitable artificial intelligence systems and optimized it with a novel evolutionary algorithm called particle swarm optimization (PSO) for the problem of cooling load (CL) in energy-efficient building (EEB) system. Then, the mentioned methods are utilised to identify a relationship between the input and output parameters of the EEB system. The amount of CL was taken as the essential output of the EEB system, while the input parameters were channel length, channel depth, channel width, and air mass flow rate. The predicted results for data sets from each of the abovementioned models were evaluated according to several known statistical indices such as correlation coefficient (R2), mean absolute error (MAE), root mean squared error (RMSE), relative absolute error (RAE), and root relative squared error (RRSE) as well as novel ranking systems of colour intensity rating and total ranking method. The M5Rules has been proposed as the best predictive network in this study. The results of the M5Rules network indicated the R2, MAE, RMSE, RAE, and RRSE for the training and testing data sets were 0.9982, 0.0426, 0.0653, 6.2344, and 6.0298 and 0.7626, 0.9903, 0.9593, and 0.9981, respectively. According to R2, RMSE, and VAF, values of 0.99983, 0.0066, and 99.98 and 0.9982, 0.065, and 84.5 were obtained for testing data set and values of proposed PSO-M5Rules prediction network models, respectively. This indicates higher reliability of the introduced PSO-M5Rules model in approximating CL of an EEB system.

Cloudlets Activation Scheme for Scalable Mobile Edge Computing with Transmission Power Control and Virtual Machine Migration

Mobile devices have several restrictions due to design choices that guarantee their mobility. A way of surpassing such limitations is to utilize cloud servers called cloudlets on the edge of the network through Mobile Edge Computing. However, as the number of clients and devices grows, the service must also increase its scalability in order to guarantee a latency limit and quality threshold. This can be achieved by deploying and activating more cloudlets, but this solution is expensive due to the cost of the physical servers. The best choice is to optimize the resources of the cloudlets through an intelligent choice of configuration that lowers delay and raises scalability. Thus, in this paper we propose an algorithm that utilizes Virtual Machine Migration and Transmission Power Control, together with a mathematical model of delay in Mobile Edge Computing and a heuristic algorithm called Particle Swarm Optimization, to balance the workload between cloudlets and consequently maximize cost-effectiveness. Our proposal is the first to consider simultaneously communication, computation, and migration in our assumed scale and, due to that, manages to outperform other conventional methods in terms of number of serviced users.

Discrete Non-Integer Order Differentiator Models Using Moth-Flame Optimization Algorithm

Discrete rational approximation models to the non-integer order differentiator sλ, where λ ε (0, 1), using Moth-Flame Optimization (MFO) algorithm is proposed in this paper. The proposed metaheuristic optimization approach used to design the discrete non-integer order differentiators (DNODs) does not employ any s-to-z domain mapping function to perform the discretization operation. Frequency domain characteristics of DNODs, solution reliability, and algorithm convergence performances are investigated among MFO and an advanced evolutionary algorithm called Particle Swarm Optimization with adaptive inertia weight (PSO-w). Results demonstrate the effectiveness of MFO in outperforming PSO-w in solving this non-linear and multimodal optimization problem. The proposed DNODs also exhibit better performance in comparison with the designs based on techniques such as Nelder-Mead Simplex algorithm and Cuckoo Search Algorithm published in recent literature.

MULTIBAND MILLIMETER WAVE T-SHAPED ANTENNA WITH OPTIMIZED PATCH PARAMETER USING PARTICLE SWARM OPTIMIZATION

This paper proposed a simple T-shaped patch antenna for millimeter waveband frequency operation. Millimeter wave is a frequency ranges between 30GHz to 300GHz in an electromagnetic spectrum. The proposed antenna consists of T-shape radiating patch mounted on rectangular substrate (FR4-4) and microstrip line for antenna feeding. An evolutionary algorithm called particle swarm optimization was used to optimize the length and width of the proposed antenna patch. The proposed antenna gives triple bands with central frequencies at 42GHz, 51.5GHz and 60GHz. The antenna offers minimum return loss of -19db, -24db and -19.5db at 42GHz, 51.5GHz and 60GHz respectively. The return loss impedance bandwidth of 5GHz for the first band, 8.4GHz for the second band and 5GHz for the third band was obtained. The proposed antenna was analyzed using Ansoft High Frequency Structure Simulator (HFSS) and MATLAB 2013. Radiation characteristics of this patch antenna are observed at various resonating frequencies.  http://dx.doi.org/10.4314/njt.v36i3.33

MULTIBAND MILLIMETER WAVE T-SHAPED ANTENNA WITH OPTIMIZED PATCH PARAMETER USING PARTICLE SWARM OPTIMIZATION

This paper proposed a simple T-shaped patch antenna for millimeter waveband frequency operation. Millimeter wave is a frequency ranges between 30GHz to 300GHz in an electromagnetic spectrum. The proposed antenna consists of T-shape radiating patch mounted on rectangular substrate (FR4-4) and microstrip line for antenna feeding. An evolutionary algorithm called particle swarm optimization was used to optimize the length and width of the proposed antenna patch. The proposed antenna gives triple bands with central frequencies at 42GHz, 51.5GHz and 60GHz. The antenna offers minimum return loss of -19db, -24db and -19.5db at 42GHz, 51.5GHz and 60GHz respectively. The return loss impedance bandwidth of 5GHz for the first band, 8.4GHz for the second band and 5GHz for the third band was obtained. The proposed antenna was analyzed using Ansoft High Frequency Structure Simulator (HFSS) and MATLAB 2013. Radiation characteristics of this patch antenna are observed at various resonating frequencies. http://dx.doi.org/10.4314/njt.v36i3.33

Detection of Apple Marssonina Blotch Disease Using Particle Swarm Optimization

<abstract> <b><sc>Abstract.</sc></b> Apple Marssonina blotch (AMB) is a devastating disease that is predominantly found in Asian countries, such as Japan, India, and South Korea. The disease has been known to cause huge economic losses in the regions where it has been found. AMB causes early defoliation, which ultimately leads to low quality and quantity of harvested apples. In this work, spectroscopic measurements were collected and analyzed for two datasets from 2014 and 2015. A stochastic algorithm called particle swarm optimization (PSO) was used to find optimal features for classification. A total of ten spectral features were found by the algorithm by selecting pairs of bands that resulted in the highest discrimination between every two classes. A support vector machine classifier resulted in 100% classification accuracy for both healthy and diseased samples. Abundance estimation and spectral unmixing analyses of early-stage AMB (ambE) samples were also conducted using PSO to extract symptomatic and asymptomatic endmembers. Results showed reasonable separation between healthy, seemingly healthy, and symptomatic classes. Quantitative analysis, using varying degrees of infection of ambE samples, was performed by applying a combination of partial least squares and stepwise multiple linear regression models, and coefficients of determination (R²) of 0.76 and 0.71 were achieved for the calibration and validation datasets, respectively. The results demonstrate the potential of using spectroscopic technology as a non-invasive method for early detection of AMB disease.

Constrained multi-objective optimization of EDM process parameters using kriging model and particle swarm algorithm

ABSTRACTThis paper investigates the highly nonlinear relationship between process parameters and machining responses, including material removal rate (MRR), surface roughness (SR), and electrode wear rate (EWR) of electric discharge machining (EDM) using Kriging model. Subsequently, an emerging multi-objective optimization algorithm called particle swarm is used to determine the best machining conditions that not only maximize the machining speed but also minimize the EWR with a constraint of the SR. The experiment was carried out with P20 steel on a CNC EDM machine using copper electrode. The research result shows that the MRR increases sharply when increasing the discharge current just like other researches pointed out. However, the relationship between EWR and current is complicated. EWR appears the minimum value when the current is around 30 A. The speed of change of MRR per unit of EWR is the highest when the SR is around 14.5 µm. The combination of Kriging regression model and particle swarm optimization is considered as an intelligent process modeling and optimization of EDM machining. The proper selection of process parameters helps the EDM operator to reduce the machining time and cost.