Equilibrium Optimization Algorithm Research Articles

Equilibrium Optimization Algorithm with Deep Learning Based Brain Tumor Segmentation and Classification on Magnetic Resonance Imaging

Equilibrium Optimization Algorithm with Deep Learning Based Brain Tumor Segmentation and Classification on Magnetic Resonance Imaging

Modified Equilibrium Optimization Algorithm With Deep Learning-Based DDoS Attack Classification in 5G Networks

Modified Equilibrium Optimization Algorithm With Deep Learning-Based DDoS Attack Classification in 5G Networks

Equilibrium Optimization Algorithm with Ensemble Learning Based Cervical Precancerous Lesion Classification Model.

Recently, artificial intelligence (AI) with deep learning (DL) and machine learning (ML) has been extensively used to automate labor-intensive and time-consuming work and to help in prognosis and diagnosis. AI's role in biomedical and biological imaging is an emerging field of research and reveals future trends. Cervical cell (CCL) classification is crucial in screening cervical cancer (CC) at an earlier stage. Unlike the traditional classification method, which depends on hand-engineered or crafted features, convolution neural network (CNN) usually categorizes CCLs through learned features. Moreover, the latent correlation of images might be disregarded in CNN feature learning and thereby influence the representative capability of the CNN feature. This study develops an equilibrium optimizer with ensemble learning-based cervical precancerous lesion classification on colposcopy images (EOEL-PCLCCI) technique. The presented EOEL-PCLCCI technique mainly focuses on identifying and classifying cervical cancer on colposcopy images. In the presented EOEL-PCLCCI technique, the DenseNet-264 architecture is used for the feature extractor, and the EO algorithm is applied as a hyperparameter optimizer. An ensemble of weighted voting classifications, namely long short-term memory (LSTM) and gated recurrent unit (GRU), is used for the classification process. A widespread simulation analysis is performed on a benchmark dataset to depict the superior performance of the EOEL-PCLCCI approach, and the results demonstrated the betterment of the EOEL-PCLCCI algorithm over other DL models.

Prediction of the Sound Absorption Coefficient of Three-Layer Aluminum Foam by Hybrid Neural Network Optimization Algorithm

The combination of multilayer aluminum foam can have high sound absorption coefficients (SAC) at low and medium frequencies, and predicting its absorption coefficient can help the optimal structural design. In this study, a hybrid EO-GRNN model was proposed for predicting the sound absorption coefficient of the three-layer composite structure of the aluminum foam. The generalized regression neural network (GRNN) model was used to predict the sound absorption coefficient of three-layer composite structural aluminum foam due to its outstanding nonlinear problem-handling capability. An equilibrium optimization (EO) algorithm was used to determine the parameters in the neuronal network. The prediction results show that this method has good accuracy and high precision. The calculation result shows that this proposed hybrid model outperforms the single GRNN model, the GRNN model optimized by PSO (PSO-GRNN), and the GRNN model optimized by FOA(FOA-GRNN). The prediction results are expressed in terms of root mean square error (RMSE), absolute error, and relative error, and this method performs well with an average RMSE of only 0.011.

A fuzzy intelligent forecasting system based on combined fuzzification strategy and improved optimization algorithm for renewable energy power generation

• Develop a novel hybrid forecasting system focusing on small sample forecasting. • Forecast the renewable energy power generation of different regions in the world. • Improve the fuzzification ability by combined strategy and hesitant fuzzy sets. • Search the optimal aggregated weights based on improved optimization algorithm. • Introduce the chaotic map into the equilibrium optimization algorithm. Renewable energy power generation has significant potential to electricity supply sector with great sense to greenhouse gas control. Thus, it is vital to develop an effective forecasting model for renewable energy power generation forecasting which can provide a reference and basis for power generation planning and the energy strategic deployment. However, influenced by the complex data characteristic and sample size limitation, the application of some traditional forecasting models is restricted with poor forecasting performance. In this paper, a novel fuzzy time series forecasting based on combined fuzzification strategy and improved optimization algorithm is proposed for renewable energy power generation forecasting. The hesitant fuzzy sets are applied to deal with the combined fuzzification strategy and the improved optimization algorithm is developed to optimize the aggregate weights of the hesitant fuzzy sets. The experimental analysis and discussion all demonstrated the excellent performance of the proposed forecasting system in small sample forecasting for renewable energy power generation forecasting.

Stochastic-Metaheuristic Model for Multi-Criteria Allocation of Wind Energy Resources in Distribution Network Using Improved Equilibrium Optimization Algorithm

In this paper, a stochastic-meta-heuristic model (SMM) for multi-criteria allocation of wind turbines (WT) in a distribution network is performed for minimizing the power losses, enhancing voltage profile and stability, and enhancing network reliability defined as energy not-supplied cost (ENSC) incorporating uncertainty of resource production and network demand. The proposed methodology has been implemented using the SMM, considering the uncertainty modeling of WT generation with Weibull probability distribution function (PDF) and load demand based on the normal PDF and using a new meta-heuristic method named the improved equilibrium optimization algorithm (IEOA). The traditional equilibrium optimization algorithm (EOA) is modeled by the simple dynamic equilibrium of the mass with proper composition in a control volume in which the nonlinear inertia weight reduction strategy is applied to improve the global search capability of the algorithm and prevent premature convergence. First, the problem is implemented without considering the uncertainty as a deterministic meta-heuristic model (DMM), and then the SMM is implemented considering the uncertainties. The results of DMM reveal the better capability of the IEOA method in achieving the lowest losses and the better voltage profile and stability and the higher level of the reliability in comparison with conventional EOA, particle swarm optimization (PSO), manta ray foraging optimization (MRFO) and spotted hyena optimization (SHO). The results show that in the DMM solving using the IEOA, traditional EOA, PSO, MRFO, and SHO, the ENSC is reduced from $3223.5 for the base network to $632.05, $636.90, $638.14, $635.67, and $636.18, respectively, and the losses decreased from 202.68 kW to 79.54 kW, 80.32 kW, 80.60 kW, 80.05 kW and 80.22 kW, respectively, while the network minimum voltage increased from 0.91308 p.u to 0.9588 p.u, 0.9585 p.u, 0.9584 p.u, 0.9586 p.u, and 0.9586 p.u, respectively, and the VSI improved from 26.28 p.u to 30.05 p.u, 30.03 p.u, 30.03 p.u, 30.04 p.u and 30.04 p.u; respectively. The results of the SMM showed that incorporating uncertainties increases the losses, weakens the voltage profile and stability and also reduces the network reliability. Compared to the DMM, the SMM-based problem is robust to prediction errors caused by uncertainties. Therefore, SMM based on existing uncertainties can lead to correct decision-making in the conditions of inherent-probabilistic changes in resource generation and load demand by the network operator.

Optimal Allocation of Distributed Thyristor Controlled Series Compensators in Power System Considering Overload, Voltage, and Losses with Reliability Effect

In this paper, optimal allocation of a distributed thyristor-controlled series compensator (DTCSC) in a power system is presented to minimize overload, voltage deviations, and power losses while improving system reliability. The decision variable was defined as the optimal reactance of the DTCSC in the power system, which was determined using a new meta-heuristic algorithm named the improved equilibrium optimization algorithm (IEOA). A nonlinear inertia weight reduction strategy was used to improve the performance of traditional EOA in preventing premature convergence and facilitate a quick global optimum solution. The effect of system critical line outage was evaluated for each of the considered goals. To evaluate the effectiveness of the proposed methodology, IEOA capability was compared with particle swarm optimization (PSO) and manta ray foraging optimizer (MRFO) methods. Simulations were carried out considering different scenarios on 14- and 118-bus test systems. The results showed that, for all scenarios, optimal allocation of DTCSC could result in a significant reduction in overloading, voltage deviation of network buses, as well as power losses under the condition of line outage, due to the optimal injection of reactive power. In all investigated scenarios, our results attested to the superiority of the IEOA over the traditional EOA, PSO, and MRFO in achieving a better value for the objective function. In addition, the results showed that improving reliability in the objective function could eliminate overloading, and hence, introduce further improvement in each of the objectives.

Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem

We consider, in this paper, the NP-hard problem of finding the minimum connected domination metric dimension of graphs. A vertex set B of a connected graph G = (V, E) resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraphB¯induced by B is a nontrivial connected subgraph of G. A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B. The cardinality of the smallest resolving set of G, the cardinality of the minimal connected resolving set, and the cardinality of the minimal connected domination resolving set are the metric dimension of G, connected metric dimension of G, and connected domination metric dimension of G, respectively. We present the first attempt to compute heuristically the minimum connected dominant resolving set of graphs by a binary version of the equilibrium optimization algorithm (BEOA). The particles of BEOA are binary-encoded and used to represent which one of the vertices of the graph belongs to the connected domination resolving set. The feasibility is enforced by repairing particles such that an additional vertex generated from vertices of G is added to B, and this repairing process is iterated until B becomes the connected domination resolving set. The proposed BEOA is tested using graph results that are computed theoretically and compared to competitive algorithms. Computational results and their analysis show that BEOA outperforms the binary Grey Wolf Optimizer (BGWO), the binary Particle Swarm Optimizer (BPSO), the binary Whale Optimizer (BWO), the binary Slime Mould Optimizer (BSMO), the binary Grasshopper Optimizer (BGO), the binary Artificial Ecosystem Optimizer (BAEO), and the binary Elephant Herding Optimizer (BEHO).

Grid Feature-Based Weighted Simulation Method for Multi-Objective Reliability-Based Design Optimization

Reliability analysis and reliability-based design have attracted huge attention since their origin, especially in the engineering design optimization field. Integrating a novel grid feature (GF) mechanism into the weighted simulation method (WSM), a grid feature-based weighted simulation method (GFWSM) is proposed in this paper. By sorting the samples in the random variable space, the GF mechanism serializes the failure probability calculation process, which can reduce the number of performance function evaluations required by the WSM. The proposed GFWSM is integrated into an efficient evolutionary multi-objective optimizer, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), for solving multi-objective reliability-based design optimization (MORBDO) problems. Different reliability analysis examples are employed to verify the advantages of the proposed GFWSM. Various constrained multi-objective reliability-based design optimization problems have been selected to test the effectiveness of the GFWSM-DMOEOA algorithm. The simulation results indicate that GFWSM and GFWSM-DMOEOA algorithm have achieved a good balance between accuracy and efficiency.

An optimization method of mine ventilation system based on R2 index hybrid multi-objective equilibrium optimization algorithm

With the increase of mining years, the mine ventilation system becomes more and more complex, causing serious energy waste. The traditional single-objective optimization model cannot​ accurately describe the complex mine ventilation system. In order to solve this problem, this paper establishes a multi-objective optimization model for mine ventilation systems considering ventilation energy consumption, fan shaft power, and fan efficiency. Furthermore, we proposed an R2 index hybrid multi-objective equilibrium optimization algorithm(R2HMEOA). Firstly, We use R2 index to improve the sorting rules of the Pareto solution. Secondly, improve the reference point strategy, and propose an elite archiving strategy based on R2 index. We use classical test functions to test the proposed algorithm. The results show that the algorithm has obvious advantages. Furthermore, we apply the algorithm to the ventilation system optimization of Wangjialing mine of Zhongmei Huajin Energy Co. Ltd. The results show that the algorithm can effectively reduce the ventilation power consumption and improve the shaft power and efficiency of the fan, which proves the practicability of the proposed algorithm.

Using an evolutionary heterogeneous ensemble of artificial neural network and multivariate adaptive regression splines to predict bearing capacity in axial piles

Accurately estimating the bearing capacity of piles is an onerous task in structural design task that requires a powerful computation model able to elucidate nonlinear impacts of geotechnical factors and the dimension and shape of piles. This study develops a novel heterogeneous ensemble artificial intelligence model, named intelligence multivariate neural network inference model (IMNNIM), to accurately and quickly predict bearing capacity of piles. The IMNNIM was created by integrating the equilibrium optimization algorithm (EO) into a combination of multivariate adaptive regression splines (MARS) and radial basis neural network (RBFNN). The predictive values of the IMNNIM were qualified by dynamically merging prediction information generated by MARS and RBFNN and then adjusting the associated weights and assigned tuning parameter values of the learner members. The performance of the IMNNIM was evaluated using data from 472 driven pile static load test reports. The experimental results using a 10-fold cross-validation method demonstrated the IMNNIM to be the most reliable model for predicting pile-bearing-capacity by achieving the greatest values of MAPE (7.24%), RMSE (90.92kN), MAE (67.98kN), and R2 (0.930) and the lowest standard deviation values. A t-test analysis method confirmed the IMNNIM as a superior tool for pile-bearing-capacity estimation.

A new hybrid feature selection based on Improved Equilibrium Optimization

Feature selection is one of the most important preprocessing steps for analyzing high-dimensional data in the data mining and machine learning fields. In machine learning problems, Classification accuracy is highly dependent on the selected features of a dataset. The main purpose of feature selection is to remove additional and irrelevant features from the data feature set to increase the performance of algorithms. A novel feature selection model is proposed in this paper. In the first step, the features are scored based on the mRMR feature selection approach, and those with a higher score are selected. In the second step, the Wrapper feature selection approach is used to extract the best features based on the Improved Equilibrium Optimization (IMEO) algorithm. IMEO uses a new operator called Entropy-based to improve the performance of the Equilibrium Optimizer (EO) algorithm and prevents the algorithm from getting trap in local optima by controlling the exploration and exploitation abilities. Also, Levy flight is used to find new solutions in the search space and to improve the exploration phase of the EO algorithm. This mechanism will avoid local optimum by creating many short jumps and sometimes large jumps in the search space. The proposed IMEO algorithm is first tested on 23 benchmark test functions; after ensuring the efficiency of the proposed method, the Binary Improved Equilibrium Optimization (BIMEO) algorithm is defined based on the sigmoid transfer function to solve the feature selection problem. The simulation results of the BIMEO algorithm and state-of-the-art algorithms on 18 standard benchmark datasets show the performance of the proposed model compared to the other algorithms. In addition, the results of experiments on two chemical datasets prove the efficiency of the proposed algorithm, BIMEO, in terms of selective features and classification accuracy.

Classification of faults in grid-connected photovoltaic system based on wavelet packet transform and an equilibrium optimization algorithm-extreme learning machine

A novel intelligent scheme using the wavelet packet transform (WPT) and extreme learning machine (ELM) is proposed for fault event classification in the grid-connected photovoltaic (PV) system. The WPT is applied for preprocessing the cycle of the post-fault voltage samples at the point of common coupling (PCC) measurement to get the normalized logarithmic energy entropy (NLEE). The ELM is applied to classify the different fault cases. To enhance the performance of ELM for faults classification, a hybrid optimization mechanism based on an equilibrium optimization algorithm (EOA) is proposed to optimize the selection of input feature subset and the number of ELM hidden nodes. Furthermore, to evaluate the proposed scheme's performance, a comprehensive evaluation was conducted on a 250 kW grid-connected photovoltaic system. From simulation, the classification accuracy is recorded to be 100% under the no-noise condition, while at the signal-to-noise ratios (SNR) of 30, 35, and 40 dB, the accuracies are 98.96, 99.04, and 99.36%, respectively. Moreover, the practical performance of the EOA-ELM classifier is validated using IEEE 34 bus system. The obtained results validate the effectiveness of the proposed scheme in terms of robustness against measurement noise, computation time, and detection accuracy.

Wind integrated optimal power flow considering power losses, voltage deviation, and emission using equilibrium optimization algorithm

Wind integrated optimal power flow considering power losses, voltage deviation, and emission using equilibrium optimization algorithm

Maximize the penetration level of photovoltaic systems and shunt capacitors in distribution systems for reducing active power loss and eliminating conventional power source

In this paper, photovoltaic systems and shunt capacitors are optimally placed in three IEEE distribution systems. Moth swarm algorithm, Equilibrium optimization and Coot optimization algorithm are used to find the numbers, locations and sizes of the added electric components so that total active power loss is minimum and all constraints are satisfied. As reaching optimal solutions, voltage of nodes and current of conductors satisfy operating ranges while all added photovoltaic systems and all shunt capacitors respectively supply enough active and reactive power demands to loads. Among the three applied algorithms, Moth swarm algorithm is more complicated but it is much more effective than two others. In fact, it can reach less active power loss by 76.3% as compared to others and by 86.52%, 83.3% and 94.48% as compared to base systems. Thus, it concludes that the placement of photovoltaic systems and shunt capacitors can replace the conventional power source and Moth swarm algorithm is an effective approach in optimizing the placement of both photovoltaic systems and shunt capacitors.

A novel approach for clustering and routing in WSN using genetic algorithm and equilibrium optimizer

SummaryThe Internet of Things (IoT) is a new concept in the world of technology and information and has many applications in industry, communications, and various other fields. In the lowest layer of the IoT, wireless sensor networks (WSNs) play an important and pivotal role. WSN consists of a large number of sensors and is commonly used to monitor a target. It is important to reduce energy consumption in WSNs to extend network life, since it is usually impossible to replace sensor batteries. In this paper, a novel clustering and routing method is proposed. It is mainly based on genetic algorithms and equilibrium optimization. To improve scalability, the sensor nodes are clustered in the first phase using the genetic algorithm and then the best cluster heads are selected. It follows by the next step, where each node sends its collected data to the cluster head. The cluster heads first aggregate the received data and then use a multihop optimization routing algorithm by the new equilibrium optimization algorithm to send the data to the base station. Specifically, the main contribution of this work is to reduce energy consumption in WSN using a genetic algorithm for clustering and an equilibrium optimization algorithm for choosing the path between the cluster heads and the base station. The proposed method was simulated in MATLAB software, and it was compared with five other methods. It was observed that the proposed method outperforms other methods in terms of energy consumption, network lifespan, and the number of packages delivered.

An optimized nonlinear grey Bernoulli prediction model and its application in natural gas production

Natural gas, an efficient, eco-friendly and clean green energy, has become one of the important energy structures of various countries in the world, accurately predicting the production of natural gas can help the national energy agency solve “gas shortage” problem. To accurately predict natural gas production in China, this paper establishes an optimized grey system model with weighted fractional accumulation generation operation (abbreviated as WFNGBM(1,1,N)). The proposed model has all the advantages of the GMP(1,1,N) model, NGBM(1,1) model and weighted fractional accumulation generation operation, which makes it have excellent prediction performance. Moreover, five outstanding intelligent optimization algorithms (whale optimization algorithm, marine predators algorithm, grasshopper optimization algorithm, equilibrium optimization algorithm and arithmetic optimization algorithm) are used to solve the hyperparameters of the WFNGBM(1,1,N) model. It is found that the WFNGBM(1,1,N) model has the characteristics of convertibility and small sample modeling, which indicates that it is a small sample prediction model with strong compatibility. After confirming the feasibility of the proposed model compared with its competing models by using natural gas production in Germany, Italy and Canada as examples, the proposed model is used to study China’s natural gas production. The results show that this model is very suitable for predicting and analyzing natural gas production in China. Based on this, the WFNGBM(1,1,N) model is used to estimate China’s natural gas production in the next three years, and some reasonable suggestions are given according to the development trend of natural gas production.

Dynamic Electrical Models of Perovskite Solar Cells Considering Hysteresis and Charge Accumulations Effects by Using Equilibrium Optimizer

Perovskite solar cells (PSCs) are third-generation photovoltaic technology that has gained a lot of attention due to its technological and economic advantages. The PSCs are characterized with low cost, high absorption, long carrier diffusion length, and low fabrication temperature. To model the performance of PSCs, a new dynamic model is proposed to track the cells hysteresis by adding a variable voltage capacitor to the single, double, and triple diode models. The aim with adding the variable capacitor is to emulate the effect of charge accumulation at the interfaces of the device. Three modified models are presented based on one or more variable capacitors at single, double, and triple diode models. Where, the triple diode model with third order variable voltage capacitor model is the best among all models by 74.9% enhancement in comparison with single diode model. Also, the Equilibrium optimization algorithm (EOA) is proposed to determine the parameters of the proposed dynamic model based on the triple diode model. In comparison with the experimental data, for both forward and reverse scans, the findings showed that the suggested model accurately reflects cell performance. Added to that, the EOA finds well the optimal model parameters considering the root mean square as primary objective function. Based on the simulation results, it was proved that the proposed model gives very close results to reality.

Optimal FOPID Controllers for LFC Including Renewables by Bald Eagle Optimizer

In this study, a bald eagle optimizer (BEO) is used to get optimal parameters of the fractional-order proportional–integral–derivative (FOPID) controller for load frequency control (LFC). Since BEO takes only a very short time in finding the optimal solution, it is selected for designing the FOPID controller that improves the system stability and maintains the frequency within a satisfactory range at different loads. Simulations and demonstrations are carried out using MATLAB-R2020b. The performance of the BEO-FOPID controller is evaluated using a two-zone interlinked power system at different loads and under uncertainty of wind and solar energies. The robustness of the BEO-FOPID controller is examined by testing its performance under varying system time constants. The results obtained by the BEO-FOPID controller are compared with those obtained by BEO-PID and PID controllers based on recent metaheuristics optimization algorithms, namely the sine–cosine approach, Jaya approach, grey wolf optimizer, genetic algorithm, bacteria foraging optimizer, and equilibrium optimization algorithm. The results confirm that the BEO-FOPID controller obtains the finest result, with the lowest frequency deviation. The results also confirm that the BEO-FOPID controller is stable and robust at different loads, under varying system time constants, and under uncertainty of wind and solar energies.

Reduction of Total Harmonic Distortion of Wind Turbine Active Power Using Blade Angle Adaptive PI Controller

Power quality can have a large detrimental effect on industrial processes and the commercial sector. Thus, this paper proposes a new technique to improve the power quality of electric power systems. This technique relies on auto-adjusting of the blade angle to mitigate the harmonics in wind generator active power. A new adaptive PI blade-angle controller is applied in this technique to reduce the total harmonic distortion (THD) of the output power. The parameters of the adaptive PI controller are initialized by using the Harmony Search algorithm (HSA), hybrid Harmony Search optimization and Equilibrium optimization (EO), and hybrid Harmony Search optimization and Teaching learning-based optimization (TLBO). The execution of the optimization algorithms relies mainly on the optimization objective function. Two optimization objective functions are mathematically modeled and compared to enhance the power quality. The first one is to minimize the sum square of error, while the second objective is to minimize the THD. Many case studies are applied with various wind-speed profiles under normal and faulty conditions. Results show the superiority of HSA hybrid EO algorithm with the second objective functions through reducing the harmonics and enhancing the power quality. Moreover, laboratory studies are applied to investigate the effect of the blade-angle variations on the extracted active power.