A Multi-Layer Techno-Economic-Environmental Energy Management Optimization in Cooperative Multi-Microgrids with Demand Response Program and Uncertainties Consideration.

This paper presents a multi-layer, multi-objective (MLMO) optimization model for techno-economic-environmental energy management in cooperative multi-Microgrids (MMGs) that incorporates a Demand Response Program (DRP). The proposed MLMO approach simultaneously optimizes operating costs, MMG operator benefits, environmental emissions, and MMG dependency. This paper proposed a new hybrid ε-lexicography-weighted-sum that eliminates the need to normalize or scalarize objectives. The first layer of the model schedules MMG resources with DRP to minimize operating costs (local generation and power transactions with the utility grid) and maximize MMG profit. The second layer achieves the environmental operation of the MMG, while the third layer maximizes MMG reliability. This paper also proposed a new application of a recently developed enhanced equilibrium optimizer (EEO) for solving the three-layer EM problem. In addition, the uncertainties of solar power generation, wind power generation, load demand, and energy prices are considered based on the probabilistic 2m + 1 Point estimation method (PEM) approach. Three case studies are presented to verify the proposed MLMO approach on an MMG test system. In Case I, a deterministic EM is solved to simulate the MMG as a single layer to minimize costs and maximize benefits through DRP, while Case II solves the MLMO optimization problem. Simulation results show that the proposed MLMO technique reduces environmental emissions by 2.45% and 3.5% in its optimization layer and at the final layer, respectively. The independence index is also enhanced by 2.49% and 4.8% in its layer only and as a total increase, respectively. Case III is for the probabilistic EM simulation; due to the uncertain variables effect, the mean value in this case is increased by about 2.6% over Case I.

The MOEO algorithm for multi-objective optimization of the cancer immuno-chemotherapy.

In cancer treatment, chemotherapy has the disadvantage of killing both healthy and cancerous cells. Hence, the mixed-treatment of cancer such as chemo-immunotherapy is recommended. However, deriving the optimal dosage of each drug is a challenging issue. Although metaheuristic algorithms have received more attention in solving engineering problems due to their simplicity and flexibility, they have not consistently produced the best results for every problem. Thus, the need to introduce novel algorithms or extend the previous ones is felt for important optimization problems. Hence, in this paper, the multi-objective Equilibrium Optimizer algorithm, as an extension of the single-objective Equilibrium Optimizer algorithm, is recommended for cancer treatment problems. Then, the performance of the proposed algorithm is considered in both chemotherapy and mixed chemo-immunotherapy of cancer, considering the constraints of the tumor-immune dynamic system and the health level of the patients. For this purpose, two different patients with real clinical data are considered. The Pareto front obtained from the multi-objective optimization algorithm shows the points that can be selected for treatment under different criteria. Using the proposed multi-objective algorithm has reduced the total chemo-drug dose to 138.92 and 5.84 in the first patient, and 16.9 and 0.4384 in the second patient, for chemotherapy and chemo-immunotherapy, respectively. Comparing the results with previous studies demonstrates MOEO's superior performance in both chemotherapy and chemo-immunotherapy. However, it is shown that the proposed algorithm is more suitable for mixed-treatment approaches.

An improved equilibrium optimization algorithm for feature selection problem in network intrusion detection.

In this paper, an enhanced equilibrium optimization (EO) version named Levy-opposition-equilibrium optimization (LOEO) is proposed to select effective features in network intrusion detection systems (IDSs). The opposition-based learning (OBL) approach is applied by this algorithm to improve the diversity of the population. Also, the Levy flight method is utilized to escape local optima. Then, the binary rendition of the algorithm called BLOEO is employed to feature selection in IDSs. One of the main challenges in IDSs is the high-dimensional feature space, with many irrelevant or redundant features. The BLOEO algorithm is designed to intelligently select the most informative subset of features. The empirical findings on NSL-KDD, UNSW-NB15, and CIC-IDS2017 datasets demonstrate the effectiveness of the BLOEO algorithm. This algorithm has an acceptable ability to effectively reduce the number of data features, maintaining a high intrusion detection accuracy of over 95%. Specifically, on the UNSW-NB15 dataset, BLOEO selected only 10.8 features on average, achieving an accuracy of 97.6% and a precision of 100%.

Human monkeypox disease prediction using novel modified restricted Boltzmann machine-based equilibrium optimizer.

While the globe continues to struggle to recover from the devastation brought on by the COVID-19 virus's extensive distribution, the recent worrying rise in human monkeypox outbreaks in several nations raises the possibility of a novel worldwide pandemic. The symptoms of human monkeypox resemble those of chickenpox and traditional measles, with a few subtle variations like the various kinds of skin blisters. A range of deep learning techniques have demonstrated encouraging results in image-oriented tumor cell, Covid-19 diagnosis, and skin disease prediction tasks. Hence, it becomes necessary to perform the prediction of the new monkeypox disease using deep learning techniques. In this paper, an image-oriented human monkeypox disease prediction is performed with the help of novel deep learning methodology. Initially, the data is gathered from the standard benchmark dataset called Monkeypox Skin Lesion Dataset. From the collected data, the pre-processing is accomplished using image resizing and image normalization as well as data augmentation techniques. These pre-processed images undergo the feature extraction that is performed by the Convolutional Block Attention Module (CBAM) approach. The extracted features undergo the final prediction phase using the Modified Restricted Boltzmann Machine (MRBM), where the parameter tuning in RBM is accomplished by the nature inspired optimization algorithm referred to as Equilibrium Optimizer (EO), with the consideration of error minimization as the major objective function. Simulation findings demonstrate that the proposed model performed better than the remaining models at monkeypox prediction. The proposed MRBM-EO for the suggested human monkeypox disease prediction model in terms of RMSE is 75.68%, 70%, 60.87%, and 43.75% better than PSO-SVM, Xception-CBAM-Dense, ShuffleNet, and RBM respectively. Similarly, the proposed MRBM-EO for the suggested human monkeypox disease prediction model with respect to accuracy is 9.22%, 7.75%, 3.77%, and 10.90% better than PSO-SVM, Xception-CBAM-Dense, ShuffleNet, and RBM respectively.

Application of hybridized ensemble learning and equilibrium optimization in estimating damping ratios of municipal solid waste.

The dynamic analysis of municipal solid waste (MSW) is essential for optimizing landfills and advancing sustainable development goals. Assessing damping ratio (D), a critical dynamic parameter, under laboratory conditions is costly and time-consuming, requiring specialized equipment and expertise. To streamline this process, this research leveraged several novel ensemble machine learning models integrated with the equilibrium optimizer algorithm (EOA) for the predictive analysis of damping characteristics. Data were gathered from 153 cyclic triaxial experiments on MSW, which examined the age, shear strain, weight, frequency, and percentage of plastic content. Analysis of a correlation heatmap indicated a significant dependence of D on shear strain within the collected MSW data. Subsequently, five advanced machine learning methods-adaptive boosting (AdaBoost), gradient boosting regression tree (GBRT), extreme gradient boosting (XGBoost), random forest (RF), and cubist regression-were employed to model D in landfill structures. Among these, the GBRT-EOA model demonstrated superior performance, with a coefficient of determination (R2) of 0.898, root mean square error of 1.659, mean absolute error of 1.194, mean absolute percentage error of 0.095, and an a20-index of 0.891 for the test data. A Shapley additive explanation analysis was conducted to validate these models further, revealing the relative contributions of each studied variable to the predicted D-MSW. This holistic approach not only enhances the understanding of MSW dynamics but also aids in the efficient design and management of landfill systems.

Meta-heuristic optimization algorithms based feature selection for joint moment prediction of sit-to-stand movement using machine learning algorithms.

The sit-to-stand (STS) movement is fundamental in daily activities, involving coordinated motion of the lower extremities and trunk, which leads to the generation of joint moments based on joint angles and limb properties. Traditional methods for determining joint moments often involve sensors or complex mathematical approaches, posing limitations in terms of movement restrictions or expertise requirements. Machine learning (ML) algorithms have emerged as promising tools for joint moment estimation, but the challenge lies in efficiently selecting relevant features from diverse datasets, especially in clinical research settings. This study aims to address this challenge by leveraging metaheuristic optimization algorithms to predict joint moments during STS using minimal input data. Motion analysis data from 20 participants with varied mass and inertia properties are utilized, and joint angles are computed alongside simulations of joint moments. Feature selection is performed using the Manta Ray Foraging Optimization (MRFO), Marine Predators Algorithm (MPA), and Equilibrium Optimizer (EO) algorithms. Subsequently, Decision Tree Regression (DTR), Random Forest Regression (RFR), Extra Tree Regression (ETR), and eXtreme Gradient Boosting Regression (XGBoost Regression) ML algorithms are deployed for joint moment prediction. The results reveal EO-ETR as the most effective algorithm for ankle, knee, and neck joint moment prediction, while MPA-ETR exhibits superior performance for hip joint prediction. This approach demonstrates potential for enhancing accuracy in joint moment estimation with minimal feature input, offering implications for biomechanical research and clinical applications.

OptiCoord: Advancing directional overcurrent and distance relay coordination with an enhanced equilibrium optimizer.

In this article, an improved optimization technique is used to get a solution to the problem of coordination between directional overcurrent relays (DOCR) and distance relays. An enhanced version of an equilibrium optimization algorithm (EO), referred to as EEO is proposed to solve this problem. The suggested approach optimises the parameter that regulates the balance between exploration and exploitation to identify the potential optimum solution while enhancing the EO algorithm's exploration properties. The main task for the EEO is to get the best settings. Also, the proposed algorithm shall maintain operation in sequence between the main and backup relays. The capability of the suggested EEO algorithm is assessed in 8-bus, IEEE thirty-bus, and IEEE 39-bus systems. The obtained results prove the effectiveness of the EEO technique in solving the coordination problem of the combined directional overcurrent relays and distance relays. Also, the results show the ability of the suggested algorithm to overcome the drawbacks of the traditional EO algorithm and achieve faster protection (the reduction ratio reaches about 12 % compared to the traditional EO.

Multi-strategy synthetized equilibrium optimizer and application.

Background: Improvement on the updating equation of an algorithm is among the most improving techniques. Due to the lack of search ability, high computational complexity and poor operability of equilibrium optimizer (EO) in solving complex optimization problems, an improved EO is proposed in this article, namely the multi-strategy on updating synthetized EO (MS-EO). Method: Firstly, a simplified updating strategy is adopted in EO to improve operability and reduce computational complexity. Secondly, an information sharing strategy updates the concentrations in the early iterative stage using a dynamic tuning strategy in the simplified EO to form a simplified sharing EO (SS-EO) and enhance the exploration ability. Thirdly, a migration strategy and a golden section strategy are used for a golden particle updating to construct a Golden SS-EO (GS-EO) and improve the search ability. Finally, an elite learning strategy is implemented for the worst particle updating in the late stage to form MS-EO and strengthen the exploitation ability. The strategies are embedded into EO to balance between exploration and exploitation by giving full play to their respective advantages. Result and Finding: Experimental results on the complex functions from CEC2013 and CEC2017 test sets demonstrate that MS-EO outperforms EO and quite a few state-of-the-art algorithms in search ability, running speed and operability. The experimental results of feature selection on several datasets show that MS-EO also provides more advantages.

Automated grape leaf nutrition deficiency disease detection and classification Equilibrium Optimizer with deep transfer learning model.

Our approach includes picture preprocessing, feature extraction utilizing the SqueezeNet model, hyperparameter optimisation utilising the Equilibrium Optimizer (EO) algorithm, and classification utilising a Stacked Autoencoder (SAE) model. Each of these processes is carried out in a series of separate steps. During the image preprocessing stage, contrast limited adaptive histogram equalisations (CLAHE) is utilized to improve the contrasts, and Adaptive Bilateral Filtering (ABF) to get rid of any noise that may be present. The SqueezeNet paradigm is utilized to obtain relevant characteristics from the pictures that have been preprocessed, and the EO technique is utilized to fine-tune the hyperparameters. Finally, the SAE model categorises the diseases that affect the grape leaf. The simulation analysis of the EODTL-GLDC technique tested New Plant Diseases Datasets and the results were inspected in many prospects. The results demonstrate that this model outperforms other deep learning techniques and methods that are more often related to machine learning. Specifically, this technique was able to attain a precision of 96.31% on the testing datasets and 96.88% on the training data set that was split 80:20. These results offer more proof that the suggested strategy is successful in automating the detection and categorization of grape leaf diseases.

From Lidar Measurement to Rotor Effective Wind Speed Prediction: Empirical Mode Decomposition and Gated Recurrent Unit Solution.

Conventional wind speed sensors face difficulties in measuring wind speeds at multiple points, and related research on predicting rotor effective wind speed (REWS) is lacking. The utilization of a lidar device allows accurate REWS prediction, enabling advanced control technologies for wind turbines. With the lidar measurements, a data-driven prediction framework based on empirical mode decomposition (EMD) and gated recurrent unit (GRU) is proposed to predict the REWS. Thereby, the time series of lidar measurements are separated by the EMD, and the intrinsic mode functions (IMF) are obtained. The IMF sequences are categorized into high-, medium-, and low-frequency and residual groups, pass through the delay processing, and are respectively used to train four GRU networks. On this basis, the outputs of the four GRU networks are lumped via weighting factors that are optimized by an equilibrium optimizer (EO), obtaining the predicted REWS. Taking advantages of the measurement information and mechanism modeling knowledge, three EMD-GRU prediction schemes with different input combinations are presented. Finally, the proposed prediction schemes are verified and compared by detailed simulations on the BLADED model with four-beam lidar. The experimental results indicate that compared to the mechanism model, the mean absolute error corresponding to the EMD-GRU model is reduced by 49.18%, 53.43%, 52.10%, 65.95%, 48.18%, and 60.33% under six datasets, respectively. The proposed method could provide accurate REWS prediction in advanced prediction control for wind turbines.

Equilibrium Optimization Algorithm with Deep Learning Enabled Prostate Cancer Detection on MRI Images.

The enlargement of the prostate gland in the reproductive system of males is considered a form of prostate cancer (PrC). The survival rate is considerably improved with earlier diagnosis of cancer; thus, timely intervention should be administered. In this study, a new automatic approach combining several deep learning (DL) techniques was introduced to detect PrC from MRI and ultrasound (US) images. Furthermore, the presented method describes why a certain decision was made given the input MRI or US images. Many pretrained custom-developed layers were added to the pretrained model and employed in the dataset. The study presents an Equilibrium Optimization Algorithm with Deep Learning-based Prostate Cancer Detection and Classification (EOADL-PCDC) technique on MRIs. The main goal of the EOADL-PCDC method lies in the detection and classification of PrC. To achieve this, the EOADL-PCDC technique applies image preprocessing to improve the image quality. In addition, the EOADL-PCDC technique follows the CapsNet (capsule network) model for the feature extraction model. The EOA is based on hyperparameter tuning used to increase the efficiency of CapsNet. The EOADL-PCDC algorithm makes use of the stacked bidirectional long short-term memory (SBiLSTM) model for prostate cancer classification. A comprehensive set of simulations of the EOADL-PCDC algorithm was tested on the benchmark MRI dataset. The experimental outcome revealed the superior performance of the EOADL-PCDC approach over existing methods in terms of different metrics.

A chaos-based adaptive equilibrium optimizer algorithm for solving global optimization problems.

The equilibrium optimizer (EO) algorithm is a newly developed physics-based optimization algorithm, which inspired by a mixed dynamic mass balance equation on a controlled fixed volume. The EO algorithm has a number of strengths, such as simple structure, easy implementation, few parameters and its effectiveness has been demonstrated on numerical optimization problems. However, the canonical EO still presents some drawbacks, such as poor balance between exploration and exploitation operation, tendency to get stuck in local optima and low convergence accuracy. To tackle these limitations, this paper proposes a new EO-based approach with an adaptive gbest-guided search mechanism and a chaos mechanism (called a chaos-based adaptive equilibrium optimizer algorithm (ACEO)). Firstly, an adaptive gbest-guided mechanism is injected to enrich the population diversity and expand the search range. Next, the chaos mechanism is incorporated to enable the algorithm to escape from the local optima. The effectiveness of the developed ACEO is demonstrated on 23 classical benchmark functions, and compared with the canonical EO, EO variants and other frontier metaheuristic approaches. The experimental results reveal that the developed ACEO method remarkably outperforms the canonical EO and other competitors. In addition, ACEO is implemented to solve a mobile robot path planning (MRPP) task, and compared with other typical metaheuristic techniques. The comparison indicates that ACEO beats its competitors, and the ACEO algorithm can provide high-quality feasible solutions for MRPP.

Adaptive Guided Equilibrium Optimizer with Spiral Search Mechanism to Solve Global Optimization Problems.

The equilibrium optimizer (EO) is a recently developed physics-based optimization technique for complex optimization problems. Although the algorithm shows excellent exploitation capability, it still has some drawbacks, such as the tendency to fall into local optima and poor population diversity. To address these shortcomings, an enhanced EO algorithm is proposed in this paper. First, a spiral search mechanism is introduced to guide the particles to more promising search regions. Then, a new inertia weight factor is employed to mitigate the oscillation phenomena of particles. To evaluate the effectiveness of the proposed algorithm, it has been tested on the CEC2017 test suite and the mobile robot path planning (MRPP) problem and compared with some advanced metaheuristic techniques. The experimental results demonstrate that our improved EO algorithm outperforms the comparison methods in solving both numerical optimization problems and practical problems. Overall, the developed EO variant has good robustness and stability and can be considered as a promising optimization tool.

A new meta-heuristic optimization-based MPPT control technique for green energy harvesting from photovoltaic systems under different atmospheric conditions.

At present, a photovoltaic (PV) system takes responsibility to reduce the risk of global warming and generate electricity. However, the PV system faces numerous problems to track global maximum peak power (GMPP) owing to the nonlinear nature of the environment especially due to partial shading conditions (PSC). To solve these difficulties, previous researchers have utilized various conventional methods for investigations. Nevertheless, these methods have oscillations around the GMPP. Hence, a new metaheuristic method such as an opposition-based equilibrium optimizer (OBEO) algorithm is used in this work for mitigating the oscillations around GMPP. To find the effectiveness of the proposed method, it can be evaluated with other methods such as SSA, GWO, and P&O. As per the simulation outcome, the proposed OBEO method provides maximum efficiency against all other methods. The efficiency for the proposed method under dynamic PSC is 95.09% in 0.16 s, similarly, 96.17% for uniform PSC and 86.25% for complex PSC.

Classification of Vogt-Koyanagi-Harada disease using feature selection and classification based on wide-field swept-source optical coherence tomography angiography.

Background: Vogt-Koyanagi-Harada (VKH) disease is a common and easily blinded uveitis entity, with choroid being the main involved site. Classification of VKH disease and its different stages is crucial because they differ in clinical manifestations and therapeutic interventions. Wide-field swept-source optical coherence tomography angiography (WSS-OCTA) provides the advantages of non-invasiveness, large-field-of-view, high resolution, and ease of measuring and calculating choroid, offering the potential feasibility of simplified VKH classification assessment based on WSS-OCTA. Methods: 15 healthy controls (HC), 13 acute-phase and 17 convalescent-phase VKH patients were included, undertaken WSS-OCTA examination with a scanning field of 15 × 9 mm2. 20 WSS-OCTA parameters were then extracted from WSS-OCTA images. To classify HC and VKH patients in acute and convalescent phases, two 2-class VKH datasets (HC and VKH) and two 3-class VKH datasets (HC, acute-phase VKH, and convalescent-phase VKH) were established by the WSS-OCTA parameters alone or in combination with best-corrected visual acuity (logMAR BCVA) and intraocular pressure (IOP), respectively. A new feature selection and classification method that combines an equilibrium optimizer and a support vector machine (called SVM-EO) was adopted to select classification-sensitive parameters among the massive datasets and to achieve outstanding classification performance. The interpretability of the VKH classification models was demonstrated based on SHapley Additive exPlanations (SHAP). Results: Based on pure WSS-OCTA parameters, we achieved classification accuracies of 91.61% ± 12.17% and 86.69% ± 8.30% for 2- and 3-class VKH classification tasks. By combining the WSS-OCTA parameters and logMAR BCVA, we achieved better classification performance of 98.82% ± 2.63% and 96.16% ± 5.88%, respectively. Through SHAP analysis, we found that logMAR BCVA and vascular perfusion density (VPD) calculated from the whole field of view region in the choriocapillaris (whole FOV CC-VPD) were the most important features for VKH classification in our models. Conclusion: We achieved excellent VKH classification performance based on a non-invasive WSS-OCTA examination, which provides the possibility for future clinical VKH classification with high sensitivity and specificity.

An Approach of Vibration Compensation for Atomic Gravimeter under Complex Vibration Environment.

Atomic gravimeter has been more frequently applied under complex and dynamic environments, but its measurement accuracy is seriously hampered by vibration-induced noise. In this case, vibration compensation provides a way to enhance the accuracy of gravity measurements by correcting the phase noise that resulted from the vibration of a Raman reflector, and improving the fitting of an interference fringe. An accurate estimation of the transfer function of vibration between the Raman reflector and the sensor plays a significant role in optimizing the effect of vibration compensation. For this reason, a vibration compensation approach was explored based on EO (equilibrium optimizer) for estimating the transfer function simplified model of a Raman reflector, and it was used to correct the interference fringe of an atomic gravimeter. The test results revealed that this approach greatly restored the actual vibration of the Raman reflector in a complex vibration environment. With a vibration compensation algorithm, it achieved the correction and fitting of the original interference fringe. In general, it dramatically reduced the RMSE (root mean square error) at the time of fitting and significantly improved the residual error in the gravity measurement. Compared with other conventional algorithms, such as GA (genetic algorithm) and PSO (particle swarm optimization), this approach realized a faster convergence and better optimization, so as to ensure more accurate gravity measurements. The study of this vibration compensation approach could provide a reference for the application of an atomic gravimeter in a wider and more complex environment.

A self-adaptive quantum equilibrium optimizer with artificial bee colony for feature selection.

Feature selection (FS) is a popular data pre-processing technique in machine learning to extract the optimal features to maintain or increase the classification accuracy of the dataset, which is a combinatorial optimization problem, requiring a powerful optimizer to obtain the optimum subset. The equilibrium optimizer (EO) is a recent physical-based metaheuristic algorithm with good performance for various optimization problems, but it may encounter premature or the local convergence in feature selection. This work presents a self-adaptive quantum EO with artificial bee colony for feature selection, named SQEOABC. In the proposed algorithm, the quantum theory and the self-adaptive mechanism are employed into the updating rule of EO to enhance convergence, and the updating mechanism from the artificial bee colony is also incorporated into EO to achieve appropriate FS solutions. In the experiments, 25 benchmark datasets from the UCI repository are investigated to verify SQEOABC, which is compared with several state-of-the-art metaheuristic algorithms and the variants of EO. The statistical results of fitness values and accuracy demonstrate that SQEOABC has better performance than the compared algorithms and the variants of EO. Finally, a real-world FS problem from COVID-19 illustrates the effectiveness and superiority of SQEOABC.

A hybrid equilibrium algorithm and pattern search technique for wind farm layout optimization problem.

The layout optimization-based model is a significant issue for increasing the utilization rate of the wind farm and minimizing its cost per unit of power. For the accurate and reliable wind farm layout optimization design, a novel algorithm based on the hybridization of equilibrium optimizer (EO) and pattern search (PS) technique, named EO-PS, is proposed in this paper. The proposed EO-PS operates in two phases. The first phase implements the EO to explore the search space and reach the promising regions by using an equilibrium pool of elite particles, which contributes to maintaining the diversity of solutions. The second phase integrates the PS to guide the searching towards better vicinities and achieve a high-quality solution by using its detecting and pattern movements to boost the exploitation ability of the proposed method in the last steps. The presented EO-PS algorithm is implemented to deal with single and multi-objective optimization aspects of wind farm layout optimization using different wind speed scenarios. Furthermore, the proposed algorithm is investigated on irregular land space in the Gulf of Suez-Red Sea in Egypt to achieve the optimal layout configuration of the wind farm, which is vital for possible practical planning trends. The comprehensive results and analyses have affirmed that the proposed EO-PS can achieve competitive performance compared to the other state-of-the-state methods, especially in terms of the solution' quality and reliability.

Development and application of equilibrium optimizer for optimal power flow calculation of power system.

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC'20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon's rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.

Orthogonal pinhole-imaging-based learning salp swarm algorithm with self-adaptive structure for global optimization.

Salp swarm algorithm (SSA) is a simple and effective bio-inspired algorithm that is gaining popularity in global optimization problems. In this paper, first, based on the pinhole imaging phenomenon and opposition-based learning mechanism, a new strategy called pinhole-imaging-based learning (PIBL) is proposed. Then, the PIBL strategy is combined with orthogonal experimental design (OED) to propose an OPIBL mechanism that helps the algorithm to jump out of the local optimum. Second, a novel effective adaptive conversion parameter method is designed to enhance the balance between exploration and exploitation ability. To validate the performance of OPLSSA, comparative experiments are conducted based on 23 widely used benchmark functions and 30 IEEE CEC2017 benchmark problems. Compared with some well-established algorithms, OPLSSA performs better in most of the benchmark problems.