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.

Quantum cloning operation, started with no-go theorem which proved that there is no capability to perform a cloning operation on an unknown quantum state, however, a number of trials proved that we can make approximate quantum state cloning that is still with some errors. To the best of our knowledge, this paper is the first of its kind to attempt using meta-heuristic algorithm such as Adaptive Guided Differential Evolution (AGDE), to tackle the problem of quantum cloning circuit parameters to enhance the cloning fidelity. To investigate the effectiveness of the AGDE, the extensive experiments have demonstrated that the AGDE can achieve outstanding performance compared to other well-known meta-heuristics including; Enhanced LSHADE-SPACMA Algorithm (ELSHADE-SPACMA), Enhanced Differential Evolution algorithm with novel control parameter adaptation (PaDE), Improved Multi-operator Differential Evolution Algorithm (IMODE), Parameters with adaptive learning mechanism (PALM), QUasi-Affine TRansformation Evolutionary algorithm (QUATRE), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Cuckoo Search (CS), Bat-inspired Algorithm (BA), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). In the present study, AGDE is applied to improve the fidelity of quantum cloning problem and the obtained parameter values minimize the cloning difference error value down to 10-8. Accordingly, the qualitative and quantitative measurements including average, standard deviation, convergence curves of the competitive algorithms over 30 independent runs, proved the superiority of AGDE to enhance the cloning fidelity.

With the complicated geology of vein deposits, their irregular and extremely skewed grade distribution, and the confined nature of gold, there is a propensity to overestimate or underestimate the ore grade. As a result, numerous estimation approaches for mineral resources have been developed. It was investigated in this study by using five machine learning algorithms to estimate highly skewed gold data in the vein-type at the Quartz Ridge region, including Gaussian Process Regression (GPR), Support Vector Regression (SVR), Decision Tree Ensemble (DTE), Fully Connected Neural Network (FCNN), and K-Nearest Neighbors (K-NN). The accuracy of MLA is compared to that of geostatistical approaches, such as ordinary and indicator kriging. Significant improvements were made during data preprocessing and splitting, ensuring that MLA was estimated accurately. The data were preprocessed with two normalization methods (z-score and logarithmic) to enhance network training performance and minimize substantial differences in the dataset’s variable ranges on predictions. The samples were divided into two equal subsets using an integrated data segmentation approach based on the Marine Predators Algorithm (MPA). The ranking shows that the GPR with logarithmic normalization is the most efficient method for estimating gold grade, far outperforming kriging techniques. In this study, the key to producing a successful mineral estimate is more than just the technique. It also has to do with how the data are processed and split.

The economic value of a mineral resource is highly dependent on the accuracy of grade estimations. Accurate predictions of mineral grades can help businesses decide whether to invest in a mining project and optimize mining operations to maximize the resource. Conventional methods of predicting gold resources are both costly and time-consuming. However, advances in machine learning and processing power are making it possible for mineral estimation to become more efficient and effective. This work introduces a novel approach for predicting the distribution of mineral grades within a deposit. The approach integrates machine learning and optimization techniques. Specifically, the authors propose an approach that integrates the random forest (RF) and k-nearest neighbor (kNN) algorithms with the marine predators optimization algorithm (MPA). The RFKNN_MPA approach uses log normalization to reduce the impact of extreme values and improve the accuracy of the machine learning models. Data segmentation and the MPA algorithm are used to create statistically equivalent subsets of the dataset for use in training and testing. Drill hole locations and rock types are used to create each model. The suggested technique’s performance indices are superior to the others, with a higher R-squared coefficient of 59.7%, a higher R-value of 77%, and lower MSE and RMSE values of 0.17 and 0.44, respectively. The RFKNN_MPA algorithm outperforms geostatistical and conventional machine-learning techniques for estimating mineral orebody grades. The introduced approach offers a novel solution to a problem with practical applications in the mining sector.