‎In this paper‎, ‎first‎, ‎we show how to define an algebraic hyperstructure by using algorithms‎. ‎Then‎, ‎we present algorithms that calculate specific elements in algebraic hyperstructures‎. ‎These specific elements are‎: ‎scalars‎, ‎scalar identities‎, ‎identities‎, ‎inverses‎, ‎zero elements‎, ‎right simplifiable elements‎, ‎left simplifiable elements‎, ‎left absorbing-like elements and right absorbing-like elements‎. ‎We also introduce some algorithms in algebraic hyperstructures to check properties or calculate specific members‎. ‎These algorithms are presented for algebraic hyperstructures with one hyperoperation‎, ‎i.e‎. ‎hypergroupoids‎. ‎However‎, ‎they can be developed for other algebraic hyperstructures‎.

In this paper, we introduce a new continuous quantum evolutionary optimization algorithm designed for optimizing nonlinear convex functions, non-convex functions, and efficiency evaluation problems using quantum computing principles. ‎ Traditional quantum evolutionary algorithms have primarily been implemented for discrete and binary decision variables‎. ‎The proposed method has been designed as a novel continuous quantum evolutionary optimization algorithm tailored to problems with continuous decision variables‎. ‎ To assess the algorithm’s performance, several numerical experiments are conducted‎, ‎and the simulated results are compared with the Grey Wolf Optimizer and Magnet Fish Optimization search algorithm‎. ‎The simulation results indicate that the proposed algorithm can approximate the optimal solution more accurately than the two compared algorithms.

‎In this paper‎, ‎we introduce a new algorithm for constructing a‎ ‎symmetric pentadiagonal matrix by using three interlacing spectrum‎, ‎say $(\lambda_i)_{i=1}^n$‎, ‎$(\mu_i)_{i=1}^n$ and $(\nu_i)_{i=1}^n$‎ ‎such that‎‎\begin{eqnarray*}‎‎0<\lambda_1<\mu_1<\lambda_2<\mu_2<...<\lambda_n<\mu_n,\\‎‎\mu_1<\nu_1<\mu_2<\nu_2<...<\mu_n<\nu_n‎,‎\end{eqnarray*}‎‎where $(\lambda_i)_{i=1}^n$ are the eigenvalues of pentadiagonal‎ ‎matrix $A$‎, ‎$(\mu_i)_{i=1}^n$ are the eigenvalues of $A^*$ (the‎   ‎matrix $A^*$ differs from $A$ only in the $(1,1)$ entry) and‎ ‎$(\nu_i)_{i=1}^n$ are the eigenvalues of $A^{**}$ (the matrix‎ ‎$A^{**}$ differs from $A^*$ only in the $(2,2)$ entry)‎. ‎From the‎‎interlacing spectrum‎, ‎we find the first and second columns of‎ ‎eigenvectors‎. ‎Sufficient conditions for the solvability of the problem‎ ‎are given‎. ‎Then we construct the pentadiagonal matrix $A$ from these‎ ‎eigenvectors and given eigenvalues by using the block Lanczos algorithm‎. ‎We‎ ‎also give an example to demonstrate the efficiency of the algorithm‎.

‎Consider a graph $G=(V(G),E(G))$‎, ‎where a perfect matching in $G$ is defined as a subset of independent edges with $\frac{|V(G)|}{2}$ elements‎. ‎A global forcing set is a subset $S$ of $E$ such that no two disjoint perfect matchings of $G$ coincide on it‎. ‎The minimum cardinality of global forcing sets of $G$ is called the global forcing number (GFN for short)‎. ‎This paper addresses the NP-hard problem of determining the global forcing number for perfect matchings‎. ‎The focus is on a Genetic Algorithm (GA) that utilizes binary encoding and standard genetic operators to solve this problem‎. ‎The proposed algorithm is implemented on some chemical graphs to illustrate the validity of the algorithm‎. ‎The solutions obtained by the GA are compared with the results from other methods that have been presented in the literature‎. ‎The presented algorithm can be applied to various bipartite graphs‎, ‎particularly hexagonal systems‎. ‎Additionally‎, ‎the results of the GA improve some results that‎ have already been presented for finding GFN‎.

The existence of different solution approaches that generate approximations to the optimal Pareto frontiers of a multi-objective optimization problem lead to different sets of non-dominated solutions. To evaluate the quality of these solution sets, one requires a comprehensive evaluation measure to consider the features of the solutions. Despite various  valuation measures, the deficiency caused by the lack of such a comprehensive measure is  visible. For this reason, in this paper, by considering some evaluation measures, first we evaluate the quality of the approximations to the optimal Pareto front resulting from the decomposition-based multi-objective evolutionary algorithm equipped with four decomposition approaches and investigate the related drawbacks. In the second step, we use the concept of Gaussian degree of closeness to combine the evaluation measures, and hence, we propose a new evaluation measure called the quasi-Gaussian integration measure. The numerical results obtained from applying the proposed measure to the standard test functions confirm the effectiveness of this measure in examining the quality of the non-dominated solution set in a more accurate manner.

The objective of this research is to numerically investigate heat transfer and pressure drop characteristic ‎of a baffle assisted multi-jet impingement of air on a heated plate subjected to constant heat flux and ‎cross flow. Two baffle configurations were considered for the present study. An array of jets with 3 x 3 ‎configurations discharging from round orifices of diameter D=5 mm and with jet-to-heated plate distance ‎ranging from 2D to 3. 5D were studied. SST k-ω turbulence model was used for numerical simulation to ‎examine the effect of blow ratio and baffle clearance on heat transfer and pressure drop characteristics. ‎Blow ratios of 0. 25, 0. 5, 0. 75 and 1. 0 and baffle clearances of 1 mm, 2 mm, and 3mm were considered ‎for CFD simulations. The split baffle configuration with baffle clearance of 3 mm is found to be more ‎advantageous when both heat transfer and pressure drop are considered. However, the segmented baffle ‎configuration with a baffle clearance of 1 mm gave better results for heat transfer alone. The present ‎study also deals with determination of optimal operating parameters with the help of Genetic Algorithm ‎and Artificial Neural Network. A pareto front was obtained for selecting the desired value of heat transfer ‎or pressure drop. It was found that Artificial Neural Network based predictions strongly agree with CFD ‎simulation results, and hence seems to be very useful in arriving at the optimum values of operating ‎parameters‎.

The boosting algorithm is a hybrid algorithm to reduce variance, a family of machine learning algorithms in supervised learning. This algorithm is a method to transform weak learning systems into strong systems based on the combination of different results. In this paper, mixture models with random effects are considered for small areas, where the errors follow the AR-GARCH model. To select the variable, machine learning algorithms, such as boosting algorithms, have been proposed. Using simulated and tax liability data, the boosting algorithm's performance is studied and compared with classical variable selection methods, such as the step-by-step method.

Many anomaly detection algorithms require knowledge of the ratio of the two labels to operate‎. ‎In real life‎, ‎however‎, ‎we may not have access to this value‎. ‎As such‎, ‎we often run anomaly detection packages with default values that may differ significantly from the actual value‎. ‎Experiments on multiple datasets show that correctly determination of this ratio or at least obtaining a close estimate can makes a significant difference in the final performance of the anomaly detection algorithm‎. ‎In this paper‎, ‎we address the problem of estimating this ratio using both theoretical and heuristic techniques‎. ‎In the theoretical method‎, ‎we maximize the mutual information between features and labels to find the exact ratio‎. ‎In the heuristic method‎, ‎we sweep the [0, 1] range in 0. 01 steps to search for the ratio‎. ‎On each iteration‎, ‎we run the anomaly detection algorithm based on the ratio for that iteration and record the correlation coefficient between the features and the label generated by the algorithm‎. ‎After the 100th iteration‎, ‎we declare the ratio that provides the maximum correlation coefficient as our estimate of the label ratio‎. ‎Our experiments on multiple datasets and several anomaly detection algorithms show that maximizing the correlation coefficient leads to the best results.

In this paper‎, ‎we introduce a novel iterative scheme that integrates the Mann iteration process with the implicit $\theta$-method to approximate fixed points of nonexpansive multivalued mappings in Banach spaces‎. ‎Under suitable assumptions‎, ‎we establish both weak and strong convergence results for the proposed algorithm‎. ‎Furthermore‎, ‎we demonstrate the applicability of our method to variational inclusion problems and convex optimization problems‎. ‎A numerical example is presented to illustrate the efficiency and effectiveness of the approach‎.

‎This study suggests a novel approach for calibrating European option pricing model by a hybrid model based on the optimized artificial neural network and Black-Scholes model‎. ‎In this model‎, ‎the inputs of the artificial neural network are the Black-Scholes equations with different maturity dates and strike prices‎. ‎The presented calibration process involves training the neural network on historical option prices and adjusting its parameters using the Levenberg-Marquardt optimization algorithm‎. ‎The resulting hybrid model shows superior accuracy and efficiency in option pricing on both in sample and out of sample dataset‎.