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Optimization has found a widespread application in many branches of science. In recent years, different methods and theories have been developed to find optimal solutions. Optimization algorithms inspired by nature as heuristics solutions to complex problems. Reverse engineering is one of the applications of optimization methods. In reverse engineering a set of scan points are defined relative to a particular coordination. In data registration process the scanned data sets separated and combined to a single coordinate system are called the process of registration. In this research, applications part has been digitized by coordinate measuring machine(CMM) and the process of point clouds registration in experimental on two pieces in position (without translation and with translation case) has been implemented. Using gravitational search algorithm (GSA), particle swarm optimization (PSO) and genetic algorithm (GA) optimization process is optimized and the registration parameters (rotation and displacement) are obtained. The algorithms mentioned, GSA the accuracy displacement, rotational accuracy and better convergence rate and the run time is less. Finally, a hybrid algorithm is proposed which is a combination of GSA, and Nelder-Mead algorithms (GSA-NM). In the proposed algorithm, the initial guess values obtained by GSA and Nelder-Mead algorithm is provided to ensure an accurate response. The proposed hybrid algorithm is superior to GSA and Nelder-Mead, in terms of the number of iterations and the amount of convergence.

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Sandwich structures have low weight and high stiffness. Sandwich panels with open and prismatic cores are a kind of these structures that have special properties. These panels are named based on the number of corrugations (n) of the core. In this paper weight optimization of these panels is carried out by Gravitational Search Algorithm based on yielding and buckling constraints. This algorithm is a heuristic algorithm that is based upon the Newtonian gravity force and the laws of motion. For optimization of the weight, core and surface thickness and panel height are assumed as design variables. The results show that for a specific panel, the design variables and the weight of panel are increased by increasing the load. Also the core and surface thickness are decreased and the weight and panel height are increased by increasing core corrugate number at a specific loading. The panels with n=1 and n=2 have the minimum weight and highest structural efficiency. By comparing the results with some previous studies, it is shown that the Gravitational Search Algorithm is a useful tool in achieving lower weight in these panels and has a good convergence rate.

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Gravitational search algorithm (for the first time) has been used for two-objective optimization of airfoil shape, in this article. 2D compressible Navier-Stokes equations with Spalart-Allmaras model has been used to simulate viscous and turbulent flow. First, efficiency and accuracy of the optimizer sets have been evaluated using inverse optimization. Objective functions were differences between drag and lift with their corresponding values of the NACA0012 objective airfoil, as a set of airfoils randomly were chosen as starter airfoils, in this case and the aim was to obtain the airfoils that satisfy the considered objective functions. In direct optimization, gravitational search algorithm that has been used in the present work, has achieved proper parameters (related to the Parsec method) and consequently has found optimized airfoils with maximum lift and minimum drag objective functions. This algorithm starts to slove using a set of airfoils and it is directed towards the airfoils that provide the mentioned objective functions. Comparison of the results (Pareto fronts) shows better and more proper performance of the gravitational search algorithm rather than particle swarm optimization algorithm and former researches (done using other meta-heuristic algorithms) for aerodynamic optimizations.

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Groundwater is the most reliable source of supply for potable water and supports a wide array of economic and environmental services. There is a significant concern that groundwater levels are declining due to intense aquifer use. The sustainable management of groundwater resources requires good planning and concerted efforts. To manage groundwater resources, it is necessary to predict the groundwater levels and its fluctuations. The prediction groundwater level can guide water managers and engineers effectively. On the other hand, there are multifarious types of equipment for measuring levels of groundwater. Sophisticated water level loggers or divers can measure the groundwater level automatically. Sounding devices with acoustic and light signals are also used to check groundwater levels. The use of devices for measuring the level of groundwater is time-consuming and costly. To reduce the time and cost of the groundwater level measuring process, many methods of Artificial Intelligence (AI) have been utilized for estimating the groundwater level. Among the AI methods, SVMs has great ability in predicting non-linear hydrological processes. Support vector machines (SVMs) is as an intelligent computational method for predicting hydrological processes. Recently, (SVMs) have been successfully applied in classification problems, regression and predicting; as techniques of machine learning, statistics and mathematical analysis. The SVM is based on the structural risk minimization (SRM), which can escape from various difficulties, such as the necessity of a large number of control parameters and a local minimum in artificial neural networks (ANNs). The weighted least squares support vector machines (WLSSVM) was first introduced by Suykens et al., and has proved to be much more robust in several fields, especially for noise mixed data, than least squares version of SVM (LSSVM). Their powerful scientific research provides motivation for employing WLSSVM method in estimating groundwater level. The accurate value of WLSSVM parameters  effect on the estimation, these optimal parameters can be achieved optimization algorithms. Therefore, weighted least square support vector machine (WLS-SVM) model was coupled with particle swarm optimization (PSO) and gravitational search algorithm (GSA) as metaheuristic algorithms for estimating well water level. In this study, an attempt has been made to use the hybrid model with high accuracy to estimate the groundwater level. In order to estimate the groundwater level, ten wells data in Bagheyn plain of Kerman province is considered during ten-year time series. The estimated value obtained by the WLSSVM-PSO and WLSSVM-GSA models are compared with the observed value, and showed the estimated results have nearly coincidence with observed values. Numerical results show the merits of the suggested technique for groundwater level simulation. In order to verify the hybrid learning machine metaheuristic model, Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Average Absolute Error (AAE), and Model Efficiency (EF) are computed, and these statistical indicators stand on the good acceptable range, and find WLSSVM-GSA is more accurate than WLSSVM-PSO. The results demonstrate that the new hybrid WLSSVM-GSA model has high efficiency and accuracy with observed values, and the modelling method is an innovative and powerful idea in estimating well water level.