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In this paper, a methodology is presented for optimum shape design of double-layer grids subject to gravity and earthquake loadings. The design variables are the number of divisions in two directions, the height between two layers and the cross-sectional areas of the structural elements. The objective function is the weight of the structure and the design constraints are some limitations on stress and slenderness of the elements besides the vertical displacements of the joints. To achieve the optimization task a variant of particle swarm optimization (PSO) entitled as quantum-behaved particle swarm optimization (QPSO) algorithm is employed. The computational burden of the optimization process due to performing time history analysis is very high. In order to decrease the optimization time, the radial basis function (RBF) neural networks are employed to predict the desired responses of the structures during the optimization process. The numerical results demonstrate the effectiveness of the presented methodology

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Jellyfish Search (JS) is a recently developed population-based metaheuristic inspired by the food-finding behavior of jellyfish in the ocean. The purpose of this paper is to propose a quantum-based Jellyfish Search algorithm, named Quantum JS (QJS), for solving structural optimization problems. Compared to the classical JS, three main improvements are made in the proposed QJS: (1) a quantum-based update rule is adopted to encourage the diversification in the search space, (2) a new boundary handling mechanism is used to avoid getting trapped in local optima, and (3) modifications of the time control mechanism are added to strike a better balance between global and local searches. The proposed QJS is applied to solve frequency-constrained large-scale cyclic symmetric dome optimization problems. To the best of our knowledge, this is the first time that JS is applied in frequency-constrained optimization problems. An efficient eigensolution method for free vibration analysis of rotationally repetitive structures is employed to perform structural analyses required in the optimization process. The efficient eigensolution method leads to a considerable saving in computational time as compared to the existing classical eigensolution method. Numerical results confirm that the proposed QJS considerably outperforms the classical JS and has superior or comparable performance to other state-of-the-art optimization algorithms. Moreover, it is shown that the present eigensolution method significantly reduces the required computational time of the optimization process compared to the classical eigensolution method.

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As a novel strategy, Quantum-behaved particles use uncertainty law and a distinct formulation obtained from solving the time-independent Schrodinger differential equation in the delta-potential-well function to update the solution candidates’ positions. In this case, the local attractors as potential solutions between the best solution and the others are introduced to explore the solution space. Also,  the difference between the average and another solution is established as a new step size. In the present paper, the quantum teacher phase is introduced to improve the performance of the current version of the teacher phase of the Teaching-Learning-Based Optimization algorithm (TLBO) by using the formulation obtained from solving the time-independent Schrodinger equation predicting the probable positions of optimal solutions. The results show that QTLBO, an acronym for the Quantum Teaching- Learning- Based Optimization, improves the stability and robustness of the TLBO by defining the quantum teacher phase. The two circulant space trusses with multiple frequency constraints are chosen to verify the quality and performance of QTLBO. Comparing the results obtained from the proposed algorithm with those of the standard version of the TLBO algorithm and other literature methods shows that QTLBO increases the chance of finding a better solution besides improving the statistical criteria compared to the current TLBO.