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Structural reliability theory allows structural engineers to take the random nature of structural parameters into account in the analysis and design of structures. The aim of this research is to develop a logical framework for system reliability analysis of truss structures and simultaneous size and geometry optimization of truss structures subjected to structural system reliability constraint. The framework is in the form of a computer program called RBO-S>S. The objective of the optimization is to minimize the total weight of the truss structures against the aforementioned constraint. System reliability analysis of truss structures is performed through branch-and-bound method. Also, optimization is carried out by genetic algorithm. The research results show that system reliability analysis of truss structures can be performed with sufficient accurately using the RBO-S>S program. In addition, it can be used for optimal design of truss structures. Solutions are suggested to reduce the time required for reliability analysis of truss structures and to increase the precision of their reliability analysis.

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The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for embedding graphs in the plane. The algorithms consist of Artificial Bee Colony algorithm, Big Bang-Big Crunch algorithm, Teaching-Learning-Based Optimization algorithm, Cuckoo Search algorithm, Charged System Search algorithm, Tug of War Optimization algorithm, Water Evaporation Optimization algorithm, and Vibrating Particles System algorithm. The performance of the utilized algorithms is investigated through various examples including six complete graphs and eight complete bipartite graphs. Convergence histories of the algorithms are provided to better understanding of their performance. In addition, optimum results at different stages of the optimization process are extracted to enable to compare the meta-heuristics algorithms.

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Meta-heuristic algorithms are applied in optimization problems in a variety of fields, including engineering, economics, and computer science. In this paper, seven population-based meta-heuristic algorithms are employed for size and geometry optimization of truss structures. These algorithms consist of the Artificial Bee Colony algorithm, Cyclical Parthenogenesis Algorithm, Cuckoo Search algorithm, Teaching-Learning-Based Optimization algorithm, Vibrating Particles System algorithm, Water Evaporation Optimization, and a hybridized ABC-TLBO algorithm. The Taguchi method is employed to tune the parameters of the meta-heuristics. Optimization aims to minimize the weight of truss structures while satisfying some constraints on their natural frequencies. The capability and robustness of the algorithms is investigated through four well-known benchmark truss structure examples.

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In this paper, set theoretical variants of the artificial bee colony (ABC) and water evaporation optmization (WEO) algorithms are proposed. The set theoretical variants are designed based on a set theoretical framework in which the population of candidate solutions is divided into some number of smaller well-arranged sub-populations. The framework aims to improve the compromise between diversification and intensification of the search and makes it possible to design various variants of a P-metaheuristic. In order to verify the stability and robustness of the set theoretical framework, the proposed algorithms are applied to solve three different benchmark structural design optimization problems. The results show that the set theoretical framework improves the performance of the ABC and WEO algorithms, especially in terms of robustness and convergence characteristics.

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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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The arithmetic optimization algorithm (AOA) is a recently developed metaheuristic optimization algorithm that simulates the distribution characteristics of the four basic arithmetic operations (i.e., addition, subtraction, multiplication, and division) and has been successfully applied to solve some optimization problems. However, the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when dealing with multi-dimensional optimization problems. More recently, in order to overcome the shortcomings of the original AOA, an improved version of AOA, named IAOA, has been proposed and successfully applied to discrete structural optimization problems. Compared to the original AOA, two major improvements have been made in IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The IAOA requires fewer algorithm-specific parameters compared with the original AOA, which makes it easy to be implemented. In this paper, IAOA is applied to the optimal design of large-scale dome-like truss structures with multiple frequency constraints. To the best of our knowledge, this is the first time that IAOA is applied to structural optimization problems with frequency constraints. Three benchmark dome-shaped truss optimization problems with frequency constraints are investigated to demonstrate the efficiency and robustness of the IAOA. Experimental results indicate that IAOA significantly outperforms the original AOA and achieves results comparable or superior to other state-of-the-art algorithms.

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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.