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The main aim of the present study is to propose a modified harmony search (MHS) algorithm for size and shape optimization of structures. The standard harmony search (HS) algorithm is conceptualized using the musical process of searching for a perfect state of the harmony. It uses a stochastic random search instead of a gradient search. The proposed MHS algorithm is designed based on elitism. In fact the MHS is a multi-staged version of the HS and in each stage a new harmony memory is created using the information of the previous stages. Numerical results reveal that the proposed algorithm is a powerful optimization technique with improved exploitation characteristics compared with the standard HS.

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Engineering optimization needs easy-to-use and efficient optimization tools that can be employed for practical purposes. In this context, stochastic search techniques have good reputation and wide acceptability as being powerful tools for solving complex engineering optimization problems. However, increased complexity of some metaheuristic algorithms sometimes makes it difficult for engineers to utilize such techniques in their applications. Big- Bang Big-Crunch (BB-BC) algorithm is a simple metaheuristic optimization method emerged from the Big Bang and Big Crunch theories of the universe evolution. The present study is an attempt to evaluate the efficiency of this algorithm in solving engineering optimization problems. The performance of the algorithm is investigated through various benchmark examples that have different features. The obtained results reveal the efficiency and robustness of the BB-BC algorithm in finding promising solutions for engineering optimization problems.

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This paper is concerned with the economical comparison between two commonly used configurations for double layer grids and determining their optimum span-depth ratio. Two ranges of spans as small and big sizes with certain bays of equal length in two directions and various types of element grouping are considered for each type of square grids. In order to carry out a precise comparison between different systems, optimum design procedure based on the Cuckoo Search (CS) algorithm is developed. The CS is a meta-heuristic algorithm recently developed that is inspired by the behavior of some Cuckoo species in combination with the Lévy flight behavior of some birds and insects. The design algorithm obtains minimum weight grid through appropriate selection of tube sections available in AISC Load and Resistance Factor Design (LRFD). Strength constraints of AISC-LRFD specification and displacement constraints are imposed on grids. The comparison is aimed at finding the depth at which each of the different configurations shows its advantages. The results are graphically presented from which the optimum depth can easily be estimated for each type, while the influence of element grouping can also be realized at the same time.

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For reliability-based topology optimization (RBTO) of double layer grids, a two-stage optimization method is presented by applying “Solid Isotropic Material with Penalization” and “Ant Colony Optimization” (SIMP-ACO method). To achieve this aim, first, the structural stiffness is maximized using SIMP. Then, the characteristics of the obtained topology are used to enhance ACO through six modifications. As numerical examples, reliability-based topology designs of typical double layer grids are obtained by ACO and SIMP-ACO methods. Their numerical results reveal the effectiveness of the proposed SIMPACO method for the RBTO of double layer grids.

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In recent years, the importance of economical considerations in the field of dam engineering has motivated many researchers to propose new methods for minimizing the cost of dames and in particular arch dams. This paper presents a method for shape optimization of double curvature arch dams corresponding to minimum construction cost while satisfying different constraints such as natural frequencies, stability and geometrical limitations. For optimization, the charged system search (CSS) and particle swarm optimization (PSO) are employed. To validate the finite element model, a real arch dam is considered as a test example. The results of the present method are compared to those of other optimization algorithms for the selected example from literature.

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In this paper, an efficient multi-objective model is proposed to solve time-cost trade off problem considering cash flows. The proposed multi-objective meta-heuristic is based on Ant colony optimization and is called Non Dominated Archiving Ant Colony Optimization (NAACO). The significant feature of this work is consideration of uncertainties in time, cost and more importantly interest rate. A fuzzy approach is adopted to account for uncertainties. Mathematics of cash-flow analysis in a fuzzy environment is described. A case study is done using the proposed approach

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In this paper nonlinear analysis of structures are performed considering material and geometric nonlinearity using force method and energy concepts. For this purpose, the complementary energy of the structure is minimized using ant colony algorithms. Considering the energy term next to the weight of the structure, optimal design of structures is performed. The first part of this paper contains the formulation of the complementary energy of truss and frame structures for the purpose of linear analysis. In the second part material and geometric nonlinearity of structure is considered using Ramberg-Osgood relationships. In the last part optimal simultaneous analysis and design of structure is studied. In each part, the efficiency of the methods is illustrated by means simple examples.

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A hybrid meta-heuristic optimization method is introduced to efficiently find the optimal shape of concrete gravity dams including dam-water-foundation rock interaction subjected to earthquake loading. The hybrid meta-heuristic optimization method is based on a hybrid of gravitational search algorithm (GSA) and particle swarm optimization (PSO), which is called GSA-PSO. The operation of GSA-PSO includes three phases. In the first phase, a preliminary optimization is accomplished using GSA as local search. In the second phase, an optimal initial swarm is produced using the optimum result of GSA. Finally, PSO is employed to find the optimum design using the optimal initial swarm. In order to reduce the computational cost of dam analysis subject to earthquake loading, weighted least squares support vector machine (WLS-SVM) is employed to accurately predict dynamic responses of gravity dams. Numerical results demonstrate the high performance of the hybrid meta-heuristic optimization for optimal shape design of concrete gravity dams. The solutions obtained by GSA-PSO are compared with those of GSA and PSO. It is revealed that GSA-PSO converges to a superior solution compared to GSA and PSO, and has a lower computation cost.

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One primary problem in shape optimization of structures is making a robust link between design model (geometric description) and analysis model. This paper investigates the potential of Isogeometric Analysis (IGA) for solving this problem. The generic framework of shape optimization of structures is presented based on Isogeometric analysis. By discretization of domain via NURBS functions, the analysis model will precisely demonstrate the geometry of structure. In this study Particle Swarm Optimization (PSO) is used for Isogeometric shape optimization. The option of selecting the position and weight of control points as design variables, needless to sensitivity analysis relationships, is the superiority of the proposed method over gradient-based methods. The other advantages of this method are its straightforward implementation

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In the present paper, an approach is proposed for structural topology optimization based on combination of Radial Basis Function (RBF) Level Set Method (LSM) with Isogeometric Analysis (IGA). The corresponding combined algorithm is detailed. First, in this approach, the discrete problem is formulated in Isogeometric Analysis framework. The objective function based on compliance of particular locations of materials in the structure is used and find the optimal distribution of material in the domain to minimize the compliance of the system under a volume constraint. The refinement is employed for construction of the physical mesh to be consistent with the mesh is used for level set function. Then a parameterized level set method with radial basis functions (RBFs) is used for structural topology optimization. Finally, several numerical examples are provided to confirm the validity of the method.

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The present study is an attempt to propose a mutation-based real-coded genetic algorithm (MBRCGA) for sizing and layout optimization of planar and spatial truss structures. The Gaussian mutation operator is used to create the reproduction operators. An adaptive tournament selection mechanism in combination with adaptive Gaussian mutation operators are proposed to achieve an effective search in the design space. The standard deviation of design variables is used as a key factor in the adaptation of mutation operators. The reliability of the proposed algorithm is investigated in typical sizing and layout optimization problems with both discrete and continuous design variables. The numerical results clearly indicated the competitiveness of MBRCGA in comparison with previously presented methods in the literature.

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Ant colony optimization algorithms (ACOs) have been basically introduced to discrete variable problems and applied to different research domains in several engineering fields. Meanwhile, abundant studies have been already involved to adapt different ant models to continuous search spaces. Assessments indicate competitive performance of ACOs on discrete or continuous domains. Therefore, as potent optimization algorithms, it is encouraging to involve ant models to mixed-variable domains which simultaneously tackle discrete and continuous variables. This paper introduces four ant-based methods to solve mixed-variable problems. Each method is based upon superlative ant algorithms in discrete and/or continuous domains. Proposed methods’ performances are then tested on a set of three mathematical functions and also a water main design problem in engineering field, which are elaborately subject to linear and non-linear constraints. All proposed methods perform rather satisfactorily on considered problems and it is suggested to further extend the application of methods to other engineering studies.

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This paper provides a test method to make a fair comparison between different heuristics in structure optimization. When statistical methods are applied to the structural optimization (namely heuristics or meta-heuristics with several tunable parameters and starting seeds), the "one problem - one result" is extremely far from the fair comparison. From statistical point of view, the minimal requirement is a so-called "small-sample" according to the fundamental elements of the theory of the experimental design and evaluation and the protocol used in the drug development processes. The viability and efficiency of the proposed statistically correct methodology is demonstrated using the well-known ten-bar truss on a set of the heuristics from the brutal-force-search up to the most sophisticated hybrid approaches.

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Endurance Time Acceleration Functions are specially predesigned intensifying excitation functions that their amplitude increases with time. On the other hand, wavelet transform is a mathematical tool that indicates time variations of frequency in a signal. In this paper, an approach is presented for generating endurance time acceleration functions (ETAFs) whose response spectrum is compatible with the European Code regulations (EC8) elastic spectrum. Method applied is a modification of data in time and frequency domain. For this purpose, wavelet transform has been used to decompose a series of random points to several levels such that each level covers a special range of frequency, then every level is divided into the numbers of equal time intervals and each interval of time is multiplied by a variable. Subsequently, the mathematical unconstrained optimization algorithm is used to calculate the variables and minimize error between response and target spectra. The prosed procedure is used in two methods. Then with two methods, two different acceleration functions are produced.

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This paper presents the study of the optimized bi-dimensional wood structures, truss type, applying the method of genetic algorithms. Assessment is performed by means of a computer program called OPS (Optimization of Plane Structures). The purpose is to meet the optimum geometric configuration taking into account the volume reduction. Different strategies are considered for the positioning of diagonals and struts in the upper chord. It is concluded that the trussed system efficiency depends on the dimensions and the position of the members, where the purlin’s location is not mandatory for struts and diagonal positions.

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In this article optimal design of shear walls is performed under seismic loading. For practical aims, a database of special shear walls is created. Special shear walls are used for seismic design optimization employing the charged system search algorithm as an optimizer. Constraints consist of design and performance limitations. Nonlinear behavior of the shear wall is taken into account and performance based seismic design optimization is accomplished. Capacity curves of the optimal solution are determined and compared incorporates soil–structure interaction. Also an optimization based method is proposed for bilinear approximation of capacity curve. These are a new methodology for seismic RC shear wall optimum design.

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In the present study, the computational performance of the particle swarm optimization (PSO) harmony search (HS) and firefly algorithm (FA), as popular metaheuristics, is investigated for size and shape optimization of truss structures. The PSO was inspired by the social behavior of organisms such as bird flocking. The HS imitates the musical performance process which takes place when a musician searches for a better state of harmony, while the FA was based on the idealized behavior of the flashing characteristics of natural fireflies. These algorithms were inspired from different natural sources and their convergence behavior is focused in this paper. Several benchmark size and shape optimization problems of truss structures are solved using PSO, HS and FA and the results are compared. The numerical results demonstrate the superiority of FA to HS and PSO.

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Based on introducing two optimization algorithms, group search optimization (GSO) algorithm and particle swarm optimization (PSO) algorithm, a new hybrid optimization algorithm which named particle swarm-group search optimization (PS-GSO) algorithm is presented and its application to optimal structural design is analyzed. The PS-GSO is used to investigate the spatial truss structures with discrete variables and is tested by truss optimization problems. The optimization results are compared with that of the HPSO and GSO algorithm. The results show that the PS-GSO is able to accelerate the convergence rate effectively and has the fastest convergence rate among these three algorithms. The research shows the proposed PS-GSO algorithm can be effectively applied to optimal design of spatial structures with discrete variables.

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This paper deals with the optimization of reinforced concrete (RC) structures under earthquake loads by introducing a simple methodology. One of the most important problems in the design of RC structures is the existing of various design scenarios that all of them satisfy design constraints. Despite of the steel structures, a large number of design candidates due to a large number of design variables can be utilized. Doubtless, the economical and practical aspects are two effective parameters on accepting a design candidate. As such, in this paper the conventional design process that uses a trial and error process is replaced with an automated process using optimization technique. Also, the cost of construction is selected as an objective function in the automated process. A real valued model of particle swarm optimization (PSO) algorithm is utilized to perform the optimization process. Design constraints conform to the ACI318-08 code and standard 2800-code recommendations. Three ground motion records modified based on Iranian Design Spectrum is considered as earthquake excitations. Moreover, to reveal the effectiveness and robustness of the presented methodology, for example, a three-bay eighteen-story RC frame is optimized against the combination of gravity and earthquake loads. The entire process is summarized in a computer programming using a link between MATLAB platform and OpenSEES as open source object-oriented software.

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Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems so far. In the present study, a simple optimization (SOPT) algorithm with two main steps namely exploration and exploitation, is provided for practical applications. Aside from a reasonable rate of convergence attained, the ease in its implementation and dependency on few parameters only are among the advantageous characteristics of the proposed SOPT algorithm. The efficiency of the developed algorithm is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.