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Genetic Algorithm is known as a generalized method of stochastic search and has been successfully applied to various types of optimization problems. By GA s it is expected to improve the solution at the expense of additional computational effort. One of the key points which controls the accuracy and convergence rate of such a process is the selected method of coding/decoding of the original problem variables and the discrete feasibility space to be searched by GAS. In this paper, a direct index coding (DIC) is developed and utilized for the discrete sizing optimization of structures. The GA operators are specialized and adopted for this kind of encoded chromosomes and are compared to those of traditional GA S. The well-known lO-bar truss example from literature is treated here as a comparison benchmark, and the outstanding computational efficiency and stability of the proposed method is illustrated. The application of the proposed encoding method is not limited to truss structures and can also be directly applied to frame sizing problems.

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The main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. This is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the :::union::: of the eigenvalues of the healed submodels result in the eigenvalues of the entire model. Thus the critical load of the frame is obtained using the eigenvalues of its submodels.

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In this paper, the Rayleigh's quotient and the inverse vector iteration method are presented. The latter approach helps to obtain the natural frequencies and mode shapes of a structure. Inverse vector iteration method with shifting enables to determine the higher modes. Some basic theorems of linear algebra are presented and extended to study the free vibration of structures. The variation theorems are presented for predicting the eigenvalues and eigenvectors of the modified structures. These theorems reduce the number of cycles of the iterations used for calculating the eigenvalues and eigenvectors of the modified structures. Finally, an example is solved to show the ability of the present approach.

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In this paper, the problem of layout optimization for X-bracing of steel frames is studied using the ant system (AS). A new design method is employed to share the gravity and the lateral loads between the main frame and the bracings according to the requirements of the IBC2006 code. An algorithm is developed which is called optimum steel designer (OSD). An optimization method based on an approximate analysis is also developed for layout optimization of braced frames. This method is called the approximate optimum steel designer (AOSD) and uses a simple deterministic optimization algorithm leading to the optimum patterns and it is much faster than the OSD. Several numerical examples are treated by the proposed methods. Efficiency and accuracy of the methods are then discussed. A comparison is also made with Genetic algorithm for one of the frames.

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Cost optimization of the reinforced concrete cantilever soil retaining wall of a given height satisfying some structural and geotechnical design constraints is performed utilizing harmony search and improved harmony search algorithms. The objective function considered is the cost of the structure, and design is based on ACI 318-05. This function is minimized subjected to design constraints. A numerical example of the cost optimization of a reinforced concrete cantilever retaining wall is presented to illustrate the performance of the presented algorithms and the necessary sensitivity analysis is performed.

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This article presents the application of two algorithms: heuristic big bang-big crunch (HBB-BC) and a heuristic particle swarm

ant colony optimization (HPSACO) to discrete optimization of reinforced concrete planar frames subject to combinations of

gravity and lateral loads based on ACI 318-08 code. The objective function is the total cost of the frame which includes the cost

of concrete, formwork and reinforcing steel for all members of the frame. The heuristic big bang-big crunch (HBB-BC) is based

on BB-BC and a harmony search (HS) scheme to deal with the variable constraints. The HPSACO algorithm is a combination of

particle swarm with passive congregation (PSOPC), ant colony optimization (ACO), and harmony search scheme (HS)

algorithms. In this paper, by using the capacity of BB-BC in ACO stage of HPSACO, its performance is improved. Some design

examples are tested using these methods and the results are compared.

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This paper presents a strategy for using Harmony Search algorithm in facility layout optimization problems. In this paper an

adapted harmony search algorithm is developed for solving facility layout optimization problems. This method finds an optimal

facility arrangement in an existing layout. Two real-world case studies are employed to demonstrate the efficiency of this model.

A comparison is also made to illustrate the efficiency of these strategies in facility layout optimization

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In this paper the conditional location problem is discussed. Conditional location problems have a wide range of applications

in location science. A new meta-heuristic algorithm for solving conditional p-median problems is proposed and results are

compared to those of the previous studies. This algorithm produces much better results than the previous formulations.

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In this paper a discrete Big Bang-Big Crunch algorithm is applied to optimal design of reinforced concrete planar frames under

the gravity and lateral loads. Optimization is based on ACI 318-08 code. Columns are assumed to resist axial loads and bending

moments, while beams resist only bending moments. Second-order effects are also considered for the compression members, and

columns are checked for their slenderness and their end moments are magnified when necessary. The main aim of the BB-BC

process is to minimize the cost of material and construction of the reinforced concrete frames under the applied loads such that

the strength requirements of the ACI 318 code are fulfilled. In the process of optimization, the cost per unit length of the sections

is used for the formation of the subsequent generation. Three bending frames are optimized using BB-BC and the results are

compared to those of the genetic algorithm.

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Barrel vaults are attractive space structures that cover large area without intermediate supports. In this paper, the charged

search system (CSS) optimization algorithm is employed for optimal design of barrel vaults. This method utilizes the governing

laws of Coulomb and Gauss from electrostatics and the Newtonian law of mechanics. The results demonstrate the efficiency of

the discrete CSS algorithm compared to other meta-heuristic algorithms.

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For the analysis of structures, the first step consists of configuration processing followed by data generation. This step is the most time consuming part of the analysis for large-scale structures. In this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. The graph products are extensively used in graph theory and combinatorial optimization, however, the triangular and circular products defined in this paper are more suitable for the formation of practical space structural models which can not be generated easily by the previous products. The new products are employed for the configuration processing of space structures that are of triangular or a combination of triangular and rectangular shapes, and also in circular shapes as domes and some other space structural models. Cut out products are other new types of graph products which are defined to eliminate all of the connected elements to the considered node to configure the model or grid with some vacant panels inside of the model. The application of the presented graph products can be extended to the formation of finite element models.

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In this research, the Charged System Search (CSS) and Enhanced Charged System Search (ECSS) algorithm are used to obtain the optimum design of irregular grillage systems with different spacing and various boundary conditions. The cross-sectional properties of the beams are selected as the design variables and the weight of structure is used as the objective function. The displacement limitations and permissible stress constraints are employed from LRFD-AISC and are considered in the formulation of the design problem. Furthermore, in obtaining the response of the grillage systems, the effect of warping is also taken into account. The comparison of the results shows that warping changes the beam spacing, and different boundary conditions have substantial effects on the optimum design of irregular grillage systems

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In the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. For these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. However, by adding or removing some elements or nodes, such methods cannot be utilized. Here, an efficient method is developed for the analysis of irregular structures in the form a regular structure with additional or missing nodes or with additional or missing supports. In this method, the saving in computational time is considerable. The power of the method becomes more apparent when the analysis should be repeated very many times as it is the case in optimal design or non-linear analysis.

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In this paper, a new enhanced version of the Particle Swarm Optimization (PSO) is presented. An important modification is made by adding probabilistic functions into PSO, and it is named Probabilistic Particle Swarm Optimization (PPSO). Since the variation of the velocity of particles in PSO constitutes its search engine, it should provide two phases of optimization process which are: exploration and exploitation. However, this aim is unachievable due to the lack of balanced particles’ velocity formula in the PSO. The main feature presented in the study is the introduction of a probabilistic scheme for updating the velocity of each particle. The Probabilistic Particle Swarm Optimization (PPSO) formulation thus developed allows us to find the best sequence of the exploration and exploitation phases entailed by the optimization search process. The validity of the present approach is demonstrated by solving three classical sizing optimization problems of spatial truss structures.

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It is well known that damaged structural members may alter the behaviour of the structures considerably. Careful observation of these changes has often been viewed as a means to identify and assess the location and severity of damages in structures. Among the responses of a structure, natural frequencies and natural modes are both relatively easy to obtain and independent from external excitation, and therefore, can be used as a measure of the structural behaviour before and after an extreme event which might have led to damage in the structure. This paper applies Charged System Search algorithm to the problem of damage detection using vibration data. The objective is to identify the location and extent of multi-damage in a structure. Both natural frequencies and mode shapes are used to form the required objective function. To moderate the effect of noise on measured data, a penalty approach is applied. Varity of numerical examples including beams, frames and trusses are examined. The results show that the present methodology can reliably identify damage scenarios using noisy measurements and incomplete data.

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Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method.

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The paper presents a hybrid-enhanced algorithm based on CSS for discrete problems whit the focus on traveling salesman problem. The CSS algorithm based on some principles from physics and mechanics, utilize the governing Coulomb law from electrostatics and Newtonian laws of mechanics. However, the CSS is more suitable for continuous problems compared with discrete problems. In this paper, we have tried to resolve this defect of CSS algorithm with the help of local search methods and nearest neighbor for discrete problems whit the focus on traveling salesman problem (TSP). To prove the efficiency of the proposed algorithm, results compared with the results of benchmark problems. Then, the proposed algorithm is used to solve the TSP, using as a method for solving the single row facility layout problem (SRFLP). To prove the efficiency, the results are compared with the results of benchmark problems reported in the recent literatures.

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In this paper, the problem of simultaneous shape and size optimization of single-layer barrel vault frames which contains both of discrete and continuous variables is addressed. In this method, the improved magnetic charged system search (IMCSS) is utilized as the optimization algorithm and the open application programming interface (OAPI) plays the role of interfacing analysis software with the programming language. A comparison between the results of the present method and some existing algorithms confirms the high ability of this approach in simultaneous shape and size optimization of the practical and large-scale spatial structures.

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The main aim of this paper is to find the optimum shape of arch dams subjected to multiple natural frequency constraints by using an efficient methodology. The optimization is carried out by charged system search algorithm and its enhanced version. Computing the natural frequencies by Finite Element Analysis (FEA) during the optimization process is time consuming. In order to reduce the computational burden, Back Propagation (BP) neural network is trained and utilized to predict the arch dam natural frequencies. It is demonstrated that the optimum design obtained by the Enhanced Charged System Search using the BP network is the best compared with the results of other algorithms. The numerical results show the computational advantageous of the proposed methodology.

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Resource allocation project scheduling problem (RCPSP) has been one of the challenging subjects amongst researchers in the last decades. Most of the researches in this scope have used deterministic variables, however in a real project activities are exposed to risks and uncertainties that cause to delay in project’s duration. There are some researchers that have considered the risks for scheduling, however, new metahuristics are available to solve this problem for finding better solution with less computational time. In this paper, two new metahuristic algorithms are applied for solving fuzzy resource allocation project scheduling problem (FRCPSP) known as charged system search (CSS) and colliding body optimization (CBO). The results show that both of these algorithms find reasonable solutions, however CBO finds the results in a less computational time having a better quality. A case study is conducted to evaluate the performance and applicability of the proposed algorithms.