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In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multi-variable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a large number of variables and constraints are chosen to show the robustness of the algorithm.

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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the non-regular part of such model are ordered followed by ordering the nodes of the regular part. With this ordering the graph matrices will be separated into two blocks. The eigensolution of the non-regular part can be performed by an iterative method, and those of the regular part can easily be calculated using decomposition approaches studied in our previous articles. Some numerical examples are included to illustrate the efficiency of the new method.

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In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was not possible, first their Laplacian matrices are transformed into single block diagonal forms and then using the concept of determinant, the calculations are performed.

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Runway length is usually a critical point in an airport system so, a great interest has been created for optimal use of this runway length. The most important factors in modeling of aircraft landing problem are time and cost while, the costs imposed on the system because of moving away from target times have different performances in terms of impact. In this paper, firstly, aircraft landing problem (ALP) and the works conducted in subject literature are briefly reviewed and presented. Then, this problem is formulated and proposed as a three-objective mathematical modeling which leads to more applicable formulation. Following this, the model introduced to solve this problem is solved for two groups including 20 and 50 aircrafts using the second version of NSGA and the results and recommendations will be provided.

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The present study is concerned with the simultaneous optimization of the size of components and the arrangement of connections for performance-based seismic design of low-rise SPSWs. Design variables include the size of beams and columns, the thickness of the infill panels, the type of each beam-to-column connection and the type of each infill-to-boundary frame connection. The objective function is considered to be the sum of the material cost and rigid connection fabrication cost. For comparison purposes, the SPSW model is also optimized with regard to two fixed connection arrangements. To fulfill the optimization task a new hybrid optimization algorithm called CBO-Jaya is proposed. The performance of the proposed hybrid optimization algorithm is assessed by two benchmark optimization problems. The results of the application of the proposed algorithm to the benchmark problem indicate the efficiency, robustness, and the fast convergence of the proposed algorithm compared with other meta-heuristic algorithms. The achieved results for the SPSWs demonstrate that incorporating the optimal arrangement of beam-to-column and infill-to-boundary frame connections into the optimization procedure results in considerable reduction of the overall cost.

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The present study sets out to integrate the performance-based seismic design approach with the connection topology optimization method. Performance-based connection topology optimization concept aims to simultaneously optimize the size of members and the type of connections with respect to the framework of performance-based seismic design. This new optimization concept is carried out for unbraced and X-braced steel frames in order to assess its efficiency. The cross-sectional area of components and the type of beam-to-column connections are regarded as design variables. The objective function is formulated in terms of the material costs and the cost of rigid connections. The nonlinear pushover analysis is adopted to acquire the response of the structure at various performance levels. In order to cope with the optimization problem, CBO algorithm is employed. The achieved results demonstrate that incorporating the optimal arrangement of beam-to-column connections into the optimum performance-based design procedure of either unbraced or X-braced steel frame could lead to a design that significantly reduces the overall cost of the structure and offers a predictable and reliable performance for the structure subjected to hazard levels.

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Structural damage detection is a field that has attracted a great interest in the scientific community in recent years. Most of these studies use dynamic analysis data of the beams as a diagnostic tool for damage. In this paper, a massless rotational spring was used to represent the cracked sections of beams and the natural frequencies and mode shape were obtained. For calculation of rotational spring stiffness equivalent of uncracked and cracked sections, finite element models and experimental test were used. The damage identification problem was addressed with two optimization techniques of different philosophers: ECBO, PSO and SQP methods. The objective functions used in the optimization process are based on the dynamic analysis data such as natural frequencies and mode shapes. This data was obtained by developing a software that performs the dynamic analysis of structures using the Finite Element Method (FEM). Comparison between the detected cracks using optimization method and real beam shows an acceptable agreement.

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In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calculation and new population generation in these two methods are completely different. At each stage of the ECM algorithm, successful distributions are identified and the covariance matrix of the successful distributions is formed. Subsequently, by the help of the principal component analysis (PCA), the scattering directions of these distributions will be achieved. The new population is generated by the combination of weighted directions that have a successful distribution and using random normal distribution. In the discrete ECM method, in case of succeeding in a certain number of cycles the step size is increased, otherwise the step size is reduced. In order to determine the efficiency of this method, three benchmark steel frames were optimized due to the resistance and displacement criteria specifications of the AISC-LRFD, and the results were compared to other optimization methods. Considerable outputs of this algorithm show that this method can handle the complex problems of optimizing discrete steel frames.

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Force Density Method is a well-known form-finding method for discrete networks that is based on geometrical equilibrium of forces and could be used to design efficient structural forms. The choice of force density distribution along the structure is mostly upon user which in most cases is set be constant, with peripheral members having relatively larger force density to prevent excessive shrinking. In order to direct FDM towards more efficient structures, an optimization strategy can be used to inform the form-finding process by minimizing certain objective function, e.g. weight of the structure. Desired structural, constructional or geometrical constraints can also be incorporated in this framework that otherwise user may not have direct control over. It has been shown that considerable weight reduction is possible compared to uniform force density in the structure while satisfying additional constraints. In this way, form-finding can be augmented and novel structural forms can be designed.