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A multi-objective heuristic particle swarm optimiser (MOHPSO) based on Pareto multi-objective theory is proposed to solve multi-objective optimality problems. The optimality objectives are the roof displacement and structure weight. Two types of structure are analysed in this paper, a truss structure and a framework structure. Performance-based seismic analysis, such as classical and modal pushover analysis, is carried out for the structures. Four optimality algorithms, namely, NSGA-II, MOPSO, MGSO, and MOHPSO, were used for structural optimisation to compare the effectiveness of the algorithms. The calculation results indicate that MOHPSO outperformed the other algorithms in terms of solution stability, universality, and consistency of the distribution of the Pareto front and the ability to consider constraints. The population can converge to the true Pareto front in the latter generations, which indicates that MOHPSO is effective for engineering multi-objective optimality problems.

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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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In this paper an optimization framework is presented for automated performance-based seismic design of bridges consisting of multi-column RC pier substructures. The beneficial effects of fusing components on seismic performance of the quasi-isolated system is duly addressed in analysis and design. The proposed method is based on a two-step structural analysis consisting of a linear modal dynamic demand analysis and a nonlinear static capacity evaluation of the entire bridge structure. Results indicate that the proposed optimization method is capable of producing cost-effective design solutions combining the fusing behavior of bearings and yielding mechanism of piers. The optimal designs obtained from models addressing the performance of fusing components are far more efficient than those that do not take care of quasi-isolation behavior. 

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A dual structural fused system consists of replaceable ductile elements (fuses) that sustain major seismic damage and leave the primary structure (PS) virtually undamaged. The seismic performance of a fused structural system is determined by the combined behavior of the individual PS and fuse components. In order to design a feasible and economic structural fuse concept, we need a procedure to choose the most efficient combination of the PS and fuse systems subject to the stringent constraints of seismic performance and minimum structural cost objectives, simultaneously. In this paper, an efficient method is developed for minimum cost design of dual fused building structures using a performance-based seismic design procedure. The method involves updating a set of reference parameters to find the most suitable combination of PS and fuse structures with satisfactory seismic performance and optimum total structural cost, concurrently. For a set of preselected reference parameters, the structural design variables including primary and fuse structural member sizes are determined through individual linear elastic design processes. Therefore, a limited number of inelastic analyses are required to evaluate seismic response of the combined fused system. The proposed method is applied to seismic design optimization of a moment resisting frame equipped with BRBs as structural fuses. The obtained results indicate that proposed design optimization procedure is sufficiently robust and reliable to design cost-effective structural fuse systems with satisfactory seismic performance.