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For most practical purposes, true topology optimization of a braced frame should be synchronized with its sizing. An integrated layout optimization is formulated here to simultaneously account for both member sizing and bracings’ topology in such a problem. Code-specific seismic design spectrum is applied to unify the earthquake excitation. The problem is solved for minimal structural weight under codified stress, deformation and also user-defined weak-storey and architectural constraints. Particle swarm optimization is hybridized with an extra memory consideration strategy to solve this problem. As another issue, Baldwin effect of memetic algorithm is utilized in the proposed method to enhance its search capability regarding the geometrical and topological constraints. Treating a number of planar braced frames revealed superior performance of the proposed hybrid method partiqularly in avoiding premature convergence over the common particle swarm optimiztion for such a discrete problem.

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Practical design of tall frame-tube and diagrids are formulated as two discrete optimization problems searching for minimal weight undercodified constraints under gravitational and wind loading due to Iranian codes of practice for steel structures (Part 6 & Part 10). Particular encoding of design vector is proposed to efficiently handle both problems leading to minimal search space. Two types of modeling are employed for the sizing problem one by rigid floors without rotational degrees of freedom and the other with both translational and rotational degrees of freedom. The optimal layout of diagrids using rigid model is searched as the second problem. Then performance of Mine Blast Optimization as a recent meta-heuristic is evaluated in these problems treating a number of three-dimensional structural models via comparative study with the common Harmony Search and Particle Swarm Optimization. Considerable benefit in material cost minimization is obtained by these algorithms using tuned parameters. Consequently, effectiveness of HS is observed less than the other two while MBO has shown considerable convergence rate and particle swarm optimiztion is found more trustable in global search of the second problem.

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This study investigates the efficacy of optimal semi-active dampers for achieving the best results in seismic response mitigation of adjacent buildings connected to each other by magnetorheological (MR) dampers under earthquakes. One of the challenges in the application of this study is to develop an effective optimal control strategy that can fully utilize the capabilities of the MR dampers. Hence, a SIMULINK block in MATLAB program was developed to compute the desired control forces at each floor level and to the obtain number of dampers. Linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers are used for obtaining the desired control forces, while the desired voltage is calculated based on clipped voltage law (CVL). The control objective is to minimize both the maximum displacement and acceleration responses of the structure. As a result, MR dampers can provide significant displacement response control that is possible with less voltage for the shorter building.

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Stochastic nature of earthquake has raised a challenge for engineers to choose which record for their analyses. Clustering is offered as a solution for such a data mining problem to automatically distinguish between ground motion records based on similarities in the corresponding seismic attributes. The present work formulates an optimization problem to seek for the best clustering measures. In order to solve this problem, the well-known K-means algorithm and colliding bodies optimization are employed. The latter acts like a parameter-less meta-heuristic while the former provides strong intensification. Consequently, a hybrid algorithm is proposed by combining features of both the algorithms to enhance the search and avoid premature convergence. Numerical simulations show competative performance of the proposed method in the treated example of optimal ground motion clustering; regarding global optimization and quality of final solutions.

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Preliminary layout design of buildings has a substantial effect on the ultimate design of structural components and accordingly influences the construction cost. Exploring structurally efficient forms and shapes during the conceptual design stage of a project can also facilitate the optimum integrated design of buildings. This paper presents an automated method of determining column layout design of rectilinear orthogonal building frames using Charged System Search (CSS) algorithm. The layout design problem is presented as a combinatorial optimization problem named multi-dimensional knapsack problem by setting some constraints to the problem, where the minimum cost and maximum plan regularity are the objectives. The efficiency and robustness of CSS to solve the combinatorial optimization problem are demonstrated through a numerical design problem. The results of the algorithm are compared to those of an ant colony algorithm in order to validate the solution.

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Graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. The combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. This paper presents a Charged System Search (CSS) algorithm for the free shape optimizations of thin-walled steel sections, represented by some popular graph theory based methods. The objective is to find shapes of minimum mass and/or maximum strength for thin-walled steel sections that satisfy design constraints, which results in a general formulation for a bi-objective combinatorial optimization problem. A numerical example involving the shape optimization of thin-walled open and closed steel sections is presented to demonstrate the robustness of the method.

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The most recent approaches of multi-objective optimization constitute application of meta-heuristic algorithms for which, parameter tuning is still a challenge. The present work hybridizes swarm intelligence with fuzzy operators to extend crisp values of the main control parameters into especial fuzzy sets that are constructed based on a number of prescribed facts. Such parameter-less particle swarm optimization is employed as the core of a multi-objective optimization framework with a repository to save Pareto solutions. The proposed method is tested on a variety of benchmark functions and structural sizing examples. Results show that it can provide Pareto front by lower computational time in competition with some other popular multi-objective algorithms.

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Opposition-based learning was first introduced as a solution for machine learning; however, it is being extended to other artificial intelligence and soft computing fields including meta-heuristic optimization. It not only utilizes an estimate of a solution but also enters its counter-part information into the search process. The present work applies such an approach to Colliding Bodies Optimization as a powerful meta-heuristic with several engineering applications. Special combination of static and dynamic opposition-based operators are hybridized with CBO so that its performance is enhanced. The proposed OCBO is validated in a variety of benchmark test functions in addition to structural optimization and optimal clustering. According to the results, the proposed method of opposition-based learning has been quite effective in performance enhancement of parameter-less colliding bodies optimization.

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Imperialist Competitive Algorithm, ICA is a meta-heuristic which simulates collapse of weak empires by more powerful ones that take possession of their colonies. In order to enhance performance, ICA is hybridized with proper features of Teaching-Learning-Based Optimization, TLBO. In addition, ICA walks are modified with an extra term to intensify looking for the global best solution. The number of control parameters and consequent tuning effort has been reduced in the proposed Imperialist Competitive Learner-Based Optimization, ICLBO with respect to ICA and several other methods. Efficiency and effectiveness of ICLBO is further evaluated treating a number of test functions in addition to continuous and discrete engineering problems. It is discussed and traced that balancing between exploration and exploitation is enhanced due to the proposed hybridization. Numerical results exhibit superior performance of ICLBO vs. ICA and a variety of other well-known meta-heuristics.

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Partricular features of overpassing local optima and providing near-optimal soultion in practical time has led researchers to apply metaheuristics in several engineering problems. Optimal design of diagrids as one of the most efficient structural systems in tall buildings has been concerned here. Jaya algorithm as a recent paramter-less optimization method is employed to solve the problem using a set of available sections. Furthermore, passive congregation is embedded in Jaya without adding any extra control parameters. Applyig the method in a number of real-size structural examples including diagrids, exhibits performance improvement by the new hybrid algorithm with respect to Jaya.

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Meta-heuristics have received increasing attention in recent years. The present article introduces a novel method in such a class that distinguishes a number of artificial search agents called players within two teams. At each iteration, the active player concerns some other players in both teams to construct its special movements and to get more score. At the end of some iterations (like quarters of a sports game) the teams switch their places for fair play. The algorithm is developed to solve a general purpose optimization problem; however, in this article its application is illustrated on structural sizing design. Switching Teams Algorithm is presented as a parameter-less population-based algorithm utilizing just two control parameters. The proposed method can recover diversity in a novel manner compared to other meta-heuristics in order to capture global optima.

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Passive systems are preferred tools for seismic control of buildings challenged by probabilistic nature of the input excitation. However, other types of uncertainty still exist in parameters of the control device even when optimally tuned. The present work concerns optimal design of multiple-tuned-mass-damper embedded on a shear building by a number of meta-heuristics. They include well-known genetic algorithm and particle swarm optimization as well as more recent gray wolf optimizer and its hybrid method embedding swarm intelligence. The study is two-fold: first, optimal designs by different meta-heuristics are compared concerning their reduction in structural seismic responses; second, the effect of uncertainty in Multi-Tuned-Mass-Damper parameters, is studied offering new reliability-based curves. Monte Carlo Simulation is employed to evaluate failure probabilities. A variety of structural responses are assessed against seismic excitation including maximal displacement, velocity and acceleration. It is declared that the best algorithm for efficiency and effectiveness has not coincided the best based on the reliability traces. Such traces also show that in a specific range of limit-states, algorithm selection has a serious effect on the reliability results. It was found even more than 35% and depends on the response type.  

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The present work reveals a problem formulation to minimize material consumption and improve efficiency of diagrids to resist equivalent wind loading. The integrated formulation includes not only sizing of structural members but also variation in geometry and topology of such a system. Particular encoding technique is offered to handle practical variation of diagrid modules. A variant of Pseudo-random Directional Search is utilized to solve this problem treating a number of three dimensional structural models. Several issues are investigated including the effect of variation in the building height, its aspect ratio and fixing or releasing diagrid angles. Consequently, especial trend of variation in diagrid angle is observed with superior structural responses with respect to sizing designs of the fixed-angle modules.

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Despite comprehensive literature works on developing fitness-based optimization algorithms, their performance is yet challenged by constraint handling in various engineering tasks. The present study, concerns the widely-used external penalty technique for sizing design of pin-jointed structures. Observer-teacher-learner-based optimization is employed here since previously addressed by a number of investigators as a powerful meta-heuristic algorithm. Several cases of penalty handling techniques are offered and studied using either maximum or summation of constraint violations as well as their combinations. Consequently, the most successive sequence, is identified for the treated continuous and discrete structural examples. Such a dynamic constraint handling is an affordable generalized solution for structural sizing design by iterative population-based algorithms.
 

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Beyond common practice that treats structural damage detection as an optimization problem, the present work offers another approach that updates boundaries of the damage ratios. In this approach the bandwidth between such lower and upper boundaries, is adaptively reduced aiming to coincide at the true damage state. Formulation of the proposed method is developed using modal strain energy in a system of finite elements. A resolution-based technique is applied so that the search space cardinality can be defined and then reduced. The proposed method is validated on different structural types including beam, frame and truss examples with various damage scenarios. The results exhibit high cardinality reduction and capability of the proposed iterative method in squeezing the design space for more efficient search.
 

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The real-world applications addressing the nonlinear functions of multiple variables could be implicitly assessed through structural reliability analysis. This study establishes an efficient algorithm for resolving highly nonlinear structural reliability problems. To this end, first a numerical nonlinear optimization algorithm with a new simple filter is defined to locate and estimate the most probable point in the standard normal space and the subsequent reliability index with a fast convergence rate. The problem is solved by using a modified trust-region sequential quadratic programming approach that evaluates step direction and tunes step size through a linearized procedure. Then, the probability expectation method is implemented to eliminate the linearization error. The new applications of the proposed method could overcome high nonlinearity of the limit state function and improve the accuracy of the final result, in good agreement with the Monte Carlo sampling results. The proposed algorithm robustness is comparatively shown in various numerical benchmark examples via well-established classes of the first-order reliability methods. The results demonstrate the successive performance of the proposed method in capturing an accurate reliability index with higher convergence rate and competitive effectiveness compared with the other first-order methods.
 

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In most practical cases, structural design variables are linked to a discrete list of sections for optimal design. Cardinality of such a discrete search space is governed by the number of alternatives for each member group. The present work offers an adaptive strategy to detect more efficient alternatives and set aside redundant ones during optimization. In this regard, the difference between the lower and the upper bounds on such variables is gradually reduced by a procedure that adapts history of the selected alternatives in previous iterations. The propsed strategy is implemented on a hybrid paritcle swarm optimizer and imperialist competitive algorithm. The former is a basic swarm intelligent method while the later utilizes subpopulations in its search. Spatial and large-scale structures in various shapes are treated showing successive performance improvement. Variation of a diversity index and resulting band size are traced and discussed to declare behavior merits of the proposed adaptive band strategy.  
 

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Shape optimization of a double-curved dam is formulated using control points for interpolation functions. Every design vector is decoded into the integrated water-dam-foundation rock model. An enhanced algorithm is proposed by hybridizing particle swarm algorithm with ant colony optimization and simulated annealing. The best experiences of the search agents are indirectly shared via pheromone trail deposited on a bi-partite characteristic graph. Such a stochastic search is further tuned by Boltzmann functions in simulated annealing. The proposed method earned the first rank in comparison with six well-known meta‑heuristic algorithms in solving benchmark test functions. It captured the optimal shape design of Morrow Point dam, as a widely addressed case-study, by 21% reduced concrete volume with respect to the common USBR design practice and 16% better than the particle swarm optimizer. Such an optimal design was also superior to the others in stress redistribution for better performance of the dam system.
 

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During the process of continuum topology optimization some pattern discontinuities may arise. It is an important challenge to overcome such irregularities in order to achieve or interpret the true optimal layout. The present work offers an efficient algorithm based on graph theoretical approach regarding density priorities. The developed method can recognize and handle solid continuous regions in a pre-optimized media. An illustrative example shows how the proposed priority guided trees can successfully distinguish the most crucial parts of the continuum during topology optimization.