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Different methods are available for simultaneous optimization of cross-section, topology and geometry of truss structures. Since the search space for this problem is very large, the probability of falling in local optimum is considerably high. On the other hand, different types of design variables (continuous and discrete) lead to some difficulties in the process of optimization. In this article, simultaneous optimization of cross-section, topology and geometry of truss structures is performed by utilizing the Multi Heuristic based Search Method (MHSM) that overcome the above mentioned problem and obtains good results. The presented method performs the optimization by dividing the searching space into five subsections in which an MHSM is employed. These subsections are named procedure islands. Some examples are then presented to scrutinize the method more carefully. Results show the capabilities of the present algorithm for optimal design of truss structures.

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The prevalent strategy in the topology optimization phase is to select a subset of members existing in an excessively connected truss, called Ground Structure, such that the overall weight or cost is minimized. Although finding a good topology significantly reduces the overall cost, excessive growth of the size of topology space combined with existence of varied types of design variables challenges applicability of evolutionary algorithms tailored for simultaneous optimization of topology, shape and size (TSS) in more complicated cases which are of great practical interest. In practice, large-scale truss structures are often modular, formed by joining periodically repeated units. This article organizes a novel simulation approach for this class of truss structures where the main drawbacks of the ground structure-based simulation approach are greatly moderated. The two approaches are independently employed for simultaneous TSS optimization of a modular truss example and the size of topology space as well as the required computation budget to generate an acceptable candidate design is compared. Result comparison reveals by employing the novel approach, problem complexity grows linearly with respect to the number of modules which allows for expanding application of TSS optimizers to complex modular trusses. Use of relative coordinates is also warranted for shape optimization which concludes to a more efficient optimization process.

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The present study attempts to apply an efficient yet simple optimization (SOPT) algorithm to optimum design of truss structures under stress and displacement constraints. The computational efficiency of the technique is improved through avoiding unnecessary analyses during the course of optimization using the so-called upper bound strategy (UBS). The efficiency of the UBS integrated SOPT algorithm is evaluated through benchmark sizing optimization problems of truss structures and the numerical results are reported. A comparison of the numerical results attained using the SOPT algorithm with those of modern metaheuristic techniques demonstrates that the employed algorithm is capable of locating promising designs with considerably less computational effort.

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This study deals with performance-based design optimization (PBDO) of steel moment frames employing four different metaheuristics consisting of genetic algorithm (GA), ant colony optimization (ACO), harmony search (HS), and particle swarm optimization (PSO). In order to evaluate the seismic capacity of the structures, nonlinear pushover analysis is conducted (PBDO). This method is an iterative process needed to meet code requirements. In the PBDO procedure, the metaheuristics minimize the structural weight subjected to performance constraints on inter-story drift ratios at various performance levels. Two numerical examples are presented demonstrating the superiority of the PSO to the GA, ACO and HS metaheuristic algorithms.

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In this article, the ant colony method is utilized for topology optimization of space structures. Strain energy of the structure is minimized while the material volume is limited to a certain amount. In other words, the stiffest possible structure is sought when certain given materials are used. In addition, a noise cleaning technique is addressed to prevent undesirable members in optimum topology. The performance of the method for topology optimization of space structures are demonstrated by three numerical examples.

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This paper investigates the optimized parameters of Tuned Mass Dampers (TMDs) for high-rise structures considering Soil Structure Interaction (SSI) effects. Three optimization methods, namely the ant colony optimization (ACO) technique together with artificial bee colony (ABC) and shuffled complex evolution (SCE) methods are utilized for the optimization of TMD Mass, damping coefficient and spring stiffness as the design variables. The objective is to decrease the maximum displacement of structure. The 40 story structure with three soil types is employed to design TMD for six types of far field earthquakes. The results are then utilized to obtain relations for the optimized TMD parameters with SSI effects. The relations are then applied to design TMD for the same structure with another five types of far field oscillations, and reasonable results are achieved. For further investigations, the obtained relations are utilized to design TMD for a new structure, and the reduction values are obtained for five types of earthquakes, which show acceptable results. This study improves the understanding of earthquake oscillations, and helps the designers to achieve the optimized TMD for high-rise buildings.

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A novel optimization algorithm named teaching-learning-based optimization (TLBO) algorithm and its implementation procedure were presented in this paper. TLBO is a meta-heuristic method, which simulates the phenomenon in classes. TLBO has two phases: teacher phase and learner phase. Students learn from teachers in teacher phases and obtain knowledge by mutual learning in learner phase. The suitability of TLBO for size and geometry optimization of structures in structural optimal design was tested by three truss examples. Meanwhile, these examples were used as benchmark structures to explore the effectiveness and robustness of TLBO. The results were compared with those of other algorithms. It is found that TLBO has advantages over other optimal algorithms in convergence rate and accuracy when the number of variables is the same. It is much desired for TLBO to be applied to the tasks of optimal design of engineering structures.

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In this research, optimal design and assessment of multiple tuned mass dampers (MTMDs) capability in mitigating the damage of nonlinear steel structures subjected to earthquake excitation has been studied. Optimal parameters of TMDs on nonlinear multi-degree-of-freedom (MDOF) structures have been determined based on minimizing the maximum relative displacement (drift) of structure where for solving the optimization problem the genetic algorithm (GA) has been used successfully. For numerical analysis, three and nine storey 2-D moment resisting nonlinear steel frames subjected to far-field and near-field earthquakes and optimal MTMDs has been designed for different values of mass ratio and TMDs number. According to the results of numerical simulations, it can be said that MTMDs mechanism could reduce the damage of nonlinear steel structures where the effectiveness increases by increasing TMDs mass ratio. Also the performance of MTMDs depends on earthquake characteristics, mass ratio and TMDs configuration where in this research the effective case has been locating TMDs on top floor in parallel configuration.

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This paper presents an improved multi-objective group search optimizer (IMGSO) that is based on Pareto theory that is designed to handle multi-objective optimization problems. The optimizer includes improvements in three areas: the transition-feasible region is used to address constraints, the Dealer’s Principle is used to construct the non-dominated set, and the producer is updated using a tabu search and a crowded distance operator. Two objective optimization problems, the minimum weight and maximum fundamental frequency, of four truss structures were optimized using the IMGSO. The results show that IMGSO rapidly generates the non-dominated set and is able to handle constraints. The Pareto front of the solutions from IMGSO is clearly dominant and has good diversity.

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This paper utilizes recent optimization algorithm called Ant Lion Optimizer (ALO) for optimal design of skeletal structures. The ALO is based on the hunting mechanism of Antlions in nature. The random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are main steps for this algorithm. The new algorithm is examined by designing three truss and frame design optimization problems and its performance is further compared with various classical and advanced algorithms.

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In  this  paper,  a  method  is  presented  for  damage  detection  of  bridges  using  the  Enhanced Colliding Bodies Optimization (ECBO)  utilizing time-domain responses. The finite element modeling of the structure is based on  the equation of motion under the moving load, and the flexural stiffness of the structure is determined by the acceleration responses obtained via sensors placed in different places. Damage detection problem presented in this research is an inverse  problem,  which  is  optimized  by  the  ECBO  algorithm,  and  the  damages  in  the structures  are  fully  detected.  Furthermore,  for  simulating  the  real  situation,  the  effect  of measured noises is considered on the structure, to obtain more accurate results.

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Structural  design  optimization  usually  deals  with  multiple  conflicting  objectives  to  obtain the minimum construction cost, minimum weight, and maximum safety of the final design. Therefore, finding the optimum design is hard and time-consuming for  such problems.  In this paper, we borrow the basic concept of multi-criterion decision-making and combine it with  Particle  Swarm  Optimization  (PSO)  to  develop  an  algorithm  for  accelerating convergence  toward  the  optimum  solution  in  structural  multi-objective  optimization scenarios.  The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete (RC) optimization problems. The main goal was to minimize the cost or weight of structures while satisfying all design requirements imposed by design codes.  The results confirm the ability of the proposed algorithm to efficiently find optimal solutions for structural optimization problems.

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Earthquakes are one of the most destructive natural phenomena which consist of rapid vibrations of rock near the earth’s surface. Because of their unpredictable occurrence and enormous capacity of destruction, they have brought fear to mankind since ancient times. Usually the earthquake acceleration is noted from the equipment in crisp or exact form. But in actual practice those data may not be obtained exactly at each time step, rather those may be with error. So those records at each time step are assumed here as intervals. Then using those interval acceleration data, the structural responses are found. The primary background for the present study is to model Interval Artificial Neural Network (IANN) and to compute structural response of a structural system by training the model for Indian earthquakes at Chamoli and Uttarkashi using interval ground motion data. The neural network is first trained here for real interval earthquake data. The trained IANN architecture is then used to simulate earthquakes by feeding various intensities and it is found that the predicted responses given by IANN model are good for practical purposes. The above may give an idea about the safety of the structural system in case of future earthquakes. Present paper demonstrates the procedure for simple case of a simple shear structure but the procedure may easily be generalized for higher storey structures as well.

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In this paper, a displacement-constrained volume-minimizing topology optimization model is present for two-dimensional continuum problems. The new model is a generalization of the displacement-constrained volume-minimizing model developed by Yi and Sui [1] in which the displacement is constrained in the loading point. In the original model the displacement constraint was formulated as an equality relation, which practically means that the number of “interesting points” may be exactly one. The recent model resolves this weakness replacing the equality constraint with an inequality constraint. From engineering point of view it is a very important result because we can replace the inequality constraint with a set of inequality constraints without any difficulty. The other very important fact, that the modified displacement-oriented model can be extended very easily to handle stress-oriented relations, which will be demonstrated in the forthcoming paper. Naturally, the more general theoretical model needs more sophisticated numerical problem handling method. Therefore, we replaced the original “optimality-criteria-like” solution searching process with a standard nonlinear programming approach which is able to handle linear (nonlinear) objectives with linear (nonlinear) equality (inequality) constrains. The efficiency of the new approach is demonstrated by an example investigated by several authors. The presented example with reproducible numerical results as a benchmark problem may be used for testing the quality of exact and heuristic solution procedures to be developed in the future for displacement-constrained volume-minimization problems.

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This paper presents a novel population-based meta-heuristic algorithm inspired by the game of tug of war. Utilizing a sport metaphor the algorithm, denoted as Tug of War Optimization (TWO), considers each candidate solution as a team participating in a series of rope pulling competitions.  The  teams  exert  pulling  forces  on  each  other  based  on  the  quality  of  the solutions  they  represent.  The  competing  teams  move  to  their  new  positions  according  to Newtonian laws of mechanics. Unlike many other meta-heuristic methods, the algorithm is formulated  in  such  a  way  that  considers  the  qualities  of  both  of  the  interacting  solutions. TWO  is  applicable  to  global  optimization  of  discontinuous,  multimodal,  non-smooth,  and non-convex functions. Viability of the proposed method is examined using some benchmark mathematical functions and engineering design problems. The numerical results indicate the efficiency of the proposed algorithm compared to some other methods available in literature.

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Tuned  mass  dampers  (TMDs)  are  as  a  efficient  control  tool  in  order  to  reduce  undesired vibrations  of  tall  buildings  and  large–span  bridges  against  lateral  loads  such  as  wind  and earthquake. Although many researchers has been widely  investigated  TMD systems  due to its  simplicity  and  application,  the  optimization  of  parameters  and  placement  of  TMD  are challenging tasks. Furthermore, ignoring the effects of soil–structure interaction (SSI) may lead to unrealistic desig of structure and its dampers. Hence, the  effects of SSI should be considered  in  the  design  of  TMD.  Therefore,  the  main  aim  of  this  study  is  to  optimize parameters  of  TMD  subjected  to  earthquake  and  considering  the  effects  of  SSI.  In  this regard,  the  parameters  of  TMD  including  mass,  stiffness  and   damping  optimization  are considered  as  the  variables  of  optimization.  The  maximum  absolute  displacement  and acceleration of structure are also simultaneously selected as objective functions. The multi –objective particle  swarm optimization  (MOPSO) algorithm  is adopted  to find  the  optimal parameters  of  TMD.  In  this  study,  the  Lagrangian  method  is  utilized  for  obtaining  the equations of motion for SSI system, and the time domain analysis is implemented based on Newmark method. In order to investigate the effects of SSI in the optimal design of TMD, a 40 storey shear building with a TMD subjected to the El–Centro earthquake is considered. The  numerical  results  show  that  the  SSI  effects  have  the  significant  influence  on  the optimum parameters of TMD.

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Beginning  in  2011  an  international  academic  contest  named  as  International  Student Competition  in  Structural  Optimization  (ISCSO)  has  been  organized  by  the  authors  to encourage undergraduate and graduate students to solve structural engineering optimization problems. During the past events on the one hand a unique platform is provided for a fair comparison of structural optimization algorithms; and on the other hand it is attempted to draw  the  attention  of  students  to  the  interesting  and  joyful  aspects  of  dealing  with optimization problems. This year, after five online events successfully held  with support and help of our advisory and scientific committee members from different universities all around the world, the authors  decided to gather the  test problems of the  ISCSO in this  technical report as an optimization test set. Beside the well -known traditional benchmark instances, the  provided  test  set  might  also  be  used  for  further  performance  evaluation  of  future structural optimization algorithms.

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In this study an efficient meta-heuristic is proposed for layout optimization of truss structures by combining cellular automata (CA) and firefly algorithm (FA). In the proposed meta-heuristic, called here as cellular automata firefly algorithm (CAFA), a new equation is presented for position updating of fireflies based on the concept of CA. Two benchmark examples of truss structures are presented to illustrate the efficiency of the proposed algorithm. Numerical results reveal that the proposed algorithm is a powerful optimization technique with improved convergence rate in comparison with other existing algorithms.

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This paper combines particle swarm optimization, grid search method and univariate method as a general optimization approach for any type of problems emphasizing on optimum design of steel frame structures. The new algorithm is denoted as the GSU-PSO. This method attempts to decrease the search space and only searches the space near the optimum point. To achieve this aim, the whole search space is divided into a series of grids by applying the grid search method. By using a method derived from the univariate method, the variables of the best particle change values. Finally, by considering an interval adjustment to the variables and generating particles randomly in new intervals, the particle swarm optimization allows us to swiftly find the optimum solution. This method causes converge to the optimum solution more rapidly and with less number of analyses involved. The proposed GSU-PSO algorithm is tested on several steel frames from the literature. The algorithm is implemented by interfacing MATLAB mathematical software and SAP2000 structural analysis code. The results indicated that this method has a higher convergence speed towards the optimal solution compared to the conventional and some well-known meta-heuristic algorithms. In comparison to the PSO algorithm, the proposed method required around 45% of the total number of analyses recorded and improved marginally the accuracy of solutions.

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Offshore jacket-type towers are steel structures designed and constructed in marine environments for various purposes such as oil exploration and exploitation units, oceanographic research, and undersea testing. In this paper a newly developed meta-heuristic algorithm, namely Cyclical Parthenogenesis Algorithm (CPA), is utilized for sizing optimization of a jacket-type offshore structure. The algorithm is based on some key aspects of the lives of aphids as one of the highly successful organisms, especially their ability to reproduce with and without mating. The optimal design procedure aims to obtain a minimum weight jacket-type structure subjected to API-RP 2A-WSD specifications. SAP2000 and its Open Application Programming Interface (OAPI) feature are utilized to model the jacket-type structure and the corresponding loading. The results of the optimization process are then compared with those of Particle Swarm Optimization (PSO) and its democratic version (DPSO).