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Due to the complex structural issues and increasing number of design variables, a rather fast optimization algorithm to lead to a global swift convergence history without multiple attempts may be of major concern. Genetic Algorithm (GA) includes random numerical technique that is inspired by nature and is used to solve optimization problems. In this study, a novel GA method based on self-adaptive operators is presented. Results show that this proposed method is faster than many other defined GA-based conventional algorithms. To investigate the efficiency of the proposed method, several famous optimization truss problems with semi-discrete variables are studied. The results reflect the good performance of the algorithm where relatively a less number of analyses is required for the global optimum solution.

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This study focuses on the shape optimization of concrete gravity dams considering dam–water–foundation interaction and nonlinear effects subject to earthquake. The concrete gravity dam is considered as a two–dimensional structure involving the geometry and material nonlinearity effects. For the description of the nonlinear behavior of concrete material under earthquake loads, the Drucker–Prager model based on the associated flow rule is adopted in this study. The optimum design of concrete gravity dams is achieved by the hybrid of an improved gravitational search algorithm (IGSA) and the orthogonal crossover (OC), called IGSA–OC. In order to reduce the computational cost of optimization process, the support vector machine approach is employed to approximate the dam response instead of directly evaluating it by a time–consuming finite element analysis. To demonstrate the nonlinear behavior of concrete material in the optimum design of concrete gravity dams, the shape optimization of a real dam is presented and compared with that of dam considering linear effect.

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One of the main tasks of engineers is to design structural systems light and economic as possible, yet resistant enough to withstand all possible loads arising during their service life and to absorb the induced seismic energy in a controlled and predictable fashion. The traditional trial-and-error design approach is not capable to determine an economical design satisfying also the code requirements. Structural design optimization, on the other hand, provides a numerical procedure that can replace the traditional design approach with an automated one. The objective of this work is to propose a performance-based seismic design procedure, formulated as a structural design optimization problem, for designing steel and steel-concrete composite buildings subject to interstorey drift limitations. In particular a straightforward design procedure is proposed where the influence on both record and incident angle is considered. For this purpose six test examples are considered, in particular three steel and three steel-concrete composite buildings are optimally designed for minimum initial cost.

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The interbasin water transfer is a remedy to mitigate the negative issues of water shortage in arid and semi-arid regions. In  a water transfer project  the receiving basin always  benefits while, the sending basin may suffer. In this study, the project of interbasin water transfer from Dez water resources system in south-west of Iran to the central part of the contrary is 
investigated during a drought period. To this end, a multi-objective optimization model is developed  based  on  the  Non  Dominated  Sorting  Genetic  Algorithm  (NSGA-II).  The optimum trade-off between the water supply benefits into and out of the Dez River basin as well  as  energy  production  is  derived.  Formulating  the  problem  as  a  multi-objective 
optimization provides a better insight into the gains and losses of a water transfer project. Analyzing the case study, revealed that to reach an acceptable level of reliability for meeting the water demands it is no longer possible to generate hydropower energy with high levels of reliability. 

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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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The Isogeometric Analysis (IA) is utilized for structural topology optimization  considering minimization of weight and local stress constraints. For this purpose, material density of the structure  is  assumed  as  a  continuous  function  throughout  the  design  domain  and approximated using the Non-Uniform Rational B-Spline (NURBS) basis functions. Control points of the density surface are considered as design variables of the optimization problem that can change the topology during the optimization process. For initial design, weight and stresses of the structure are obtained based on full material density over the design domain. The  Method  of  Moving  Asymptotes  (MMA)  is  employed  for  optimization  algorithm. Derivatives of the objective function and constraints with respect to the design variables are determined  through  a  direct  sensitivity  analysis.  In  order  to  avoid  singularity  a  relaxation technique  is  used  for  calculating  stress  constraints.  A  few  examples  are  presented  to demonstrate the performance of the method. It is shown that using the IA method and an appropriate stress relaxation technique can lead to reasonable optimum layouts.

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The paper deals with the reliability–based design optimization (RBDO) of concrete gravity dams subjected to earthquake load using subset simulation. The optimization problem is formulated such that the optimal shape of concrete gravity dam described by a number of variables is found by minimizing the total cost of concrete gravity dam for the given target reliability. In order to achieve this purpose, a framework is presented whereby subset simulation is integrated with a hybrid optimization method to solve the RBDO approach of concrete gravity dam. Subset simulation with Markov Chain Monte Carlo (MCMC) sampling is utilized to estimate accurately the failure probability of dams with a minimum number of samples. In this study, the concrete gravity dam is treated as a two–dimensional structure involving the material nonlinearity effects and dam–reservoir–foundation interaction. An efficient metamodel in conjunction with subset simulation–MCMC is provided to reduce the computational cost of dynamic analysis of dam–reservoir–foundation system. The results demonstrate that the RBDO approach is more appropriate than the deterministic optimum approach for the optimal shape design of concrete gravity dams.

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This study focuses on the topology optimization of structures using a hybrid of level set method (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient method as sensitivity analysis is also utilized to precisely design new holes in the interior domain. The hybrid of these gradients can yield an efficient algorithm which has more flexibility in changing topology of structure and escape from local optimal in the optimization process. Finally, instead of the conventional finite element method (FEM) a Non–Uniform Rational B–Splines (NURBS)–based IGA is applied to describe the field variables as the geometry of the domain. In IGA approach, control points play the same role with nodes in FEM, and B–Spline functions are utilized as shape functions of FEM for analysis of structure. To demonstrate the performance of the proposed method, three benchmark examples widely used in topology optimization are presented. Numerical results show that the proposed method outperform other LSMs.

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The big bang-big crunch (BB-BC) algorithm is a popular metaheuristic optimization technique proposed based on one of the theories for the evolution of the universe. The algorithm utilizes a two-phase search mechanism: big-bang phase and big-crunch phase. In the big-bang phase the concept of energy dissipation is considered to produce disorder and randomness in the candidate population while in the big-crunch phase the randomly created solutions are shrunk into a single point in the design space. In recent years, numerous studies have been conducted on application of the BB-BC algorithm in solving structural design optimization instances. The objective of this review study is to identify and summarize the latest promising applications of the BB-BC algorithm in optimal structural design. Different variants of the algorithm as well as attempts to reduce the total computational effort of the technique in structural optimization problems are covered and discussed. Furthermore, an empirical comparison is performed between the runtimes of three different variants of the algorithm. It is worth mentioning that the scope of this review is limited to the main applications of the BB-BC algorithm and does not cover the entire literature.

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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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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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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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Keeping the eigenfrequencies of a structure away from the external excitation frequencies is one of the main goals in the design of vibrating structures in order to avoid risk of resonance. This paper is devoted to the topological design of freely vibrating continuum structures with the aim of maximizing the fundamental eigenfrequency. Since in the process of topology optimization some areas of domain can potentially be removed, it is quite possible to encounter the problem of localized modes. Hence, the modified Solid Isotropic Material with Penalization (SIMP) model is here used to avoid artificial modes in low density areas. As during the optimization process, the first natural frequency increases, it may become close to the second natural frequency. Due to lack of the usual differentiability of the multiple eigenfrequencies, their sensitivity are calculated by the mathematical perturbation analysis. The optimization problem is formulated by a variable bound formulation and it is solved by the Method of Moving Asymptotes (MMA). Two dimensional plane elasticity problems with different sets of boundary conditions and attachment of a concentrated nonstructural mass are considered. Numerical results show the validity and supremacy of this approach.

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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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In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was previously found by other researchers, via a different mathematical process. Several benchmark structures, which have geometric nonlinear behavior, are analyzed with the proposed methods. The finite element method is utilized to analyze these problems. The abilities of suggested schemes are evaluated in tracing the complex equilibrium paths. Moreover, comparison study for the required number of increments and iterations is performed. Results reflect the robustness of the authors’ formulations.

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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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The objective of the present paper is to propose a sequential enhanced colliding bodies optimization (SECBO) algorithm for implementation of seismic optimization of steel braced frames in the framework of performance-based design (PBD). In order to achieve this purpose, the ECBO is sequentially employed in a multi-stage scheme where in each stage an initial population is generated based on the information derived from the results of previous stages. The required structural seismic responses, at performance levels, are evaluated by performing nonlinear pushover analysis. Two numerical examples are presented to illustrate the efficiency of the proposed SECBO for tackling the seismic performance-based optimization problem. The numerical results demonstrate the computational advantages of the SECBO algorithm.

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In this study, the recently developed method, Tug of War Optimization (TWO), is employed for simultaneous analysis, design and optimization of Water Distribution Systems (WDSs). In this method, analysis procedure is carried out using Tug of War Optimization algorithm. Design and cost optimization of WDSs are performed simultaneous with analysis process using an objective function in order to satisfying the analysis criteria, design constraints and cost optimization. A number of practical examples of WDSs are selected to demonstrate the efficiency of the presented algorithm. The findings of this study clearly signify the efficiency of the TWO algorithm in reducing the water distribution networks construction cost.