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This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jacobi equation, so it is free of the CFL condition and the reinitialization scheme. This favorable properties lead to a great time advantage in this method. In this paper, the BLSM is implemented with the additive operator splitting (AOS) scheme and several numerical issues of the implementation are discussed. The proposed scheme is much more efficient than the conventional level set method. Several 2D examples are presented which demonstrate the effectiveness and robustness of the proposed method.

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Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discrete sizing variables and integrated discrete sizing and continuous geometric variables. The HS algorithm uses a stochastic random search instead of a gradient search so the former has a new-paradigmed derivative. Several truss examples from the literature are also presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods.

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In some cases the optimum is the minimum of the objective function (mathematical optimum), but in other cases the optimum is given by a technical constraint (technical optimum). The present paper shows the both types in two problems. The first problem is to find the optimum dimensions of a ring-stiffened circular cylindrical shell subject to external pressure, which minimize the structural cost. The calculation shows that the cost decreases when the shell diameter decreases. The decrease of diameter is limited by a fabrication constraint that the diameter should be minimum 2 m to make it possible the welding and painting inside of the shell. The second problem is to find the optimum dimensions of a cantilever column loaded by compression and bending. The column is constructed as circular or conical unstiffened shell. The cost comparison of both structural versions shows the most economic one.

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In this article, an efficient methodology is presented to optimize the topology of structural systems under transient loads. Equivalent static loads concept is used to deal with transient loads and to solve an alternate quasi-static optimization problem. The maximum strain energy of the structure under the transient load during the loading interval is used as objective function. The objective function is calculated in each iteration and then the dynamic optimization problem is replaced by a static optimization problem, which is subsequently solved by a convex linearization approach combining linear and reciprocal approximation functions. The optimal layout of a deep beam subjected to transient loads is considered as a case study to verify the effectiveness of the presented methodology. Results indicate that the optimal layout is dependant of the loading interval.

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A two-stage optimization method is presented by employing the evolutionary structural optimization (ESO) and ant colony optimization (ACO), which is called ESO-ACO method. To implement ESO-ACO, size optimization is performed using ESO, first. Then, the outcomes of ESO are employed to enhance ACO. In optimization process, the weight of double layer grid is minimized under various constraints which artificial ground motion is used to calculate the structural responses. The presence or absence of elements in bottom and web grids and also cross-sectional areas are selected as design variables. The numerical results reveal the computational advantages and effectiveness of the proposed method.

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Structural optimization, when approached by conventional (gradient based) minimization algorithms presents several difficulties, mainly related to computational aspects for the huge number of nonlinear analyses required, that regard both Objective Functions (OFs) and Constraints. Moreover, from the early '80s to today's, Evolutionary Algorithms have been successfully developed and applied as a computational alternative to many optimization problems, such as structural ones. In this study the effectiveness of a relatively new Evolutionary Algorithm, namely Differential Evolutionary, is investigated for constrained optimization. This presents many interesting advantages and so that it is a candidate to be widely used in many real structural optimization problems. The algorithm version here used has been developed by hybridizing some recent versions of Differential Evolutionary algorithms proposed in literature, and uses a specific way for dealing with constraints which, always, concern real structural optimization problems. The effectiveness of proposed approach has been demonstrated by developing two cases of study, which regard simple but very significant structural problems for steel structures, one of which is a standard benchmark in structural optimization. The analyses show the simplicity and effectiveness of the proposed approach, so that it can be suitably ready for practical uses out of academic contest.

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This paper provides a test method to make a fair comparison between different heuristics in structure optimization. When statistical methods are applied to the structural optimization (namely heuristics or meta-heuristics with several tunable parameters and starting seeds), the "one problem - one result" is extremely far from the fair comparison. From statistical point of view, the minimal requirement is a so-called "small-sample" according to the fundamental elements of the theory of the experimental design and evaluation and the protocol used in the drug development processes. The viability and efficiency of the proposed statistically correct methodology is demonstrated using the well-known ten-bar truss on a set of the heuristics from the brutal-force-search up to the most sophisticated hybrid approaches.

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In this article optimal design of shear walls is performed under seismic loading. For practical aims, a database of special shear walls is created. Special shear walls are used for seismic design optimization employing the charged system search algorithm as an optimizer. Constraints consist of design and performance limitations. Nonlinear behavior of the shear wall is taken into account and performance based seismic design optimization is accomplished. Capacity curves of the optimal solution are determined and compared incorporates soil–structure interaction. Also an optimization based method is proposed for bilinear approximation of capacity curve. These are a new methodology for seismic RC shear wall optimum design.

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The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of the finite element method. For this purpose, the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. The coordinates of control points which are also used for constructing the density function, are considered as design variables of the optimization problem. In order to change the design variables towards optimum, the Method of Moving Asymptotes (MMA) is used. To alleviate the formation of layouts with porous media, the density function is penalized during the optimization process. A few examples are presented to demonstrate the performance of the method.

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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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The main aim of the present study is to achieve optimum design of reinforced concrete (RC) plane moment frames using bat algorithm (BA) which is a newly developed meta-heuristic optimization algorithm based on the echolocation behaviour of bats. The objective function is the total cost of the frame and the design constraints are checked during the optimization process based on ACI 318-08 code. Design variables are the cross-sectional assignments of the structural members and are selected from a data set containing a finite number of sectional properties of beams and columns in a practical range. Three design examples including four, eight and twelve story RC frames are presented and the results are compared with those of other algorithms. The numerical results demonstrate the superiority of the BA to the other meta-heuristic algorithms in terms of the frame optimal cost and the convergence rate.

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In the present study, the reliability assessment of performance-based optimally seismic designed reinforced concrete (RC) and steel moment frames is investigated. In order to achieve this task, an efficient methodology is proposed by integrating Monte Carlo simulation (MCS) and neural networks (NN). Two NN models including radial basis function (RBF) and back propagation (BP) models are examined in this study. In the proposed methodology, MCS is used to estimate the total exceedence probability associated with immediate occupancy (IO), life safety (LS) and collapse prevention (CP) performance levels. To reduce the computational burden of MCS process, the required nonlinear responses of the generated structures are predicted by RBF and BP models. The numerical results imply the superiority of BP to RBF in prediction of structural responses associated with performance levels. Finally, the obtained results demonstrate the high efficiency of the proposed methodology for reliability assessment of RC and steel frame structures.

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Computational cost of metaheuristic based optimum design algorithms grows excessively with structure size. This results in computational inefficiency of modern metaheuristic algorithms in tackling optimum design problems of large scale structural systems. This paper attempts to provide a computationally efficient optimization tool for optimum design of large scale steel frame structures to AISC-LRFD specifications. To this end an upper bound strategy (UBS), which is a recently proposed strategy for reducing the total number of structural analyses in metaheuristic optimization algorithms, is used in conjunction with an exponential variant of the well-known big bang-big crunch optimization algorithm. The performance of the UBS integrated algorithm is investigated in the optimum design of two large-scale steel frame structures with 3860 and 11540 structural members. The obtained numerical results clearly reveal the usefulness of the employed technique in practical optimum design of large-scale structural systems even using regular computers.

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Colliding bodies optimization (CBO) is a new population-based stochastic optimization algorithm based on the governing laws of one dimensional collision between two bodies from the physics. Each agent is modeled as a body with a specified mass and velocity. A collision occurs between pairs of objects to find the global or near-global solutions. Enhanced colliding bodies optimization (ECBO) uses memory to save some best solutions and utilizes a mechanism to escape from local optima. The performances of the CBO and ECBO are shown through truss and frame design optimization problems. The codes of these methods are presented in MATLAB and C++.

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This article aims to study the self-supporting truss towers used to support large wind turbines. The goal is to evaluate and validate numerically by finite element method the structural analysis when the lattice structures of the towers of wind turbines are subjected to static loads and these from common usage. With this, it is expected to minimize the cost of transportation and installation of the tower and maximize the generation of electricity, considering technical standards and restrictions of structural integrity and safety, making vibration analysis and the required static and dynamic loads, thereby preventing failures by fractures or mechanical fatigue. Practical examples of towers will be designed by the system and will be tested in structural simulation programs using the Finite Element Method. This analysis is performed on the entire region coupling action of the turbine, with variable sensitivity to vibration levels. The results obtained for freestanding lattice tower are compared with the information of a tubular one designed to support the generator with the same characteristics. At the end of this work it was possible to observe the feasibility of using lattice towers that proved better as its structural performance but with caveats about its dynamic performance since the appearance of several other modes natural frequency thus reducing the intervals between them in low frequency and theoretically increase the risk of resonance.

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This study presents shape optimization of a gravity dam imposing stability and principal stress constraints. A gravity dam is a large scale hydraulic structure consisting of huge amount of concrete material. Hence, an optimum design gives a cost-benefit structure due to the fact that small changes in shape of dam cross-section leads to large saving of concrete volume. Three recently developed meta-heuristics are utilized for optimizing the structure. These algorithms are charged system search (CSS), colliding bodies optimization (CBO) and its enhanced edition (ECBO). This article also provides useful formulations for stability analysis of gravity dams which can be extended to further researches.

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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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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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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 paper, MATLAB code for a recently developed meta-heuristic methodology, the vibrating particles system (VPS) algorithm, is presented. The VPS is a population-based algorithm which simulates a free vibration of single degree of freedom systems with viscous damping. The particles gradually approach to their equilibrium positions that are achieved from current population and historically best position. Two truss towers with 942 and 2386 elements are examined for the validity of the present algorithm; however, the performance VPS has already been proven through truss and frame design optimization problems.