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This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference of recorded acceleration of real damaged structure and hypothetical damaged structure, by updating physical parameters in each phase using iterative process of Levenberg-Marquardt algorithm. This algorithm is based on sensitivity analysis and provides a linear solution for nonlinear damage detection problem. The presented method is capable of detecting the exact location and ratio of structural damage in the presence of noise or incomplete data.

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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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Simplified Dolphin Echolocation (SDE) optimization is an improved version of the Dolphin Echolocation optimization. The dolphin echolocation (DE) is a recently proposed metaheuristic algorithm, which was imitated dolphin’s hunting process. The global or near global optimum solution modeled as dolphin’s bait, dolphins send sound in different directions to discover the best bait among their search space. This paper introduced a new optimization method called SDE for weight optimization of steel truss structures problems. SDE applies some new approaches for generating new solutions. These improvements enhance the accuracy and convergence rate of the DE SDE does not depend on any empirical parameter. The results of the SDE for mathematical and engineering optimization problems are compared to those of the standard DE and some popular metaheuristic algorithms. The results show that SDE is competitive with other algorithms.

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The main aim of the present paper is to propose efficient multi-objective optimization algorithms (MOOAs) to tackle truss structure optimization problems. The proposed meta-heuristic algorithms are based on the firefly algorithm (FA) and bat algorithm (BA), which have been recently developed for single-objective optimization. In order to produce a well distributed Pareto front, some improvements are implemented on the basic algorithms. The proposed MOOAs are examined for three truss optimization problems, and the results are compared to those of some other well-known methods. The numerical results demonstrate that the proposed MOOAs possess better computational performance compared to the other algorithms.

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In this paper, based on maximizing the outrigger-belt truss system’s strain energy, a methodology for determining the optimum location of a flexible outrigger system is presented. Tall building structures with combined systems of framed tube, shear core, belt truss and outrigger system are modeled using continuum approach. In this approach, the framed tube system is modeled as a cantilevered beam with box cross section. The effect of outrigger and shear core systems on framed tube’s response under lateral loading is modeled by a rotational spring placed at the location of belt truss and outrigger system. Optimum location of this spring is obtained when energy absorbed by the spring is maximized. For this purpose, first derivative of the energy equation with respect to spring location as measured from base of the structure, is set to zero. Optimum location for outrigger and belt truss system is calculated for three types of lateral loadings, i.e. uniformly and triangularly distributed loads along structure’s height, and concentrated load at top of the structure. Accuracy of the proposed method is verified through numerical examples. The results show that the proposed method is reasonably accurate. In addition, for different stiffness of shear core and outrigger system, several figures are presented that can be used to determine the optimum location of belt truss and outrigger system.

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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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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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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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Vibrating particles system (VPS) is a new meta-heuristic algorithm based on the free vibration of freedom system’ single degree with viscous damping. In this algorithm, each agent gradually approach to its equilibrium position; new agents are generated according to current agents and a historically best position. Enhanced vibrating particles system (EVPS) employs a new alternative procedure to enhance the performance of the VPS algorithm. Two different truss structures are investigated to demonstrate the performance of the VPS and EVPS weight optimization of structures.

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Structural reliability theory allows structural engineers to take the random nature of structural parameters into account in the analysis and design of structures. The aim of this research is to develop a logical framework for system reliability analysis of truss structures and simultaneous size and geometry optimization of truss structures subjected to structural system reliability constraint. The framework is in the form of a computer program called RBO-S>S. The objective of the optimization is to minimize the total weight of the truss structures against the aforementioned constraint. System reliability analysis of truss structures is performed through branch-and-bound method. Also, optimization is carried out by genetic algorithm. The research results show that system reliability analysis of truss structures can be performed with sufficient accurately using the RBO-S>S program. In addition, it can be used for optimal design of truss structures. Solutions are suggested to reduce the time required for reliability analysis of truss structures and to increase the precision of their reliability analysis.

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In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelligence. It works with doing random search in the search space and creating the initial random population by modeling DNA-based computing operators and applies the operators derived from genetic algorithm to achieve the optimum solution of the objective function. Generalized Convex Approximation (GCA) method is a gradient-based method that with approximation of the main function and starting from a point, finds the optimum solution using information about functions and their gradient. In this research, in order to minimize the weight of truss, the cross-section areas of the elements as discrete variables are optimized by DNA computing algorithm, and the coordinates of truss nodes as continuous variables are optimized by Generalized Convex Approximation (GCA) method. Therefore, to simultaneously optimize the size and geometry of truss structures, these two methods are used in combination. The results of numerical examples show the proper functioning of this process.

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This paper proposes a modified sine cosine algorithm (MSCA) for discrete sizing optimization of truss structures. The original sine cosine algorithm (SCA) is a population-based metaheuristic that fluctuates the search agents about the best solution based on sine and cosine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical functions has been demonstrated in literature. However, its performance in tackling the discrete optimization problems of truss structures is not competitive compared with the existing metaheuristic algorithms. In the framework of the proposed MSCA, a number of worst solutions of the current population is replaced by some variants of the global best solution found so far. Moreover, an efficient mutation operator is added to the algorithm that reduces the probability of getting stuck in local optima. The efficiency of the proposed MSCA is illustrated through multiple benchmark optimization problems of truss structures.

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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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Meta-heuristic algorithms are applied in optimization problems in a variety of fields, including engineering, economics, and computer science. In this paper, seven population-based meta-heuristic algorithms are employed for size and geometry optimization of truss structures. These algorithms consist of the Artificial Bee Colony algorithm, Cyclical Parthenogenesis Algorithm, Cuckoo Search algorithm, Teaching-Learning-Based Optimization algorithm, Vibrating Particles System algorithm, Water Evaporation Optimization, and a hybridized ABC-TLBO algorithm. The Taguchi method is employed to tune the parameters of the meta-heuristics. Optimization aims to minimize the weight of truss structures while satisfying some constraints on their natural frequencies. The capability and robustness of the algorithms is investigated through four well-known benchmark truss structure examples.

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This research presents a novel design approach to achieve an optimal structure established upon multiple objective functions by simultaneous utilization of the Enhanced Time Evolutionary Optimization method and Fuzzy Logic (FLETEO). For this purpose, at first, modeling of the structure design problem in this space is performed using fuzzy logic concepts. Thus, a new problem creates with functions and constraints regarding the design in fuzzy space as well as membership functions corresponded to every single of them. Then, the problem is solved by means of the Enhanced Time Evolutionary Optimization method (ETEO), eventually, based on the acquired results, the values of optimal design variables are obtained in the main problem. In the current paper, to validate the proposed approach and evaluate its performance, the optimal design of several standard structures has been carried out. Comparing the acquired results and previous ones is an indication of the high power of the proposed method in finding the best possible design with high convergence speed and deprived of contravening the constraints governing the problems.

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This study is devoted to discrete sizing optimization of truss structures employing an efficient discrete evolutionary meta-heuristic algorithm which uses the Newton gradient-based method as its updating scheme and it is named here as Newton Meta-heuristic Algorithm (NMA). In order to enable the NMA population-based meta-heuristic to effectively explore the discrete design space, a term containing the best solution found is added to the basic updating rule of the algorithm. The efficiency of the proposed NMA metaheuristic is illustrated by presenting five benchmark discrete truss optimization problems and comparing the results with literature. The numerical results demonstrate that the NMA is a robust and powerful meta-heuristic algorithm for dealing with the discrete sizing optimization problems of steel trusses.

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Due to the random nature of the variables affecting the analysis and design of structures, the reliability method is considered as one of the most important and widely used topics in structural engineering. Despite the simplicity of moment methods, the answer to problems with multiple design points (the point with the highest probability of failure) such as transmission line towers depends a lot on the starting point of the search; and it may converge to the local optima answer which is not desirable. Simulation methods also require a large number of evaluations of the limit state function and increase the volume and time of calculations. Also, the design point is not calculated in most of these methods. In this study, the reliability index of four transmission line towers was calculated with four metaheuristic algorithms in which the limit state function was defined based on the displacement of nodes and the results were compared with the results of Monte Carlo Simulation (MCS) method. For this purpose, the objective function was defined as the geometric distance between the point on the function of the boundary condition to the origin in the standard normal coordinate system and the constraint of the problem (the limit state function) based on the displacement of the nodes. Random variables in these problems consisting of the cross-sectional area of the members, the modulus of elasticity, and the nodal loads.

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In this paper, set theoretical variants of the artificial bee colony (ABC) and water evaporation optmization (WEO) algorithms are proposed. The set theoretical variants are designed based on a set theoretical framework in which the population of candidate solutions is divided into some number of smaller well-arranged sub-populations. The framework aims to improve the compromise between diversification and intensification of the search and makes it possible to design various variants of a P-metaheuristic. In order to verify the stability and robustness of the set theoretical framework, the proposed algorithms are applied to solve three different benchmark structural design optimization problems. The results show that the set theoretical framework improves the performance of the ABC and WEO algorithms, especially in terms of robustness and convergence characteristics.

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Nowadays, the optimal design of structures based on reliability has been converted to an active topic in structural engineering. The Reliability-Based Design Optimization (RBDO) methods provide the structural design with lower cost and more safety, simultaneously. In this study, the optimal design based on reliability of dome truss structures with probability constraint of the frequency limitation is discussed. To solve the RBDO problem, nested double-loop method is considered; one of the loops performs the optimization process and the other one assesses the reliability of the structure. The optimization process is implemented using ECBO and EVPS algorithms and the reliability index is calculated using the Monte Carlo simulation method. Finally, the size and shape reliability-based optimization of 52-bar and 120-bar dome trusses has been investigated.