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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.

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Optimal design of cantilever reinforced concrete retaining wall can lead considerable cost saving if its involvement in hill road formation and railway line formation is significant.  A study of weight reduction optimization of reinforced cantilever retaining wall subjected to a sloped backfill using Differential Evolution Algorithm (DEA) is carried out in the present research.  The retaining wall carrying a sloped backfill is investigated manually and the problem is solved using the algorithm and results were compared. The Indian Standard design philosophy is followed throughout the research. The design variables, constraint equations were determined and optimized with DEA. The single objective constrained optimization problem deals with seven design variables of cantilever retaining wall in which four design variables constitutes  to geometric dimensions and remaining three variables constitutes to the reinforcement steel area. Ten different constraints are considered and each of it deals with ten failure modes of retaining wall. Further, a sensitivity analysis is carried out by varying the parameters namely, height of the stem and thickness of stem at top, both of it being a constant design variable in the normal optimization problem. Results show that about 15% weight reduction is achieved while comparing with manual solution.

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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).

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This paper presents an improved multi-objective evolutionary algorithm (IMOEA) for the design of planar steel frames. By considering constraints as a new objective function, single objective optimization problems turned to multi objective optimization problems. To increase efficiency of IMOEA different Crossover and Mutation are employed. Also to avoid local optima dynamic interference of mutation and crossover are considered. Feasible particles called elites which are very helpful for better mutation and crossover considered as a tool to increase efficiency of proposed algorithm. The proposed evolutionary algorithm (IMOEA) is utilized to solve three well-known classical weight minimization problems of steel moment frames. In order to verify the suitability of the present method, the results of optimum design for planar steel frames are obtained by present study compared to other researches. Results indicate that, as far as the convergence, speed of the optimization process and quality of optimum design are concerned behavior, IMOEA is significantly superior to other meta-heuristic optimization algorithms with an acceptable global answer.

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Structural optimization of offshore wind turbine structures has become an important issue in the past years due to the noticeable developments in offshore wind industry. However, considering the offshore wind turbines’ size and environment, this task is outstandingly difficult. To overcome this barrier, in this paper, a metaheuristic algorithm called Enhanced Colliding Bodies Optimization (ECBO) is utilized to investigate the optimal design of jacket supporting structures for offshore wind turbines when a number of structural constraints, including a frequency constraint, are considered. The algorithm is validated using a design example. The OC4 reference jacket, which has been widely referenced in offshore wind industry, is the considered design example in this paper. The whole steps of this research, including loading, analysis, design, and optimization of the structure, are coded in MATLAB. Both Ultimate Limit States (ULS) and frequency constraints are considered as design constraints in this paper. Huge weight reduction is observed during this optimization problem, indicating the efficiency of the ECBO algorithm and its application in the optimization of offshore wind turbine structures.

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The main aim of the present study is to optimize steel moment frames in the framework of performance-based design and to assess the seismic collapse capacity of the optimal structures. In the first phase of this study, four well-known metaheuristic algorithms are employed to achieve the optimization task. In the second phase, the seismic collapse safety of the obtained optimal designs is evaluated by conducting incremental dynamic analysis and generating fragility curves. Three illustrative examples including 3-, 6-, and 12-story steel moment frames are presented. The numerical results demonstrate that all the performance-based optimal designs obtained by the metahuristic algorithms are of acceptable collapse margin ratio.

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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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In this research, a new objective function has been proposed for optimal design of the Buckling Restrained Braced Frames (BRBFs) is performed using nonlinear time history analysis. The BRBF is a particular type of bracing system that has been widely utilized in recent years. The nonlinear time history analysis also provides a detailed view of the behavior of the structure. The purpose of this study is to provide an optimal design based on minimizing the weight of the structure while increasing the energy dissipation capability of the structure. Due to the complexity of the problem, the Enhanced Vibrating Particles Systems (EVPS) meta-heuristic algorithm is used to perform the optimization. Here, a 3-story frame, a 6-story frame and a 9-story frame are investigated simultaneously considering the continuous and discrete optimization.

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The present work is aimed at assessing the impact of strong column-weak beam (SCWB) criterion on seismic performance of optimally designed steel moment frames. To this end, different SCWB ratios are considered for steel special moment resisting frame (SMRF) structures and performance-based design optimization process is implemented with the aid of an efficient metaheuristic. The seismic collapse performance of the optimally designed SMRFs is assessed by performing incremental dynamic analysis (IDA) and determining their adjusted collapse margin ratios. Three design examples of 5-, 10-, and 15-story SMRFs are presented to illustrate the efficiency of the proposed methodology.

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This paper proposes a GA-based reduced search space technique (GA-RSS) for the optimal design of steel moment frames. It tries to reduce the computation time by focusing the search around the boundaries of the constraints, using a ranking-based constraint handling to enhance the efficiency of the algorithm. This attempt to reduce the search space is due to the fact that in most optimization problems the optimal solution lies on or near the boundaries of the feasible region. All the analyses/optimization steps have been implemented in MATLAB and the method has been validated by optimizing three moment-frame benchmark problems. According to the results, the algorithm performs fit and needs relatively fewer analyses than other metaheuristic algorithms to reach a global optimum solution.

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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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The main purpose of the present work is to investigate the impact of soil-structure interaction on performance-based design optimization of steel moment resisting frame (MRF) structures. To this end, the seismic performance of optimally designed MRFs with rigid supports is compared with that of the optimal designs with a flexible base in the context of performance-based design. Two efficient metaheuristic algorithms, namely center of mass optimization and improved fireworks, are used to implement the optimization task. During the optimization process, nonlinear structural response-history analysis is carried out to evaluate the structural response. Two illustrative design examples of 6- and 12-story steel MRFs are presented, and it is observed that the performance-based design optimization considering soil-structure interaction decreases the structural weight and increases nonlinear structural response in comparison to rigid-based models. Therefore, in order to obtain more realistic optimal designs, soil-structure interaction should be included in the performance-based design optimization process of steel MRFs.

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In this work, a new hybrid Symbiotic Organisms Search (SOS) algorithm introduced to design and optimize spatial and planar structures under structural constraints. The SOS algorithm is inspired by the interactive behavior between organisms to propagate in nature. But one of the disadvantages of the SOS algorithm is that due to its vast search space and a large number of organisms, it may trap in a local optimum. To fix this problem Harmony search (HS) algorithm, which has a high exploration and high exploitation, is applied as a complement to the SOS algorithm. The weight of the structures' elements is the objective function which minimized under displacement and stress constraints using finite element analysis. To prove the high capabilities of the new algorithm several spatial and planar benchmark truss structures, designed and optimized and the results have been compared with those of other researchers. The results show that the new algorithm has performed better in both exploitation and exploration than other meta-heuristic and mathematics methods.

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Jellyfish Search (JS) is a recently developed population-based metaheuristic inspired by the food-finding behavior of jellyfish in the ocean. The purpose of this paper is to propose a quantum-based Jellyfish Search algorithm, named Quantum JS (QJS), for solving structural optimization problems. Compared to the classical JS, three main improvements are made in the proposed QJS: (1) a quantum-based update rule is adopted to encourage the diversification in the search space, (2) a new boundary handling mechanism is used to avoid getting trapped in local optima, and (3) modifications of the time control mechanism are added to strike a better balance between global and local searches. The proposed QJS is applied to solve frequency-constrained large-scale cyclic symmetric dome optimization problems. To the best of our knowledge, this is the first time that JS is applied in frequency-constrained optimization problems. An efficient eigensolution method for free vibration analysis of rotationally repetitive structures is employed to perform structural analyses required in the optimization process. The efficient eigensolution method leads to a considerable saving in computational time as compared to the existing classical eigensolution method. Numerical results confirm that the proposed QJS considerably outperforms the classical JS and has superior or comparable performance to other state-of-the-art optimization algorithms. Moreover, it is shown that the present eigensolution method significantly reduces the required computational time of the optimization process compared to the classical eigensolution method.

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The present work deals with optimization and reliability assessment of double layer barrel vaults. In order to achieve the optimization task an improved colliding bodies optimization algorithm is employed. In the first phase of this study, different forms of double layer barrel vaults namely, square-on-square, square-on-diagonal, diagonal-on-diagonal and diagonal-on-square are considered and designed for optimal weight by the improved colliding bodies optimization algorithm. In the second phase, in order to account for the existing uncertainties in action and resistance of the structures, the reliability of the optimally designed double layer barrel vaults is assessed using importance sampling method by taking into account a limit-state function on the maximum deflection of the structures. The results demonstrate that the minimum reliability index of the optimal designs is 0.92 which means that all the optimally designed double layer barrel vaults are reliable and safe against uncertainties.  

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Force Density Method is a well-known form-finding method for discrete networks that is based on geometrical equilibrium of forces and could be used to design efficient structural forms. The choice of force density distribution along the structure is mostly upon user which in most cases is set be constant, with peripheral members having relatively larger force density to prevent excessive shrinking. In order to direct FDM towards more efficient structures, an optimization strategy can be used to inform the form-finding process by minimizing certain objective function, e.g. weight of the structure. Desired structural, constructional or geometrical constraints can also be incorporated in this framework that otherwise user may not have direct control over. It has been shown that considerable weight reduction is possible compared to uniform force density in the structure while satisfying additional constraints. In this way, form-finding can be augmented and novel structural forms can be designed.

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The optimal design of dome structures is a challenging task and therefore the computational performance of the currently available techniques needs improvement. This paper presents a combined algorithm, that is supported by the mixture of Charged System Search (CSS) and Teaching-Learning-based optimization (TLBO). Since the CSS algorithm features a strong exploration and may explore all unknown locations within the search space, it is an appropriate complement to enhance the optimization process by solving the weaknesses with using another optimization algorithm’s strong points. To enhance the exploitation ability of this algorithm, by adding two parts of Teachers phase and Student phase of TLBO algorithm to CSS, a method is obtained that is more efficient and faster than standard versions of these algorithms. In this paper, standard optimization methods and new hybrid method are tested on three kinds of dome structures, and the results show that the new algorithm is more efficient in comparison to their standard versions.