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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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A modified dolphin monitoring (MDM) is used to augment the efficiency of particle swarm optimization (PSO) and enhanced vibrating particle system (EVPS) for the numerical crack identification problems in plate structures. The extended finite element method (XFEM) is employed for modeling the fracture. The forward problem is untangled by some cycle loading phase via dynamic XFEM. Furthermore, the inverse problem is solved and compared via two PSO and EVPS algorithms. All the problems are also dissolved by means of fine and coarse meshing. The results illustrate that the function of XFEM-PSO-MDM and XFEM-EVPS-MDM is superior to XFEM-PSO and XFEM-EVPS methods. The algorithms coupled via MDM offer a higher convergence rate with more reliable results. The MDM is found to be a suitable tool which can promotes the ability of the algorithms in achieving the optimum solutions.

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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 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.

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In recent decades, steel was used more than other materials in structural engineering. However, the safety of high-heat steel structures dramatically decreased, due to steel mechanical properties. Therefore, the design process should be done in a way that the structure has the required resistance at high temperatures and during the fire, according to the effect of heat on the performance of steel structures. In this study, the optimal design process of steel structures is considered under the fire load. In the optimal design process, the failure risk of the structure members is considered as a constraint. Therefore, the optimization process requires thermal and structural reliability analysis. A parametric model has been used to analyse the reliability of the structure in the fire limit state. The optimization process is also performed based on the Colliding Bodies Optimization (CBO) algorithm. In order to evaluate the optimal design process, 3 and 6-floors frames have been investigated. The results showed that the members' condition is effective in the structural resistance for the thermal loading. On the contrary, the structure design based on the reliability under the fire load provides a proper prediction from the behaviour of the structure and satisfies the requirements for the common state of design.

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The arithmetic optimization algorithm (AOA) is a recently developed metaheuristic optimization algorithm that simulates the distribution characteristics of the four basic arithmetic operations (i.e., addition, subtraction, multiplication, and division) and has been successfully applied to solve some optimization problems. However, the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when dealing with multi-dimensional optimization problems. More recently, in order to overcome the shortcomings of the original AOA, an improved version of AOA, named IAOA, has been proposed and successfully applied to discrete structural optimization problems. Compared to the original AOA, two major improvements have been made in IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The IAOA requires fewer algorithm-specific parameters compared with the original AOA, which makes it easy to be implemented. In this paper, IAOA is applied to the optimal design of large-scale dome-like truss structures with multiple frequency constraints. To the best of our knowledge, this is the first time that IAOA is applied to structural optimization problems with frequency constraints. Three benchmark dome-shaped truss optimization problems with frequency constraints are investigated to demonstrate the efficiency and robustness of the IAOA. Experimental results indicate that IAOA significantly outperforms the original AOA and achieves results comparable or superior to other state-of-the-art algorithms.

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In recent years many researchers prefer to use metaheuristic algorithms to reach the optimum design of structures. In this study, an Enhanced Vibrating Particle System (EVPS) is applied to get the minimum weight of large-scale dome trusses under frequency constraints. Vibration frequencies are important parameters, which can be used to control the responses of a structure that is subjected to dynamic excitation. The truss structures were analyzed by finite element method and optimization processes were implemented by the computer program coded in MATLAB. The effectiveness and efficiency of the Enhanced Vibrating Particle System (EVPS) is investigated in three large-scale dome trusses 600-, 1180-, and 1410-bar to obtain the weight optimization with frequency constraints.

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Despite comprehensive literature works on developing fitness-based optimization algorithms, their performance is yet challenged by constraint handling in various engineering tasks. The present study, concerns the widely-used external penalty technique for sizing design of pin-jointed structures. Observer-teacher-learner-based optimization is employed here since previously addressed by a number of investigators as a powerful meta-heuristic algorithm. Several cases of penalty handling techniques are offered and studied using either maximum or summation of constraint violations as well as their combinations. Consequently, the most successive sequence, is identified for the treated continuous and discrete structural examples. Such a dynamic constraint handling is an affordable generalized solution for structural sizing design by iterative population-based algorithms.
 

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Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold (DE-MEDT) metaheuristic algorithm is applied to solve the discrete and continuous optimization problems of the truss structures subject to multiple loading conditions and design constraints. DE-MEDT algorithm is a recently proposed metaheuristic developed based on a physical phenomenon called Doppler Effect (DE) with some idealized rules and a mechanism called Mean Euclidian Distance Threshold (MEDT). The efficiency of the DE-MEDT algorithm is evaluated by optimizing five large-scale truss structures with continuous and discrete variables. Comparing the results found by the DE-MEDT algorithm with those of other existing metaheuristics reveals that the DE-MEDT optimizer is a suitable optimization technique for discrete and continuous design optimization of large-scale truss structures.
 

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Metaheuristic algorithms are preferred by the many researchers to reach the reliability based design optimization (RBDO) of truss structures. The cross-sectional area of the elements of a truss is considered as design variables for the size optimization under frequency constraints. The design of dome truss structures are optimized based on reliability by a popular metaheuristic optimization technique named Enhanced Vibrating Particle System (EVPS). Finite element analyses of structures and optimization process are coded in MATLAB. Large-scale dome truss of 600-bar, 1180-bar and 1410-bar are investigated in this paper and are compared with the previous studies. Also, a comparison is made between the reliability indexes of Deterministic Design Optimization (DDO) for large dome trusses and Reliability-Based Design Optimization (RBDO).
 

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Beyond common practice that treats structural damage detection as an optimization problem, the present work offers another approach that updates boundaries of the damage ratios. In this approach the bandwidth between such lower and upper boundaries, is adaptively reduced aiming to coincide at the true damage state. Formulation of the proposed method is developed using modal strain energy in a system of finite elements. A resolution-based technique is applied so that the search space cardinality can be defined and then reduced. The proposed method is validated on different structural types including beam, frame and truss examples with various damage scenarios. The results exhibit high cardinality reduction and capability of the proposed iterative method in squeezing the design space for more efficient search.
 

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The existence of uncertainties in engineering problems makes it essential to consider these effects at all times. Robust design optimization allows a design to be made less sensitive to uncertain input parameters. Actually, robust design optimization reduces the sensitivity of the objective function and the variations in design performance when uncertainty exists. In this study, two space trusses were optimized based on the modulus of elasticity, yield stress, and cross-sectional uncertainties in order to increase the response robustness and decrease the weight. The displacement of one node has been used as the criterion for Robust Design Optimization (RDO) of these two structures. Two trusses with 72 members and 582 members are considered, which are famous trusses in the field of structural optimization. Also, the EVPS meta-heuristic algorithm was employed which is an enhanced version of the VPS algorithm based on the single degrees of freedom of a system with viscous damping.
 

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In this paper, the improved shuffled-based Jaya algorithm (IS-Jaya) is applied to the size optimization of the braced dome with the frequency constraints. IS-Jaya is the enhanced version of the Jaya algorithm that the shuffling process and escaping from local optima are added for it. These two modifications increase the population diversity and ability the escape from the local optima of the Jaya. The robustness and performance of the IS-Jaya are evaluated by the three design examples. The results show that the IS-Jaya algorithm outperforms other state-of-the-art optimization techniques considered in the literature.
 

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This paper deals with the optimum design of the mixed structures that consists of two parts, a lower part made of concrete and an upper part made of steel. Current codes and available commercial software packages do not provide analytical solutions for such structural systems, especially if a decoupled analysis is performed where the lower part is excited by ground motion and its response of total accelerations is used for the upper part. Due to irregular damping ratios, mass and stiffness, dynamic response of each part of a mixed structure differs significantly. The present paper aims at comparing of the optimum design of these structures under the coupled and decoupled models. Toward that goal, the coupled and decoupled time history analyses are performed and the optimum design of the two methods are compared. The results of the two approach show that the cost of the decoupled analysis is higher than the cost of the coupled analysis and the design of the decoupled method may be uneconomical, because the interaction between the two upper and lower parts is neglected.
 

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Most structures are asymmetric due to functionality requirements and limitations. This study investigates the effect of asymmetry on damage detection. For this purpose, the asymmetry has been applied to models by considering different spans’ length and also different geometry properties for the section of members. Two types of structures comprising symmetric and asymmetric truss and frame have been modeled considering multiple damage scenarios and noise-contaminated data. Three objective functions based on flexibility matrix, natural frequency and modal frequency are proposed. These objective functions are optimized utilizing multiverse optimizer (MVO). For the symmetric models using limited modal data, flexibility-based objective function has the most accurate results, while by increasing the number of mode shapes, its accuracy reduced. Among asymmetric models of truss, damage detection results of the model is more accurate than those of its symmetric pair. Between asymmetric models of frame, the results obtained from frames which have only different spans’ length are more precise than those of the symmetric model. This is while frequency-based objective functions have their least accurate results for the frame model having asymmetry only in the section properties of its elements.
 

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Shape optimization of a double-curved dam is formulated using control points for interpolation functions. Every design vector is decoded into the integrated water-dam-foundation rock model. An enhanced algorithm is proposed by hybridizing particle swarm algorithm with ant colony optimization and simulated annealing. The best experiences of the search agents are indirectly shared via pheromone trail deposited on a bi-partite characteristic graph. Such a stochastic search is further tuned by Boltzmann functions in simulated annealing. The proposed method earned the first rank in comparison with six well-known meta‑heuristic algorithms in solving benchmark test functions. It captured the optimal shape design of Morrow Point dam, as a widely addressed case-study, by 21% reduced concrete volume with respect to the common USBR design practice and 16% better than the particle swarm optimizer. Such an optimal design was also superior to the others in stress redistribution for better performance of the dam system.
 

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This paper presents the chaotic variants of the particle swarm optimization-statistical regeneration mechanism (PSO-SRM). The nine chaotic maps named Chebyshev, Circle, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal, and Tent are used to increase the performance of the PSO-SRM. These maps are utilized instead of the random number, which defines the solution generation method. The robustness and performance of these methods are tested in the three steel frame design problems, including the 1-bay 10-story steel frame, 3-bay 15-story steel frame, and 3-bay 24-story steel frame. The optimization results reveal that the applied chaotic maps improve the performance of the PSO-SRM.
 

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The primary objective of this paper is to propose a novel technique for hybridizing various metaheuristic algorithms to optimize the size of discrete structures. To accomplish this goal, two well-known metaheuristic algorithms, particle swarm optimization (PSO) and enhanced colliding bodies optimization (ECBO) are hybridized to propose a new algorithm called hybrid PSO-ECBO (HPE) algorithm. The performance of the new HPE algorithm is investigated in solving the challenging structural optimization problems of discrete steel trusses and an improvement in results has been achieved. The numerical results demonstrate the superiority of the proposed HPE algorithm over the original versions of PSO, ECBO, and some other algorithms in the literature.
 

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In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the natural frequencies and mode shapes. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO algorithms consist of Colliding Bodies Optimization (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.

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The contourlet transform as an extension of the wavelet transform in two dimensions uses the multiscale and directional filter banks, and has a more adequate performance in comparison with the classical multi-scale representations. In this study, the efficiency of the contourlet transform is assessed for identifying the damage of plate structures in various conditions. The conditions include single damage and multi–damages with different shapes and severities, the different supports (i.e., boundary conditions), and the higher mode shapes,. For achieving this purpose, the process of the damage detection of plate structures using contourlet transform is implemented in the three steps. In the first step, the first mode shapes of a damaged plate and a reference state as the intact plate are obtained using the finite element method. In the second step, the damage indices are achieved by applying the contourlet transform to the responses of the first mode shapes for the damaged and intact plates. Finally, the location and the approximate shape of the damage are identified by plotting the damage indices. The obtained results indicate that the various conditions influence the performance of the contourlet transform for identifying the location and approximate shape of damages in plate structures.