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Evolution Strategies (ES) are a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection. Gaussian mutation captures pair-wise dependencies between the variables through a covariance matrix. Covariance Matrix Adaptation (CMA) is a method to update this covariance matrix. In this paper, the CMA-ES, which has found many applications in solving continuous optimization problems, is employed for size optimization of steel space trusses. Design examples reveal competitive performance of the algorithm compared to the other advanced metaheuristics.

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Although Genetic algorithm (GA), Ant colony (AC) and Particle swarm optimization algorithm (PSO) have already been extended to various types of engineering problems, the effects of initial sampling beside constraints in the efficiency of algorithms, is still an interesting field. In this paper we show that, initial sampling with a special series of constraints play an important role in the convergence and robustness of a metaheuristic algorithm. Random initial sampling, Latin Hypercube Design, Sobol sequence, Hammersley and Halton sequences are employed for approximating initial design. Comparative studies demonstrate that well distributed initial sampling speeds up the convergence to near optimal design and reduce the required computational cost of purely random sampling methodologies. In addition different penalty functions that define the Augmented Lagrangian methods considered in this paper to improve the algorithms. Some examples presented to show these applications.

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Engineering optimization needs easy-to-use and efficient optimization tools that can be employed for practical purposes. In this context, stochastic search techniques have good reputation and wide acceptability as being powerful tools for solving complex engineering optimization problems. However, increased complexity of some metaheuristic algorithms sometimes makes it difficult for engineers to utilize such techniques in their applications. Big- Bang Big-Crunch (BB-BC) algorithm is a simple metaheuristic optimization method emerged from the Big Bang and Big Crunch theories of the universe evolution. The present study is an attempt to evaluate the efficiency of this algorithm in solving engineering optimization problems. The performance of the algorithm is investigated through various benchmark examples that have different features. The obtained results reveal the efficiency and robustness of the BB-BC algorithm in finding promising solutions for engineering optimization problems.

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In the present study, the computational performance of the particle swarm optimization (PSO) harmony search (HS) and firefly algorithm (FA), as popular metaheuristics, is investigated for size and shape optimization of truss structures. The PSO was inspired by the social behavior of organisms such as bird flocking. The HS imitates the musical performance process which takes place when a musician searches for a better state of harmony, while the FA was based on the idealized behavior of the flashing characteristics of natural fireflies. These algorithms were inspired from different natural sources and their convergence behavior is focused in this paper. Several benchmark size and shape optimization problems of truss structures are solved using PSO, HS and FA and the results are compared. The numerical results demonstrate the superiority of FA to HS and PSO.

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Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems so far. In the present study, a simple optimization (SOPT) algorithm with two main steps namely exploration and exploitation, is provided for practical applications. Aside from a reasonable rate of convergence attained, the ease in its implementation and dependency on few parameters only are among the advantageous characteristics of the proposed SOPT algorithm. The efficiency of the developed algorithm is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

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Many optimization techniques have been proposed since the inception of engineering optimization in 1960s. Traditional mathematical modeling-based approaches are incompetent to solve the engineering optimization problems, as these problems have complex system that involves large number of design variables as well as equality or inequality constraints. In order to overcome the various difficulties encountered in obtaining the solution of these problems, new techniques called metaheuristic algorithms are suggested. These techniques are numerical optimization algorithms that are based on a natural phenomenon. In this study, a state-of-art improved harmony search method with a new adaptive error strategy is proposed to handle the design constraints. Number of numerical examples is presented to demonstrate the efficiency of the proposed algorithm in solving engineering optimization problems.

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Water cycle algorithm (WCA) is a new metaheuristic algorithm which the fundamental concepts of WCA are derived from nature and are based on the observation of water cycle process and how rivers and streams flow to sea in the real world. In this paper, the task of sizing optimization of truss structures including discrete and continues variables carried out using WCA, and the optimization results were compared with other well-known optimizers. The obtained statistical results show that the WCA is able to provide faster convergence rate and also manages to achieve better optimal solutions compared to other efficient optimizers.

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The present study attempts to apply an efficient yet simple optimization (SOPT) algorithm to optimum design of truss structures under stress and displacement constraints. The computational efficiency of the technique is improved through avoiding unnecessary analyses during the course of optimization using the so-called upper bound strategy (UBS). The efficiency of the UBS integrated SOPT algorithm is evaluated through benchmark sizing optimization problems of truss structures and the numerical results are reported. A comparison of the numerical results attained using the SOPT algorithm with those of modern metaheuristic techniques demonstrates that the employed algorithm is capable of locating promising designs with considerably less computational effort.

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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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This paper attempts to improve the computational efficiency of the well known particle swarm optimization (PSO) algorithm for tackling discrete sizing optimization problems of steel frame structures. It is generally known that, in structural design optimization applications, PSO entails enormously time-consuming structural analyses to locate an optimum solution. Hence, in the present study it is attempted to lessen the computational effort of the algorithm, using the so called upper bound strategy (UBS), which is a recently proposed strategy for reducing the total number of structural analyses involved in the course of design optimization. In the UBS, the key issue is to identify those candidate solutions which have no chance to improve the search during the optimum design process. After identifying those non-improving solutions, they are directly excluded from the structural analysis stage, diminishing the total computational cost. The performance of the UBS integrated PSO algorithm (UPSO) is evaluated in discrete sizing optimization of a real scale steel frame to AISC-LRFD specifications. The numerical results demonstrate that the UPSO outperforms the original PSO algorithm in terms of the computational efficiency.

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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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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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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 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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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 the present study, two new hybrid approaches are proposed for predicting peak ground acceleration (PGA) parameter. The proposed approaches are based on the combinations of Adaptive Neuro-Fuzzy System (ANFIS) with Genetic Algorithm (GA), and with Particle Swarm Optimization (PSO). In these approaches, the PSO and GA algorithms are employed to enhance the accuracy of ANFIS model. To develop hybrid models, a comprehensive database from Pacific Earthquake Engineering Research Center (PEER) are used to train and test the proposed models. Earthquake magnitude, earthquake source to site distance, average shear-wave velocity, and faulting mechanisms are used as predictive parameters. The performances of developed hybrid models (PSO-ANFIS-PSO and GA-ANFIS-GA) are compared with the ANFIS model and also the most common soft computing approaches available in the literature. According to the obtained results, three developed models can be effectively used to predict the PGA parameter, but the comparison of models shows that the PSO-ANFIS–PSO model provides better results.

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In this paper the performance of four well-known metaheuristics consisting of Artificial Bee Colony (ABC), Biogeographic Based Optimization (BBO), Harmony Search (HS) and Teaching Learning Based Optimization (TLBO) are investigated on optimal domain decomposition for parallel computing. A clique graph is used for transforming the connectivity of a finite element model (FEM) into that of the corresponding graph, and k-median approach is employed. The performance of these methods is investigated through four FE models with different topology and number of meshes. A comparison of the numerical results using different algorithms indicates, in most cases the BBO is capable of performing better or identical using less time with equal computational effort.

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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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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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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.