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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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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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In this paper we present a unified (probabilistic/possibilistic) model for resource-constrained project scheduling problem (RCPSP) with uncertain activity durations and a concept of a heuristic approach connected to the theoretical model. It is shown that the uncertainty management can be built into any heuristic algorithm developed to solve RCPSP with deterministic activity durations. The essence and viability of our unified model are illustrated by fuzzy examples presented in the recent fuzzy RCPSP literature.

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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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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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A new meta-heuristic method, based on Neuronal Communication (NC), is introduced in this article. The neuronal communication illustrates how data is exchanged between neurons in neural system. Actually, this pattern works efficiently in the nature. The present paper shows it is the same to find the global minimum. In addition, since few numbers of neurons participate in each step of the method, the cost of calculation is less than the other comparable meta-heuristic methods. Besides, gradient calculation and a continuous domain are not necessary for the process of the algorithm. In this article, some new weighting functions are introduced to improve the convergence of the algorithm. In the end, various benchmark functions and engineering problems are examined and the results are illustrated to show the capability, efficiency of the method. It is valuable to note that the average number of iterations for fifty independent runs of functions have been decreased by using Neuronal Communication algorithm in comparison to a majority of methods.

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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 utilizes the Colliding Bodies of Optimization (CBO), Enhanced Colliding Bodies of Optimization (ECBO) and Vibrating Particles System (VPS) algorithms to optimize the reservoir system operation. CBO is based on physics equations governing the one-dimensional collisions between bodies, with each agent solution being considered as an object or body with mass and ECBO utilizes memory to save some historically best solutions and uses a random procedure to escape from local optima. VPS is based on simulating free vibration of single degree of freedom systems with viscous damping. To evaluate the performance of these three recent population-based meta-heuristic algorithms, they are applied to one of the most complex and challenging issues related to water resource management, called reservoir operation optimization problems. Hypothetical 4 and 10-reservoir systems are studied to demonstrate the effectiveness and robustness of the algorithms. The aim is on discovering the optimum mix of releases, which will lead to maximum benefit generation throughout the system. Comparative results show the successful performance of the VPS algorithm in comparison to the CBO and its enhanced version.

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In this paper, the optimum design of a reinforced concrete one-way ribbed slab, is presented via recently developed metaheuristic algorithm, namely, the Mouth Brooding Fish (MBF). Meta-heuristics based on evolutionary computation and swarm intelligence are outstanding examples of nature-inspired solution techniques. The MBF algorithm simulates the symbiotic interaction strategies adopted by organisms to survive and propagate in the ecosystem. This algorithm uses the movement, dispersion and protection behavior of Mouth Brooding Fish as a pattern to find the best possible answer. The cost of the system is considered to be the objective function, and the design is based on the American Concrete Institute’s ACI 318-08 standard. The performance of this algorithm is compared with harmony search (HS), colliding bodies optimization (CBO), particle swarm optimization (PSO), democratic particle swarm optimization (DPSO), charged system search (CSS) and enhanced charged system search (ECSS). The numerical results demonstrate that the MBF algorithm is able to construct very promising results and has merits in solving challenging optimization problems.

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The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for embedding graphs in the plane. The algorithms consist of Artificial Bee Colony algorithm, Big Bang-Big Crunch algorithm, Teaching-Learning-Based Optimization algorithm, Cuckoo Search algorithm, Charged System Search algorithm, Tug of War Optimization algorithm, Water Evaporation Optimization algorithm, and Vibrating Particles System algorithm. The performance of the utilized algorithms is investigated through various examples including six complete graphs and eight complete bipartite graphs. Convergence histories of the algorithms are provided to better understanding of their performance. In addition, optimum results at different stages of the optimization process are extracted to enable to compare the meta-heuristics algorithms.

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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 paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calculation and new population generation in these two methods are completely different. At each stage of the ECM algorithm, successful distributions are identified and the covariance matrix of the successful distributions is formed. Subsequently, by the help of the principal component analysis (PCA), the scattering directions of these distributions will be achieved. The new population is generated by the combination of weighted directions that have a successful distribution and using random normal distribution. In the discrete ECM method, in case of succeeding in a certain number of cycles the step size is increased, otherwise the step size is reduced. In order to determine the efficiency of this method, three benchmark steel frames were optimized due to the resistance and displacement criteria specifications of the AISC-LRFD, and the results were compared to other optimization methods. Considerable outputs of this algorithm show that this method can handle the complex problems of optimizing discrete steel frames.

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Meta-heuristics have received increasing attention in recent years. The present article introduces a novel method in such a class that distinguishes a number of artificial search agents called players within two teams. At each iteration, the active player concerns some other players in both teams to construct its special movements and to get more score. At the end of some iterations (like quarters of a sports game) the teams switch their places for fair play. The algorithm is developed to solve a general purpose optimization problem; however, in this article its application is illustrated on structural sizing design. Switching Teams Algorithm is presented as a parameter-less population-based algorithm utilizing just two control parameters. The proposed method can recover diversity in a novel manner compared to other meta-heuristics in order to capture global optima.

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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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Passive systems are preferred tools for seismic control of buildings challenged by probabilistic nature of the input excitation. However, other types of uncertainty still exist in parameters of the control device even when optimally tuned. The present work concerns optimal design of multiple-tuned-mass-damper embedded on a shear building by a number of meta-heuristics. They include well-known genetic algorithm and particle swarm optimization as well as more recent gray wolf optimizer and its hybrid method embedding swarm intelligence. The study is two-fold: first, optimal designs by different meta-heuristics are compared concerning their reduction in structural seismic responses; second, the effect of uncertainty in Multi-Tuned-Mass-Damper parameters, is studied offering new reliability-based curves. Monte Carlo Simulation is employed to evaluate failure probabilities. A variety of structural responses are assessed against seismic excitation including maximal displacement, velocity and acceleration. It is declared that the best algorithm for efficiency and effectiveness has not coincided the best based on the reliability traces. Such traces also show that in a specific range of limit-states, algorithm selection has a serious effect on the reliability results. It was found even more than 35% and depends on the response type.  

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One of the most crucial problems in geo-engineering is the instability of unsaturated slopes, causing severe loss of life and property worldwide. In this study, five novel meta-heuristic methods are employed to optimize locating the Critical Failure Surface (CFS) and corresponding Factor of Safety (FOS). A Finite Element Method (FEM) code is incorporated to convert the strong form of the Richard’s differential equation to the weak form. More importantly, the derived code can consider both the seismic and seepage conditions additional to the static loading. Eventually, the proposed optimization procedure is validated against benchmark examples and some insights are provided.

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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.

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By incorporating structural engineering, animal husbandry, and veterinary, this interdisciplinary research accomplishes the following two main objectives: 1) design and optimization to reduce the weight of the steel structure skeleton of the stable with ECBO & CBO algorithms; 2) improving the performance of the natural ventilation system in the stable with some changes in the structure's geometric design.
In this study, each algorithm's performance will be investigated in the course of accomplishing the aforementioned objective. Furthermore, using stress ratios by algorithms in each member will be studied. Finally, using the algorithms, a stable steel structure with lower weight is designed.
In this paper, through changing and improving the structure's geometric design, a structure more compatible with the natural ventilation system's requirements is designed. These changes are as follows: 1) design of a taller stable structure; 2) larger design of the air inlets in the joint line between the upper part of the side walls and the lower part of the pitched roof.

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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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Nowadays, energy crisis is one of the most important issues faced by most countries. Given the accommodation of a large population, high-rise buildings have a significant role in creating or resolving this crisis. A recent solution with regard to the optimization and reduction of energy consumption is using smart systems in buildings. In fact, with the help of modern knowledge, smart buildings consume energy in the right place and time. By transforming a simple building into a dynamic one, not only will it be able to adapt to changing environmental conditions, it will also consider the living habits of dwellers and comfort standards in order to provide maximum satisfaction. Moreover, the money spent on making smart appliances will be fully compensated after a short while, saving the overall costs and energy. This descriptive-analytical study, conducted using library resources, e-books and papers, is an attempt to examine the effect of smartization on optimizing and increasing the efficiency of high-rise buildings. The results of comprehensive surveys in various sectors related to smart buildings show that one can optimize energy consumption to take an effective step in solving global energy issues using smart systems in buildings. This study is devoted to energy consumption of smart systems employing an efficient continuous evolutionary meta-heuristic algorithm.