---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

Optimization has always been a human concern from ancient times to the present day, also in light of advances in computing equipment and systems, optimization techniques have become increasingly important in different applications. The role of metaheuristic algorithms in optimizing and solving engineering problems is expanding every day, optimization has also had many applications in water engineering. Every year, the effects of climate change and the water crisis deepen and worsen in many parts of the world, and existing water management becomes much more vital and critical. One of the main centers for water management and control dams reservoirs. In this paper, applying the CBO metaheuristic algorithm, the results of optimization in the operation of the Haraz dam reservoir in northern Iran, which has previously been done with FA and GA algorithms and standard operation system (SOP), are reviewed and compared. With the implementation of the CBO algorithm, all results and key outputs such as program runtime, annual water shortages, and vulnerabilities are much better than previous calculations, all the results are mentioned in the text of the article, but for example, the annual water shortage has reached about 38% of the FA algorithm, about 25% of the GA algorithm and about 13% of the SOP method. The numerical results demonstrate that the CBO algorithm has merits in solving challenging optimization problems and using this innovative algorithm can be an important starting point in the operation of dam reservoirs around the world.

---

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.

---

Metaheuristics are considered the first choice in addressing structural optimization problems. One of the complicated structural optimization problems is the highly nonlinear dynamic truss shape and size optimization with multiple natural frequency constraints. On the other hand, natural frequency constraints are useful to control the responses of a dynamically exciting structure. In this regard, this study uses for the first time the water evaporation optimization (WEO) algorithm to address this problem. Four benchmark trusses are considered for experimental investigation of the WEO. Obtained results indicate the comparative performance of WEO to the best-known algorithms in this problem, high performance in comparison to those of different optimization techniques, and high performance in comparison to all algorithms in terms of robustness. The simulation results clearly show a good balance between the global and local exploration abilities of WEO and its potential robust efficiency for other complicated constrained engineering optimization problems.

---

In this paper, a new robust metaheuristic optimization algorithm called improved time evolutionary optimization (ITEO) is applied to design reinforced concrete one-way ribbed slabs. Geometric and strength characteristics of concrete slabs are considered as design variables. The optimal design is such that in addition to achieving the minimum cost, all design constraints are satisfied under American Concrete Institute’s ACI 318-05 Standard. So, the numerical examples considered in this study have a large number of design variables and design constraints that make it complicated to converge the global optimal design. The ITEO has an excellent balance between the two phases of exploration and extraction and it has a high ability to find the optimal point of such problems. The comparison results between the ITEO and some other metaheuristic algorithms show the proposed method is competitive compared to others, and in some cases, superior to some other available metaheuristic techniques in terms of the faster convergence rate, performance, robustness of finding an optimal design solution, and needs a smaller number of function evaluations for designing considered constrained engineering problems.
 

---

The cycle basis of a graph arises in a wide range of engineering problems and has a variety of applications. Minimal and optimal cycle bases reduce the time and memory required for most of such applications. One of the important applications of cycle basis in civil engineering is its use in the force method to frame analysis to generate sparse flexibility matrices, which is needed for optimal analysis.
In this paper, the simulated annealing algorithm has been employed to form suboptimal cycle basis. The simulated annealing algorithm works by using local search generating neighbor solution, and also escapes local optima by accepting worse solutions. The results show that this algorithm can be used to generate suboptimal and subminimal cycle bases. Compared to the existing heuristic algorithms, it provides better results. One of the advantages of this algorithm is its simplicity and its ease for implementation.
 

---

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).
 

---

Design optimization of cable-stayed bridges is a challenging optimization problem because a large number of variables is usually involved in the optimization process. For these structures the design variables are cross-sectional areas of the cables. In this study, an efficient metaheuristic algorithm namely, momentum search algorithm (MSA) is used to optimize the design of cable-stayed bridges. The MSA is inspired by the Physics and its superiority over many metaheuristics has been demonstrated in tackling several standard benchmark test functions. In the current work, the performance of MSA is compared with that of two other metaheuristics and it is shown that the MSA is an efficient algorithm to tackle the optimization problem of cable-stayed bridges.
 

---

Colliding Bodies Optimization (CBO) is a population-based metaheuristic algorithm that complies physics laws of momentum and energy. Due to the stagnation susceptibility of CBO by premature convergence and falling into local optima, some meritorious methodologies based on Sine Cosine Algorithm and a mutation operator were considered to mitigate the shortcomings mentioned earlier. Sine Cosine Algorithm (SCA) is a stochastic optimization method that employs sine and cosine based mathematical models to update a randomly generated initial population. In this paper, we developed a new hybrid approach called hybrid CBO with SCA (HCBOSCA) to obtain reliable structural design optimization of discrete and continuous variable structures, where a memory was defined to intensify the convergence speed of the algorithm. Finally, three structural problems were studied and compared to some state of the art optimization methods. The experimental results confirmed the competence of the proposed algorithm.
 

---

Optimization methods are essential in today's world. Several types of optimization methods exist, and deterministic methods cannot solve some problems, so approximate optimization methods are used. The use of approximate optimization methods is therefore widespread. One of the metaheuristic algorithms for optimization, the EVPS algorithm has been successfully applied to engineering problems, particularly structural engineering problems. As this algorithm requires experimental parameters, this research presents a method for determining these parameters for each problem and a self-adaptive algorithm called the SA-EVPS algorithm. In this study, the SA-EVPS algorithm is compared with the EVPS algorithm using the 72-bar spatial truss structure and three classical benchmarked functions
 

---

Despite the advantages of the plastic limit analysis of structures, this robust method suffers from some drawbacks such as intense computational cost. Through two recent decades, metaheuristic algorithms have improved the performance of plastic limit analysis, especially in structural problems. Additionally, graph theoretical algorithms have decreased the computational time of the process impressively. However, the iterative procedure and its relative computational memory and time have remained a challenge, up to now. In this paper, a metaheuristic-based artificial neural network (ANN), which is categorized as a supervised machine learning technique, has been employed to determine the collapse load factors of two-dimensional frames in an absolutely fast manner. The numerical examples indicate that the proposed method's performance and accuracy are satisfactory.
 

---

In this paper, three recently improved metaheuristic algorithms are utilized for the optimum design of the frame structures using the force method. These algorithms include enhanced colliding bodies optimization (ECBO), improved shuffled Jaya algorithm (IS-Jaya), and Vibrating particles system - statistical regeneration mechanism algorithm (VPS-SRM). The structures considered in this study have a lower degree of statical indeterminacy (DSI) than their degree of kinematical indeterminacy (DKI). Therefore, the force method is the most suitable analysis method for these structures. The robustness and performance of these methods are evaluated by the three design examples named 1-bay 10-story steel frame, 3-bay 15-story steel frame, and 3-bay 24-story steel frame.
 

---

The main objective of this study is to optimize reinforced concrete (RC) frames in the framework of performance-based design using metaheuristics. Three improved and efficient metaheuristics are employed in this work, namely, improved multi-verse (IMV), improved black hole (IBH) and modified newton metaheuristic algorithm (MNMA). These metaheuristic algorithms are applied for performance-based design optimization of 6- and 12-story planar RC frames. The seismic response of the structures is evaluated using pushover analysis during the optimization process. The obtained results show that the IBH outperforms the other algorithms.
 

---

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.
 

---

Structural topology optimization provides an insight into efficient designing as it seeks optimal distribution of material to minimize the total cost and weight of the structures. This paper presents an optimum design of steel moment frames and connections of structures subjected to serviceability and strength constraints in accordance with AISC-Load and Resistance Factor Design (LRFD). In connection topology optimizations, different beam and column sections and connections and also to optimize two steel moment frames a genetic algorithm was used and their performance was compared. Initially, two common steel moment frames were studied, only for the purpose of minimizing the weight of the structure and the members of structure are considered as design variables. Since the cost of a steel moment frame is not solely related to the weight of the structure, in order to obtain a realistic plan, in the second part of this study, for the other two frames the cost of the connections is also added to the variables. The results indicate that the steel frame optimization by applying real genetic algorithm could be optimal for structural designing. The findings highlighted the prominent performance and lower costs of the steel moment frames when different connections are used.