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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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Different kinds of meta-heuristic algorithms have been recently utilized to overcome the complex nature of optimum design of structures. In this paper, an integrated optimization procedure with the objective of minimizing the self-weight of real size structures is simply performed interfacing SAP2000 and MATLAB® softwares in the form of parallel computing. The meta-heuristic algorithm chosen here is Cuckoo Search (CS) recently developed as a type of population based algorithm inspired by the behavior of some Cuckoo species in combination with the Lévy flight behavior. The CS algorithm performs suitable selection of sections from the American Institute of Steel Construction (AISC) wide-flange (W) shapes list. Strength constraints of the AISC load and resistance factor design specification, geometric limitations and displacement constraints are imposed on frames. Effective time-saving procedure using simple parallel computing, as well as utilizing reliable analysis and design tool are also some new features of the present study. The results show that the proposed method is effective in optimizing practical structures.

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To ensure efficient performance of irrigation canals, the losses from the canals need to be minimized. In this paper a modified formulation is presented to solve the optimization model for the design of different canal geometries for minimum seepage loss, in meta-heuristic environment. The complex non-linear and non-convex optimization model for canal design is solved using a probabilistic search algorithm namely Probabilistic Global Search Lausanne (PGSL). The solutions are found to be competitive to those reported in literature while applied for different example problems. To suit for real field applications, three site specific constraints are considered and the sensitivity of solutions for the most popular trapezoidal canals is investigated. The study shows the potential of the proposed approach to perform optimal design of irrigation canals for minimum seepage loss.

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The Big Bang-Big Crunch (BB–BC) method is a relatively new meta-heuristic algorithm which inspired by one of the theories of the evolution of universe. In the BB–BC optimization algorithm, firstly random points are produced in the Big Bang phase then these points are shrunk to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. In this paper, the BB–BC algorithm is presented for optimal cost design of water distribution systems and employed to optimize different types of hydraulic networks with discrete variables. The results demonstrate the efficiency of the proposed method compared to other algorithms.

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The objective of this paper is to present an optimal design for single-layer barrel vault frames via improved magnetic charged system search (IMCSS) and open application programming interface (OAPI). The IMCSS algorithm is utilized as the optimization algorithm and the OAPI is used as an interface tool between analysis software and the programming language. In the proposed algorithm, magnetic charged system search (MCSS) and improved harmony search (IHS) are utilized to achieve a good convergence and good solutions especially in final iterations. The results confirm the efficiency of OAPI as a powerful interface tool in the analysis process of barrel vault structures and also the ability of IMCSS algorithm in fast convergence and achieving optimal results.

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A quick group search optimizer (QGSO) is an intelligent optimization algorithm which has been applied in structural optimal design, including the hinged spatial structural system. The accuracy and convergence rate of QGSO are feasible to deal with a spatial structural system. In this paper, the QGSO algorithm optimization is adopted in seismic research of steel frames with semi-rigid connections which more accurately reflect the practical situation. The QGSO is combined with the constraint from the penalty coefficients and dynamic time-history analysis. The performance of the QGSO on seismic design has been tested on a two-bay five-layer steel frame in this paper. The result shows that, compared with the PSO algorithm, the QGSO algorithm has better performance in terms of convergence rate and the ability to escape from local optimums. Moreover, it is feasible and effective to apply the QGSO to the seismic optimal design of steel framework.

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In the area of semi-active control of civil structures, Magneto-Rheological (MR) damper has been an efficient mechanism for reducing the seismic response of structures. In this paper, an effective method based on defining an optimization problem for designing MR dampers has been proposed. In the proposed method, the parameters of semi-active control system are determined so that the maximum response of structure is minimized. To solve the optimization problem, the Genetic algorithm (GA) has been utilized. The modified Bouc-Wen model has been used to represent the dynamic behavior of MR damper while to determine the input voltage at any time step, the clipped optimal control algorithm with LQR controller has been applied. To evaluate the performance of the proposed method, a ten-storey shear frame subjected to the El-Centro excitation and for two different kinds of objective functions, optimal MR dampers have been designed. Then the performance of optimal MR damper has been tested under different excitations. The results of the numerical simulations have shown the effectiveness of the proposed method in designing optimal MR dampers that have the capability of reducing the response of the structures up to a significant level. In addition, the effect of selecting a proper objective function to achieve the best performance of MR dampers in decreasing different responses of structure has been shown.

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In this paper, optimal design of arch dams is performed under frequency limitations. Colliding Bodies Optimization (CBO), a recently developed meta-heuristic optimization method, which has been successfully applied to several structural problems, is revised and utilized for finding the best feasible shape of arch dams. The formulation of CBO is derived from one-dimensional collisions between bodies, where each agent solution is considered as the massed object or body. The design procedure aims to obtain minimum weight of arch dams subjected to natural frequencies, stability and geometrical limitations. Two arch dam examples from the literature are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the CBO in creating optimal design for arch dams. The results of the examples show that CBO is a powerful method for optimal design of arch dams.

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Grillages are widely used in various structures. In this research, the Colliding Bodies Optimization (CBO) and Enhanced Colliding Bodies Optimization (ECBO) algorithms are used to obtain the optimum design of irregular grillage systems. The purpose of this research is to minimize the weight of the structure while satisfying the design constraints. The design variables are considered to be the cross-sectional properties of the beams and the design constraints are employed from LRFD-AISC. In addition, optimum design of grillages is performed for two cases: (i) without considering the warping effect, and (ii) with considering the warping effect. Also, several examples are presented to show the effect of different spacing and various boundary conditions. Finally, the results show that warping effect, beam spacing and boundary conditions have significant effects on the optimum design of grillages.

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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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This paper presents a novel population-based meta-heuristic algorithm inspired by the game of tug of war. Utilizing a sport metaphor the algorithm, denoted as Tug of War Optimization (TWO), considers each candidate solution as a team participating in a series of rope pulling competitions.  The  teams  exert  pulling  forces  on  each  other  based  on  the  quality  of  the solutions  they  represent.  The  competing  teams  move  to  their  new  positions  according  to Newtonian laws of mechanics. Unlike many other meta-heuristic methods, the algorithm is formulated  in  such  a  way  that  considers  the  qualities  of  both  of  the  interacting  solutions. TWO  is  applicable  to  global  optimization  of  discontinuous,  multimodal,  non-smooth,  and non-convex functions. Viability of the proposed method is examined using some benchmark mathematical functions and engineering design problems. The numerical results indicate the efficiency of the proposed algorithm compared to some other methods available in 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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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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Water distribution networks are one of the important and costly infrastructures of cities and many meta-heuristic algorithms in standard or hybrid forms were used for optimizing water distribution networks. These algorithms require a large amount of computational cost. Therefore, the converging speed of algorithms toward the optimization goal is as important as the goal itself. In this paper, a new method is developed by linking the charged system search algorithm and firefly algorithm for optimizing water distribution networks. For evaluating the proposed method, some popular benchmark examples are considered. Simulation results demonstrate the efficiency of the proposed algorithm compared to others.

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In this paper, a design method is proposed for base isolation system under blast loading that this method is based on transforming design problem into an optimization problem. Genetic algorithm has been employed to solve the optimization problem whereas base isolation system properties have been considered as design variables and a linear combination of base drift and inter-story drift has been defined as objective function. A sensitivity analysis has been also conducted to investigate the effect of base isolation system properties on the blast performance of isolated structure. For numerical simulation, base isolation system is designed using the proposed method for controlling the response of an eight-story nonlinear shear-type building frame under blast loading. It has been found from the results that base isolation system is an effective control system under blast loading that its performance is dependent on the base isolation system characteristics especially the base mass. The optimization results also show that base isolation system designed using the proposed method is a well-designed control system for mitigating the blast response of structure and the proposed design method can be considered as an effective design approach under blast loading.

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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 article, an Advanced Charged System Search (ACSS) algorithm is applied for the optimum design of steel structures. ACSS uses the idea of Opposition-based Learning and Levy flight to enhance the optimization abilities of the standard CSS. It also utilizes the information of the position of each charged particle in the subsequent search process to increase the convergence speed. The objective function is to find a minimum weight by choosing suitable sections subjected to strength and displacement requirements specified by the American Institute of Steel Construction (AISC) standard subject to the loads defined by Load Resistance Factor Design (LRFD). To show the performance of the ACSS, four steel structures with different number of elements are optimized. The results, efficiency, and accuracy of the ACSS algorithm are compared to other meta-heuristic algorithms. The results show the superiority of the ACSS compared to the other considered algorithms.

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This article presents a new meta-heuristic optimization algorithm based on the power of human thinking and decision-making, which will be called Gold Rush Optimization (GRO). The thinking and decision-making ability of humans were used in this paper to develop a approach to create an optimization method. The hypothetical interaction between human operators in search of gold, based on the sound volume received from metal detectors, was used to develop the method. Benchmark functions, engineering design examples, and truss structures (which were optimized using different algorithms previously) were used for validation and verification of the proposed algorithm. MATLAB was used for programming. The CEC 2005 benchmark functions obtained reached the global target minimum, and the numerical engineering and truss examples were improved compared to the previous algorithms. Therefore, the proposed algorithm can be used as an alternative for the previously developed meta-heuristic optimization algorithms, which can be used in all optimization fields.

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The impact damper is a passive method for controlling vibrations of dynamic systems. It is designed by placing one or several masses in a container, which is installed on the structure. Damping performance is affected by many parameters, such as the mass ratio of the primary structure, size, number, and material of the particles, friction and restitution coefficients of the particles and gap distance. Impact damper is effective, economical, and practical and its functionality can be further enhanced by an optimal design. In this paper, first, the mathematical modeling of a rigid impact damper used in free vibration reduction of a single degree of freedom (SDOF) system is performed. The results on this step are validated with those results of previous studies, and a good agreement is achieved. Next, the robust hybrid optimization method that is called Imperialist Competitive Ant Colony Optimization (ICACO) is introduced. After that, the damper function is optimized using ICACO, and the optimum values of the effective parameters for maximizing damping effectiveness are obtained. Comparing the results of the optimized and the basic designs shows that the optimization method is robust and the optimal results are practical. The optimum design of damper parameters using ICACO method can damp more than %94 of the system’s initial energy in a short time.

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This paper introduces a reliability-based multi-objective design method for spatial truss structures. A multi-objective optimization problem has been defined considering three conflicting objective functions including truss weight, nodal deflection, and failure probability of the entire truss structure with design variables of cross sectional area of the truss members. The failure probability of the entire truss system has been determined considering the truss structure as a series system. To this end, the uncertainties of the applied load and the resistance of the truss members have been accounted by generating a set of 50 random numbers. The limitations of members' allowable have been defined as constraints. To explain the methodology, a 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the game theory concept and genetic algorithm (GA). The results show effectiveness and simplicity of the proposed method which can provide Pareto optimal solution. These optimal solutions can provide both safety and reliability for the truss structure.