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Optimal design of large-scale structures is a rather difficult task and the computational efficiency of the currently available methods needs to be improved. In view of this, the paper presents a modified Charged System Search (CSS) algorithm. The new methodology is based on the combination of CSS and Particle Swarm Optimizer. In addition, in order to improve optimization search, the sequence of tasks entailed by the optimization process is changed so that the updating of the design variables can directly be performed after each movement. In this way, the new method acts as a single-agent algorithm while preserving the positive characteristics of its original multi-agent formulation.

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This paper is concerned with application and evaluation of ant colony optimization (ACO) method to practical structural optimization problems. In particular, a size optimum design of pin-jointed truss structures is considered with ACO such that the members are chosen from ready sections for minimum weight design. The application of the algorithm is demonstrated using two design examples with practical design considerations. Both examples are formulated according to provisions of ASD-AISC (Allowable Stress Design Code of American Institute of Steel Institution) specification. The results obtained are used to discuss the computational characteristics of ACO for optimum design of truss type structures.

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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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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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Nature-inspired search algorithms have proved to be successful in solving real-world optimization problems. Firefly algorithm is a novel meta-heuristic algorithm which simulates the natural behavior of fireflies. In the present study, optimum design of truss structures with both sizing and geometry design variables is carried out using the firefly algorithm. Additionally, to improve the efficiency of the algorithm, modifications in the movement stage of artificial fireflies are proposed. In order to evaluate the performance of the proposed algorithm, optimum designs found are compared to the previously reported designs in the literature. Numerical results indicate the efficiency and robustness of the proposed approach.

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The main aim of the present study is to propose a modified harmony search (MHS) algorithm for size and shape optimization of structures. The standard harmony search (HS) algorithm is conceptualized using the musical process of searching for a perfect state of the harmony. It uses a stochastic random search instead of a gradient search. The proposed MHS algorithm is designed based on elitism. In fact the MHS is a multi-staged version of the HS and in each stage a new harmony memory is created using the information of the previous stages. Numerical results reveal that the proposed algorithm is a powerful optimization technique with improved exploitation characteristics compared with the standard HS.

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The present study is an attempt to propose a mutation-based real-coded genetic algorithm (MBRCGA) for sizing and layout optimization of planar and spatial truss structures. The Gaussian mutation operator is used to create the reproduction operators. An adaptive tournament selection mechanism in combination with adaptive Gaussian mutation operators are proposed to achieve an effective search in the design space. The standard deviation of design variables is used as a key factor in the adaptation of mutation operators. The reliability of the proposed algorithm is investigated in typical sizing and layout optimization problems with both discrete and continuous design variables. The numerical results clearly indicated the competitiveness of MBRCGA in comparison with previously presented methods in the literature.

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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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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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Different methods are available for simultaneous optimization of cross-section, topology and geometry of truss structures. Since the search space for this problem is very large, the probability of falling in local optimum is considerably high. On the other hand, different types of design variables (continuous and discrete) lead to some difficulties in the process of optimization. In this article, simultaneous optimization of cross-section, topology and geometry of truss structures is performed by utilizing the Multi Heuristic based Search Method (MHSM) that overcome the above mentioned problem and obtains good results. The presented method performs the optimization by dividing the searching space into five subsections in which an MHSM is employed. These subsections are named procedure islands. Some examples are then presented to scrutinize the method more carefully. Results show the capabilities of the present algorithm for optimal design of truss structures.

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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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A novel optimization algorithm named teaching-learning-based optimization (TLBO) algorithm and its implementation procedure were presented in this paper. TLBO is a meta-heuristic method, which simulates the phenomenon in classes. TLBO has two phases: teacher phase and learner phase. Students learn from teachers in teacher phases and obtain knowledge by mutual learning in learner phase. The suitability of TLBO for size and geometry optimization of structures in structural optimal design was tested by three truss examples. Meanwhile, these examples were used as benchmark structures to explore the effectiveness and robustness of TLBO. The results were compared with those of other algorithms. It is found that TLBO has advantages over other optimal algorithms in convergence rate and accuracy when the number of variables is the same. It is much desired for TLBO to be applied to the tasks of optimal design of engineering structures.

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This paper presents an improved multi-objective group search optimizer (IMGSO) that is based on Pareto theory that is designed to handle multi-objective optimization problems. The optimizer includes improvements in three areas: the transition-feasible region is used to address constraints, the Dealer’s Principle is used to construct the non-dominated set, and the producer is updated using a tabu search and a crowded distance operator. Two objective optimization problems, the minimum weight and maximum fundamental frequency, of four truss structures were optimized using the IMGSO. The results show that IMGSO rapidly generates the non-dominated set and is able to handle constraints. The Pareto front of the solutions from IMGSO is clearly dominant and has good diversity.

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This paper utilizes recent optimization algorithm called Ant Lion Optimizer (ALO) for optimal design of skeletal structures. The ALO is based on the hunting mechanism of Antlions in nature. The random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are main steps for this algorithm. The new algorithm is examined by designing three truss and frame design optimization problems and its performance is further compared with various classical and advanced algorithms.

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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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In this study an efficient meta-heuristic is proposed for layout optimization of truss structures by combining cellular automata (CA) and firefly algorithm (FA). In the proposed meta-heuristic, called here as cellular automata firefly algorithm (CAFA), a new equation is presented for position updating of fireflies based on the concept of CA. Two benchmark examples of truss structures are presented to illustrate the efficiency of the proposed algorithm. Numerical results reveal that the proposed algorithm is a powerful optimization technique with improved convergence rate in comparison with other existing algorithms.

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Vibrating particles system (VPS) is a new meta-heuristic algorithm based on the free vibration of freedom system’ single degree with viscous damping. In this algorithm, each agent gradually approach to its equilibrium position; new agents are generated according to current agents and a historically best position. Enhanced vibrating particles system (EVPS) employs a new alternative procedure to enhance the performance of the VPS algorithm. Two different truss structures are investigated to demonstrate the performance of the VPS and EVPS weight optimization of structures.

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Structural reliability theory allows structural engineers to take the random nature of structural parameters into account in the analysis and design of structures. The aim of this research is to develop a logical framework for system reliability analysis of truss structures and simultaneous size and geometry optimization of truss structures subjected to structural system reliability constraint. The framework is in the form of a computer program called RBO-S>S. The objective of the optimization is to minimize the total weight of the truss structures against the aforementioned constraint. System reliability analysis of truss structures is performed through branch-and-bound method. Also, optimization is carried out by genetic algorithm. The research results show that system reliability analysis of truss structures can be performed with sufficient accurately using the RBO-S>S program. In addition, it can be used for optimal design of truss structures. Solutions are suggested to reduce the time required for reliability analysis of truss structures and to increase the precision of their reliability analysis.

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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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Opposition-based learning was first introduced as a solution for machine learning; however, it is being extended to other artificial intelligence and soft computing fields including meta-heuristic optimization. It not only utilizes an estimate of a solution but also enters its counter-part information into the search process. The present work applies such an approach to Colliding Bodies Optimization as a powerful meta-heuristic with several engineering applications. Special combination of static and dynamic opposition-based operators are hybridized with CBO so that its performance is enhanced. The proposed OCBO is validated in a variety of benchmark test functions in addition to structural optimization and optimal clustering. According to the results, the proposed method of opposition-based learning has been quite effective in performance enhancement of parameter-less colliding bodies optimization.