Optimum Design Of Truss Structures Research Articles

Modified genetic algorithm for optimal design of truss structures

In this paper, topology and shape optimization of truss or frame structures is discussed. The optimization starts from a structure, into which a finite number of nodesare set; all the nodes are connected together by trusses in all possible variants. Unfit variants of the truss system are rejected. Two alternative ways of the optimization are compared: topology optimization starting from initial structure with a larger number of nodes, and topology optimization starting from initial structure with smaller number of nodes but with additional shape optimization of the obtained topology. The topology optimization is solved with original modified genetic algorithm, giving better results in comparison with classical genetic algorithm. Instead of further development of constraint system, the additional step is introduced into algorithm – purification of genotype, which allows complementary improvement of particular population individuals, and together for the optimization process retains more possibilities than stiffening of constraints. The shape optimization is solved by classical genetic algorithm. Both strategies effectively improve the solution, however the common topology/shape optimization requires less computer resources. All numerical examples are obtained with original software developed by the authors.

Shape and size optimization of truss structure by means of improved artificial rabbits optimization algorithm

ABSTRACT The main aim of this article is to use a new metaheuristic algorithm for the optimum design of truss structures. The artificial rabbits optimization (ARO) algorithm is used, in which rabbits’ natural survival strategies, such as detour foraging and random hiding, are considered in developing the main search loop of the algorithm. An improved version, I-ARO, is also proposed, using the diagonal linear uniform (DLU) initialization process instead of conventional random initialization to enhance the overall performance and convergence behaviour of the ARO algorithm. For numerical investigations, five well-known benchmark truss structures with 10, 37, 52, 72 and 120 bars are determined, considering the natural frequencies of the structures as design constraints. I-ARO is shown to be capable of providing better results than the standard ARO and other approaches in the literature. This demonstrates the capability of the DLU initialization method in enhancing the performance of the I-ARO algorithm. Highlights Optimization of truss structures is investigated Improved Artificial Rabbits Optimization (IARO) algorithm is proposed Diagonal Linear Uniform (DLU) initialization process is implemented in IARO

SABO algorithm for optimum design of truss structures with multiple frequency constraints

In this study, a very recently developed intelligent algorithm called the self-adaptive bonomo optimizer (SABO) algorithm is implemented for the size and shape optimizations of the truss structures with the multiple frequency constraints. The bonomo optimizer (BO) algorithm is a recently developed metaheuristic optimization algorithm that imitates the social behavior and reproductive schemes of the bonobos and this algorithm is successfully applied to solve some challenging and highly nonlinear optimization problems. On the other hand, the BO algorithm suffers from the poor exploration and prematurely converges to the non-optimal solutions, especially when dealing with the multi-dimensional optimization problems. In order to overcome these shortcomings, an improved version of this algorithm, the so-called self-adaptive bonomo optimizer (SABO) algorithm, is utilized to optimize the truss structures subjected to the design constraints. The objective of this study is to minimize the weight of the truss structures with the multiple frequency constraints. Five well-known benchmark problems are considered to verify the robustness and reliability of the SABO algorithm. The design results obtained by the SABO algorithm are compared with those previously reported in the literature.

Design Optimization of Truss Structures Using a Graph Neural Network-Based Surrogate Model

One of the primary objectives of truss structure design optimization is to minimize the total weight by determining the optimal sizes of the truss members while ensuring structural stability and integrity against external loads. Trusses consist of pin joints connected by straight members, analogous to vertices and edges in a mathematical graph. This characteristic motivates the idea of representing truss joints and members as graph vertices and edges. In this study, a Graph Neural Network (GNN) is employed to exploit the benefits of graph representation and develop a GNN-based surrogate model integrated with a Particle Swarm Optimization (PSO) algorithm to approximate nodal displacements of trusses during the design optimization process. This approach enables the determination of the optimal cross-sectional areas of the truss members with fewer finite element model (FEM) analyses. The validity and effectiveness of the GNN-based optimization technique are assessed by comparing its results with those of a conventional FEM-based design optimization of three truss structures: a 10-bar planar truss, a 72-bar space truss, and a 200-bar planar truss. The results demonstrate the superiority of the GNN-based optimization, which can achieve the optimal solutions without violating constraints and at a faster rate, particularly for complex truss structures like the 200-bar planar truss problem.

Comparison of Three Chaotic Meta-heuristic Algorithms for the Optimal Design of Truss Structures with Frequency Constraints

The main reasons for the success of using chaos maps in meta-heuristic algorithms are fast optimization of non-linear and non-convex problems. One of these cases is the control of the natural frequencies of structures to prevent the destructive and dangerous phenomenon of resonance. Natural frequencies have useful information about the dynamic behavior of structures, and by applying dynamic constraints, a significant improvement is achieved in the optimal design of structural weight. Applying frequency limits with traditional and gradient-based methods is very difficult and time-consuming, and in most cases, the calculation process stops at local optima. Recent research shows that chaos maps play a major role in escaping from local optima and reaching global optima. By combining these maps with meta- heuristic algorithms, while avoiding premature convergence, the access to global optima is accelerated and improved, and the ideal state of balance between the exploration and exploitation stages is realized. Today, chaotic algorithms are widely accepted by researchers and are considered as a challenging topic. In a recent research, six chaotic meta- heuristic algorithms have been investigated for the formation and improvement of results with the optimal design of truss structures. In this part the chaotic algorithms include Chaotic Water Evaporation Optimization (CWEO), Chaotic Tug-of-War Optimization (CTWO) and Chaotic Thermal Exchange Optimization (CTEO) are examined.

A comparison performance analysis of eight meta-heuristic algorithms for optimal design of truss structures with static constraints

Metaheuristics have been successfully used for solving complex structural optimization problems. Many algorithms are proposed for truss structure size and shape optimization under some constraints. This study considers eight population-based meta-heuristic methods: African Vultures Optimization Algorithm (AVOA), Flow Direction Algorithm (FDA), Arithmetic Optimization Algorithm (AOA), Generalized Normal Distribution Optimization (GNDO), Stochastic Paint Optimizer (SPO), Chaos Game Optimizer (CGO), Crystal Structure Algorithm (CRY) and Material Generation Algorithm (MGO). These meta-heuristics methods are used to optimize the size of three aluminum truss structures. Optimization aims to reduce the weight of the truss members while meeting a set of displacement and stress constraints. The performance of these methods is assessed by solving and optimizing three well-known truss structure benchmarks under some constraints. The results show that the Stochastic Paint Optimizer (SPO) outperforms the other algorithms in terms of accuracy and convergence rate.

ANNA: advanced neural network algorithm for optimisation of structures

The purpose of this study is to develop an advanced neural network algorithm as a new optimisation for the optimal design of truss structures. The central concept of the algorithm is based on biological nerve structures and artificial neural networks. The performance of the proposed method is explored in engineering design problems. Two efficient methods for improving the standard neural network algorithm are considered here. The first is an enhanced initialisation mechanism based on opposite-based learning. The second relies on using a few tunable parameters to provide proper exploration and exploitation abilities for the algorithm, enabling better solutions to be found while the required structural analyses are reduced. The new algorithm's performance is investigated by using five well-known restricted benchmarks to assess its efficiency in relation to the latest optimisation techniques. The outcome of the examples demonstrates that the upgraded version of the algorithm has increased efficacy and robustness in comparison with the original version of the algorithm and some other methods.

Metaheuristic-based optimal design of truss structures using algebraic force method

In the present study, the algebraic force method (AFM) is employed, as the analysis tool, for the optimal design of truss structures using meta-heuristics algorithms. The use of the force method in place of the displacement approach leads to a reduction of the necessary CPU time. In order to compare the performance of the AFM, three planar and spatial well-studied benchmark trusses are being considered. The results show that utilizing the AFM in structural weight optimization when the Degree of Statical Indeterminacy (DSI) is smaller than the Degree of Kinemati Indeterminacy (DKI) results in considerable time-reduction. Also, due to amenability, simplicity, and generality, the AFM can be utilized for discrete structural analysis easier than other classes of force methods. In addition, in this paper, the optimization procedure is conducted by Improved Vibrating Particle System (IVPS) algorithm as a recently developed method.

Bonobo optimizer algorithm for optimum design of truss structures with static constraints

In this study, a very recently developed intelligent algorithm called Bonobo Optimizer (BO) algorithm is implemented for the sizing optimization of the truss structures with discrete and continuous variables. The BO algorithm imitates the social behaviour and reproductive schemes of the bonobos. Like the several other primates, the bonobos also follow the fission–fusion group strategy, where they form several small parties of various sizes and move separately in their territory. The sizing optimization searches for the minimum weight of the truss structures subject to the multiple loading conditions under the required constraints on the member stresses and nodal displacements. Five well-known truss examples with fixed-geometry and up to 160 elements are tested to verify the reliability and the robustness of the BO algorithm. The results clearly indicate that the BO algorithm is a powerful search and optimization technique for the truss structures imposed by the static constraints for the discrete and continuous variables.

A multi-step approach for reliability-based robust design optimization of truss structures

There are two general methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) for the optimal design of structures with non-deterministic variables. In the problem-solving process of both RDO and RBRDO, assessing the probabilistic constraints of the problem and the standard deviation of the structural responses is time-consuming and costly. In this study, by presenting a multi-step approach, for a probable optimal solution, the deterministic constraints are first investigated. Then the limit state functions related to probabilistic constraints are computed based on the mean value of random variables (in the RBRDO problem) and in the step of uncertainties effects simulation on the response of the structure, probabilistic constraints are evaluated (in the RBRDO problem). Designs that not meeting the deterministic constraints or in the unsafe area for the mean values of the random variables are not included in calculating the first and second terms of the objective function and reliability assessment. This leads to reduce the volume of calculations. The Monte Carlo simulation method is used to assess the probabilistic constraints, and the EVPS metaheuristic algorithm is used for the optimization process. Three benchmark trusses of 10, 25, and 72 bars were studied to assess the efficiency of the proposed approach. The first objective function in these problems was the mean weight of trusses and the second objective function was the standard deviation of the displacement of a specific node in a certain direction.

Correction to: Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms

Correction to: Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms

Chaotically Enhanced Meta-Heuristic Algorithms for Optimal Design of Truss Structures with Frequency Constraints

The natural frequencies of any structure contain useful information about the dynamic behavior of that structure, and by controlling these frequencies, the destructive effects of dynamic loads, including the resonance phenomenon, can be minimized. Truss optimization by applying dynamic constraints has been widely welcomed by researchers in recent decades and has been presented as a challenging topic. The main reason for this choice is quick access to dynamic information by examining natural frequencies. Also, frequency constraint relations are highly nonlinear and non-convex and have implicit variables, so using mathematical and derivative methods will be very difficult and time consuming. In this regard, the use of meta-heuristic algorithms in truss weight optimization with frequency constraints has good results, but with the introduction of form variables, these algorithms trap at local optima. In this research, by applying chaos map in meta-heuristic algorithms, suitable conditions have been provided to escape from local optima and access to global optimums. These algorithms include Chaotic Cyclical Parthenogenesis Algorithms (CCPA), Chaotic Biogeography-Based Optimization (CBBO), Chaotic Teaching-Learning-Based Optimization (CTLBO) and Chaotic Particle Swarm Optimization (CPSO), respectively. Also, by using different scenarios, a good balance has been achieved between the exploration and exploitation of the algorithms.

Optimum design of truss structures by Material Generation Algorithm with discrete variables

Optimization is an act of decision-making for reaching a point in which the overall behaviour of the considered system is acceptable by the experts. In this paper, the optimum design of truss structures is considered utilizing the Material Generation Algorithm (MGA) as one of the recently developed metaheuristic algorithms in which the basic and advanced principles of chemistry have been used as an inspirational concept. For numerical investigations, the benchmark problems in the truss optimization field, including the 25-bar, 72-bar and 200-bar truss structures, are used while a penalty method is utilized accordingly for constraint handling purposes. Multiple optimization runs are conducted for statistical purposes, and the results are compared to the results of other metaheuristic algorithms. The obtained results proved that the MGA could provide very acceptable and optimal design sections for the considered problems, which results in the lowest possible weight.

アルゴリズミックデザインによるトラス構造最適化

The algorithmic design is a structural shape design approach based on mathematical functions that consists of several parameters. On the basis of the approach, optimual structural design problems can also be formulated with respect to a relatively limited number of design variables, generating somewhat elegant and complex resultant designs. In the current study, the approach is applied to optimal design of truss structures. We develop a formulation applicable to various types of truss structures. Some computational examples are also demonstrated.

Optimum design of truss structures with frequency constraints by an enhanced particle swarm optimization method with gradient directions based on emigration philosophy

In this article, the combined method of particle swarm optimization (PSO) with gradient directions (PSOG) is further extended to increase the capabilities of exploration and exploitation. Four different enhancements are added to the PSOG, based on emigration ideas. To investigate the power of the presented methods, 29 complicated functions are optimized with several local optima. Then, the suggested approaches are used in structural design problems with multiple frequency constraints containing sizing and shape design variables for two- and three-dimensional truss structures. The results are compared with some of the methods in the literature and the superiority of the suggested techniques is demonstrated.

Algorithm for optimum design of space trusses

Optimization technique helps to minimize the weight of steel structure by identifying the economical sections in structural design. Meta-heuristic algorithms are used for searching minimization of weight design. The main objective of this investigation is to identify the optimum design of truss structures in such a way the cost of the truss structures can be reduced. In the present method, latest Improved Cuckoo Search (ICS) optimization algorithm is used for identifying the economical sections which are used in truss structures such as 4-, 9-, 24-, and 32– bars in order to minimize the weight and cost. The same truss configuration is analysed by using other algorithms and the results of the ICS are compared with other techniques such as Genetic and Artificial bee colony techniques.

Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms

Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms

Harris Hawks Optimization for Optimum Design of Truss Structures with Discrete Variables

This article investigates the use of Harris Hawks Optimization (HHO) to solve planar and spatial trusses with design variables that are discrete. The original HHO has been used to solve continuous design variables problems. However, HHO is formulated to solve optimization problems with discrete variables in this research. HHO is a population-based metaheuristic algorithm that simulates the chasing style and the collaborative behavior of predatory birds Harris hawks. The mathematical model of HHO uses a straightforward formulation and does not require tuning of algorithmic parameters and it is a robust algorithm in exploitation. The performance of HHO is evaluated using five benchmark structural problems and the final designs are compared with ten state-of-the-art algorithms. The statistical outcomes (average and standard deviation of final designs) show that HHO is quite consistent and robust in solving truss structure optimization problems. This is an important characteristic that leads to better confidence in the final solution from a single run of the algorithm for an optimization problem.

Multi-objective optimum design of truss structures using differential evolution algorithms

Multi-objective structural optimization problems (MOSOPs) with two objectives are widely discussed in the literature. Most MOSOPs that refer to trusses are formulated to minimize the weight and the maximum nodal displacement. This paper formulates MOSOPs with several objective functions combined with various formulations. The objective functions are the weight, the natural frequencies of vibration, the maximum nodal displacement, and the critical load factor concerning the structure’s global stability. The design variables are the cross-sectional areas of the bars, the nodal coordinates, and the presence or absence of bars in the final optimized structure. The third evolution step of generalized differential evolution (GDE3), the success history–based adaptive multi-objective differential evolution (SHAMODE) and the success history–based adaptive multi-objective differential evolution with whale optimization (SHAMODE-WO), and the multi-objective meta-heuristic with iterative parameter distribution estimation (MM-IPDE) are the differential evolution algorithms used in this paper. The experiments refer to the 10-, 25-, 56-, 72-, 120-, and 582-bar trusses and a 33-bar ground-structure system. Multi-criteria decision-making (MCDM) is adopted to extract solutions from the Pareto front according to preferences of the decision-maker (DM) used in the ground-structure system. The complete data for each extracted solution are provided, including its optimized topology.

Optimal design of truss structures using a hybrid method based on particle swarm optimizer and cultural algorithm

In the present study, an efficient hybrid algorithm is proposed based on the particle swarm optimizer (PSO) and the cultural algorithm (CA) for the optimal design of truss structures. In this method, the cultural space defined by the CA has been used to improve the PSO method. The cultural space models the cultural information about individuals in the population space. In the so-called particle swarm optimizer cultural (PSOC) algorithm, three modifications are made on the standard PSO. First, the components related to the best memory of each particle are modified according to the range of cultural space. Second, cultural space is used in order to modify the variables violating the allowable range. And third, with the introduction of “Personal Current Bound Strategy (PCBS)”, any unnecessary structural analyzes, that consequently impose a lot of additional cost in the optimization process, are avoided. Therefore, if the particles move in an inappropriate direction, and in case a weaker situation is achieved, the relevant situation will initially be rectified using cultural space, and after ensuring that it has been placed in the upper limits of society, analysis will then be carried out on it. To show the computational advantages of the PSOC, several benchmark examples are presented. The results show that the PSOC algorithm can converge to a better solution and effectively accelerate the convergence rate compared to other variants of PSO and some other well-known metaheuristic methods.