Optimization Of Truss Structures Research Articles

Combined Size and Shape Optimization of Truss Structures Using the Heap-Based Optimizer (HBO) Algorithm

Combined Size and Shape Optimization of Truss Structures Using the Heap-Based Optimizer (HBO) Algorithm

Optimization of truss structures using multi-objective cheetah optimizer

In this study, a multi-objective version of the recently proposed cheetah optimizer called multi-objective cheetah optimizer (MOCO) has been proposed. MOCO draws inspiration from the targeted hunting strategy employed by cheetahs, which involves a sequence of actions: searching for prey, patiently waiting for the right moment to attack, swiftly launching the attack, and then retreating from the prey and returning to their habitat. MOCO is the result of modification and enhancement from its single-objective counterpart, utilizing a Pareto dominance-based approach. This adaptation allows MOCO to efficiently handle multiple objectives, explores and exploits promising areas in the optimization landscape, and identifies non-dominated solutions, offering valuable tradeoff choices for decision-makers. To demonstrate its practical applications, the MOCO method has been employed to address five intricate structural design problems. These problems involve a pair of competing objectives: the minimization of structural weight and the reduction of maximum nodal displacement. To gauge the efficacy and efficiency of the proposed algorithm, a comparative analysis is conducted against three alternative state-of-the-art multi-objective algorithms. Furthermore, a rigorous evaluation is carried out utilizing hypervolume testing. The findings reveal that the MOCO algorithm surpasses the performance of the other algorithms, underscored by its capacity to uncover a diverse array of non-dominated solutions. To delve deeper into the experimental results, statistical analysis employing Friedman’s rank test is employed. The solutions generated and the convergence patterns exhibited by the MOCO approach underscore its exceptional proficiency in resolving intricate design problems.

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Layout optimization of truss structures by an improved Prairie Dog algorithm integrated with a monitored convergence curve

Layout optimization of truss structures by an improved Prairie Dog algorithm integrated with a monitored convergence curve

A novel binomial strategy for simultaneous topology and size optimization of truss structures

The current work introduces a new probability-based regulatory mechanism for the simultaneous size and topology optimization of truss structures. The proposed mechanism, by leveraging the Boolean nature of the topological variables, attempts to forecast the behaviour of the search algorithm and emphasizes either topology or size actions to reduce the number of ineffective iterations. The importance of this task becomes more evident in further iterations since the optimal (or nearly optimal) structure topology is identified, and improper elimination of any member can result in infeasible mechanisms and lead to a waste of several iterations. To assess the effectiveness of the proposed auxiliary module, it is integrated with different optimization algorithms to solve distinct size and topology problems. The results demonstrate that this not only enhances the accuracy of the algorithms but also significantly reduces the required computational cost.

Size Optimization of Truss Structures Based on Genetic Algorithm by Developing Single-point Crossover with Bit-wise Mutation Using FORTRAN Programming

A truss is a collection of axially loaded structural elements connected through pin joints. Optimization of truss structures indicates the determination of best possible conditions that are necessary for achieving the most economical design in terms of lowest possible weights of the truss elements. According to recent studies, Size, Topology and Shape based optimizations are the three possible independent optimization scopes for finding the optimum weight of a truss. The current study focuses on the size optimization of truss structure and aims to identify the most cost-effective sections of the truss using a powerful evolutionary optimization technique named as Genetic Algorithm (GA). Here single point cross over method and bit wise mutation operator are adopted for expanding the search space with the assigned displacement and stress constraints. Fortran based sub routines are developed for each individual steps of GA such as fitness evaluation, selection, cross-over and mutation. Finaly the complete program is run for validation of its outcome. While comparing with the solution of an existing literature regarding a minimization of objective function having two design variables the outcomes tend to show a good correlation. Further, the study is extended for the weight minimization of two widely used truss having 10 members and 17 members respectively with standard Finite Element Method of analysis. Minimum weight of each truss is obtained via convergence plot and compared with the existing literatures. With this simple but efficient global optimization technique optimum weight of truss structure can easily be achieved.

Sizing and Shape Optimization of Discrete Truss Employing a Target-Oriented Krill Herd Algorithm

Abstract The krill herd (KH) algorithm is widely used for optimizing truss structures as no gradient information is necessary, and only a few parameters require adjustment. However, when the truss structure becomes discrete and complex, KH tends to fall into a local optimum. Therefore, a novel target-oriented KH (TOKH) algorithm is proposed in this study to optimize the design of discrete truss structures. Initially, a crossover operator is established between the “best krill” and “suboptimal krill” to generate a robust “cross krill” for global exploration. Additionally, an improved local mutation and crossover (ILMC) operator is introduced to fine-tune the “center of food” and candidate solutions for local exploitation. The proposed method and other optimization approaches are experimentally compared considering 15 benchmark functions. Then, the performance of the TOKH algorithm is evaluated based on four discrete truss structure optimization problems under multiple loading conditions. The obtained optimization results indicate that the proposed method presents competitive solutions in terms of accuracy, unlike other algorithms in the literature, and avoids falling into a local minimum.

Research and Application of Topology Optimisation Design of Truss Structures

Truss structure is a common structural form. The optimal design of truss structure has important research significance. The main purpose of this paper is to discuss the method and practice of optimal design of truss structure in order to improve the efficiency and economy of structure. This paper introduces the basic concept of truss structure optimization design, and three types optimization design methods including shape optimization, size optimization and topology optimization. Then the topology optimization design is focused on in this paper. Firstly, the solid isotropic material point method in topology optimization is introduced. Then, combined with a practical engineering case, the application of topology optimization design in truss structure is analyzed and studied. The results show that the optimized truss design has good application effect in practical engineering. By considering the structural performance, cost and environmental impact, a more efficient, economical and environmentally friendly truss structure design can be achieved.

Effects of Limiting the Number of Different Cross-Sections Used in Statically Loaded Truss Sizing and Shape Optimization.

This research aims to show the effects of adding cardinality constraints to limit the number of different cross-sections used in simultaneous sizing and shape optimization of truss structures. The optimal solutions for sizing and shape optimized trusses result in a generally high, and impractical, number of different cross-sections being used. This paper presents the influence of constraining the number of different cross-sections used on the optimal results to bring the scientific results closer to the applicable results. The savings achieved using the cardinality constraint are expected to manifest in more than just the minimization of weight but in all the other aspects of truss construction, such as labor, assembly time, total weld length, surface area to be treated, transport, logistics, and so on. It is expected that the optimal weight of the structures would be greater than when not using this constraint; however, it would still be below conventionally sized structures and have the added benefits derived from the simplicity and elegance of the solution. The results of standard test examples for each different cardinality constraint value are shown and compared to the same examples using only a single cross-section on all bars and the overall optimal solution, which does not have the cardinality constraint. An additional comparison is made with results of just the sizing optimization from previously published research where authors first used the same cardinality constraint.

Development of a non-uniform cellular automata framework for sizing, topology and layout optimization of truss structures

This article presents a bi-level non-uniform cellular automata (CA) algorithm for the solution of sizing, topology and layout optimization of truss structures. The non-uniform CA was successfully used in a previous study to solve the weight optimization problem of truss structures for topology and sizing (El Bouzouiki, Sedaghati, and Stiharu 2021. Computers & Structures 242: 106394). In this article, an extended version of the non-uniform CA algorithm is proposed, based on the fully stressed design approach and the distribution of strain energy within the structure, to find the optimal position of the cell’s (joint’s) coordinates. The proposed non-uniform CA algorithm can solve the minimum weight optimization problem of truss structures subjected to both stress and displacement constraints. Several benchmark problems are presented to demonstrate the efficiency and accuracy of the proposed methodology.

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

Topology optimization of truss structures considering local buckling stability

This paper proposes the double-layer optimization algorithm to solve the truss topology problem with bar local buckling constraints. With this algorithm, the constraints on the local buckling are treated as linear functions of the optimized variables, which ensures efficient computation. In addition, two practical algorithms are proposed to solve the problems of the existence of transient hinges and the difficulty in matching the bar sections with standard sections. In addition, the topology optimization plug-in, named Topaz, is developed in this paper in the Rhino-Grasshopper parametric modeling platform to facilitate rapid model building. Finally, numerical examples show that the optimization results satisfy the requirements of strength, local buckling, and slenderness ratio of the bar, which demonstrates the effectiveness of the proposed algorithm.

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

Multi-objective optimization of truss structure using multi-agent reinforcement learning and graph representation

This paper presents a novel method for multi-objective optimization of truss design utilizing multi-agent reinforcement learning and graph representation. The agents are trained to modify solutions to increase the hypervolume and spread the distribution of the non-dominated solutions. This iterative modification is modeled as a Markov game where multiple agents interact with the environment by changing the state of the environment, i.e., the solution and the current non-dominated solutions. Agents observe data representations of the state, modify each solution in the current non-dominated solutions, and receive their reward based on the improvement of the current non-dominated solutions. Each agent is modeled by the multi-agent deep deterministic gradient consisting of a policy function that predicts actions from its observation data and a value function that estimates rewards from the observation data, its action, and the actions of the other agents. The non-dominated solutions are represented as graph data and observed by the agents as the observation data through graph representation. The proposed method is applied to three multi-objective optimization problems: (1) a simple mathematical problem, (2) a 10-bar truss problem to minimize the structural volume and the displacement, and (3) trade-off designs of trusses to minimize the structural volume and bring the shape closer to the target shape. These numerical examples show the versatility of the trained agents to obtain superior solutions in practical structural optimization problems, compared to a conventional method.

A new decomposition-based multi-objective symbiotic organism search algorithm for solving truss optimization problems

This study presents a comprehensive study on the potential and efficacy of decomposition-based multi-objective symbiotic organism search (MOSOS/D) algorithm for truss structure optimization. The investigation is carried out on five benchmark truss structures, e.g., 37-bar, 60-bar, 72-bar, 120-bar, and 200-bar truss problems. The optimization performance of MOSOS/D is compared with other established algorithms, such as Multi-Objective Evolutionary Algorithm Based on Decomposition, Non-Dominated Sorting Genetic Algorithm-II, Multi-Objective Equilibrium Optimizer, Multi-Objective Marine Predator Algorithm, Decomposition-Based Multi-Objective Heat Transfer Search, Multi-Objective Passing Vehicle Search, Multi-Objective Evolutionary Algorithm Based on Decomposition Differential Evaluation, Multi-Objective Symbiotic Organisms Search, and Multi-Objective Multi-Verse Optimizer considering several metrics, including Generational Distance, Spacing, Spread, Inverted Generational Distance, Hypervolume and Runtime. The findings demonstrate MOSOS/D’s competitiveness in providing non-dominated solutions with less space between them. It also achieves a good balance between convergence and coverage and, thus, delivers diverse solutions with less computational complexity. However, the efficiency of the MOSOS/D algorithm varies depending on the complexity of the considered truss structure, with some algorithms occasionally outperforming it in one or two aspects for specific benchmarks. This study provides valuable insights to engineers and designers aiming to achieve optimal truss structure design.

Topology optimization of truss structure under load uncertainty with gradient‑free proportional topology optimization method

This study proposes a method for truss topology optimization (TO) that incorporates uncertain static and dynamic loads based on the efficient gradient‑free proportional topology optimization (PTO) method. The uncertain loads are modeled using probabilistic parameters and the objective function is constructed as the mean structural compliance with the constraint is imposed to the structural material volume. The univariate dimension reduction method and Gauss-type (UDRG) quadrature are used to quantify and propagate the load uncertainty to estimate the objective function. By the UDRG method, the TO of truss structures under uncertain loads can be transformed into a simple deterministic problem. To obviate the necessity for sensitivity analysis, the PTO method with comparable accuracy and efficiency as the gradient-based method is used. The proposed methodology is corroborated through multiple illustrative examples, which also serve to elucidate the ramifications of load uncertainty on optimized truss designs.

Optimization of Truss Structures by Using a Hybrid Population-Based Metaheuristic Algorithm

Optimization of Truss Structures by Using a Hybrid Population-Based Metaheuristic Algorithm

Swarm-based search algorithms: A comparative study on sizing optimization of truss structures

Metaheuristic algorithms belong to the category of non-deterministic optimization methods. Extensive research conducted in this domain has elucidated that each of these methods possesses distinctive merits and demerits. To illustrate, one algorithm may exhibit a notable penchant for exploration, whereas another algorithm may demonstrate exceptional prowess in exploitation. The judicious selection of a suitable and efficient algorithm for a given problem can profoundly influence both the rate of convergence and the level of accuracy. Over the past few decades, various swarm-based metaheuristic algorithms have been introduced in technical literature. Consequently, undertaking a comprehensive comparative evaluation of a subset of these methodologies can furnish researchers with an essential framework to discern the most appropriate algorithm for their objectives. The current investigation focuses on evaluating and comparing four swarm-based metaheuristic algorithms especially on solving size optimization of truss structures for this purpose. To cover the research conducted in the past two decades as comprehensively as possible, a hierarchical selection process was employed for choosing the methods. As a result, the following algorithms were chosen Firefly Algorithm (FA), Drosophila Food-search Algorithm (DFO), Harris Hawk Optimization (HHO), and Butterfly Optimization Algorithm (BOA). Various characteristics of the selected algorithms, such as convergence rate, diversity variation, complexity, and accuracy of the final solutions, were compared. The findings indicate Harris Hawk Optimization (HHO) could nearly outperform the other selected methods on solving structural size optimization problems.

Neural network-enabled discovery of mapping between variables and constraints for autonomous repair-based constraint handling in multi-objective structural optimization

Repairing infeasible solutions is a seldomly used constraint handling technique (CHT) in optimization because, with this technique, users must define ways to prevent constraint violation, which is difficult or impossible in many situations. To overcome this challenge, in this paper we propose an approach based on artificial neural networks to automatically discover variable-constraint mapping that specifies which variables must be modified if a constraint is violated. We embed this procedure into a recent repair-based CHT that uses members of the current population, either feasible or infeasible, to determine the new value for the repaired variables. Here, the CHT is modified to repair each constraint separately using a different solution that does not violate the same constraint. The entire technique is fully autonomous, meaning that a user does not provide any insights into the problem. The modified CHT is implemented in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and compared with four other multi-objective optimization algorithms and a few CHTs. Four test problems are considered: a mathematical benchmark problem, two truss problems and structural optimization of a chemical tanker. The tanker case is a real-world optimization problem with 94 variables and 376 nonlinear constraints. A minimum of 30 independent runs are performed with each algorithm, and various statistical results are shown. With the proposed automated mapping, the modified repair-assisted NSGA-II obtains significantly better results than NSGA-II with other CHTs on all test problems while outperforming all other algorithms and CHTs for the tanker.

Weight Optimization of Discrete Truss Structures Using Quantum-Based HS Algorithm

Recently, a new field that combines metaheuristic algorithms and quantum computing has been created and is being applied to optimization problems in various fields. However, the application of quantum computing-based metaheuristic algorithms to the optimization of structural engineering is insufficient. Therefore, in this paper, we tried to optimize the weight of the truss structure using the QbHS (quantum-based harmony search) algorithm, which combines quantum computing and conventional HS (harmony search) algorithms. First, the convergence performance according to the parameter change of the QbHS algorithm was compared. The parameters selected for the comparison of convergence performance are QHMS, QHMCR, QPAR, ϵ, and θr. The selected parameters were compared using six benchmark functions, and the range for deriving the optimal convergence performance was found. In addition, weight optimization was performed by applying it to a truss structure with a discrete cross-sectional area. The QbHS algorithm derived a lower weight than the QEA (quantum-inspired evolutionary algorithm) and confirmed that the convergence performance was better. A new algorithm that combines quantum computing and metaheuristic algorithms is required for application to various engineering problems, and this effort is essential for the expansion of future algorithm development.