Truss Optimization Research Articles

A new stochastic global algorithm for critical load optimization of dome trusses

A new stochastic global algorithm for critical load optimization of dome trusses

Optimal truss design with MOHO: A multi-objective optimization perspective.

This research article presents the Multi-Objective Hippopotamus Optimizer (MOHO), a unique approach that excels in tackling complex structural optimization problems. The Hippopotamus Optimizer (HO) is a novel approach in meta-heuristic methodology that draws inspiration from the natural behaviour of hippos. The HO is built upon a trinary-phase model that incorporates mathematical representations of crucial aspects of Hippo's behaviour, including their movements in aquatic environments, defense mechanisms against predators, and avoidance strategies. This conceptual framework forms the basis for developing the multi-objective (MO) variant MOHO, which was applied to optimize five well-known truss structures. Balancing safety precautions and size constraints concerning stresses on individual sections and constituent parts, these problems also involved competing objectives, such as reducing the weight of the structure and the maximum nodal displacement. The findings of six popular optimization methods were used to compare the results. Four industry-standard performance measures were used for this comparison and qualitative examination of the finest Pareto-front plots generated by each algorithm. The average values obtained by the Friedman rank test and comparison analysis unequivocally showed that MOHO outperformed other methods in resolving significant structure optimization problems quickly. In addition to finding and preserving more Pareto-optimal sets, the recommended algorithm produced excellent convergence and variance in the objective and decision fields. MOHO demonstrated its potential for navigating competing objectives through diversity analysis. Additionally, the swarm plots effectively visualize MOHO's solution distribution of MOHO across iterations, highlighting its superior convergence behaviour. Consequently, MOHO exhibits promise as a valuable method for tackling complex multi-objective structure optimization issues.

Gate-Based Variational Quantum Algorithm for Truss Structure Size Optimization Problem

Quantum computing has become a pivotal innovation in computational science, offering novel avenues for tackling the increasingly complex and high-dimensional optimization challenges inherent in engineering design. This paradigm shift is particularly pertinent in the domain of structural optimization, where the intricate interplay of design variables and constraints necessitates advanced computational strategies. In this vein, the gate-based variational quantum algorithm utilizes quantum superposition and entanglement to improve search efficiency in large solution spaces. This paper delves into the gate-based variational quantum algorithm for the discrete variable truss structure size optimization problem. By reformulating this optimization challenge into a quadratic, unconstrained binary optimization framework, we bridge the gap between the discrete nature of engineering optimization tasks and the quantum computational paradigm. A detailed algorithm is outlined, encompassing the translation of the truss optimization problem into the quantum problem, the initialization and iterative evolution of a quantum circuit tailored to this problem, and the integration of classical optimization techniques for parameter tuning. The proposed approach demonstrates the feasibility and potential of quantum computing to transform engineering design and optimization, with numerical experiments validating the effectiveness of the method and paving the way for future explorations in quantum-assisted engineering optimizations.

A hyper-heuristic algorithm via proximal policy optimization for multi-objective truss problems

This paper proposes a hyper-heuristic evolutionary algorithm via proximal policy optimization, named HHEA-PPO, for solving multi-objective truss optimization problems. HHEA-PPO has a two-layer structure: a high-level strategy and low-level heuristics. The high-level strategy consists of proximal policy optimization, while the low-level heuristics consist of ten predefined heuristic operators. During the iteration process, the high-level strategy selects the most promising low-level heuristic according to the state of the individuals and the population. To maintain the convergence and distribution of the external Pareto archive, a dynamic crowding distance mechanism is employed. HHEA-PPO is applied to eight multi-objective truss optimization problems and compared with thirteen state-of-the-art optimization algorithms in terms of success rate, average computation duration, and average fitness evaluations to evaluate its performance. The results show that HHEA-PPO has higher search efficiency and greater stability, demonstrating its ability to solve large-scale engineering design problems.

An efficient decoder for size optimization of trusses with automatic member grouping

This paper presents an efficient decoding method (namely SORTED decoding) for the de facto encoding in size optimization of trusses with automatic member grouping. The efficiency of the proposed method is evaluated through numerical experiments driven by two metaheuristic algorithms of different search mechanisms: Colliding Bodies Optimization and Jaya Algorithm. The first group of experiments show that the SORTED decoding method significantly outperforms the de facto and the two other decoding methods introduced in this study (ACCUMULATED and SORTED-ACCUMULATED) in terms of solution quality; moreover, the authors proved that the superiority of the SORTED decoding is not algorithm-dependent. Considerably better member-grouping configurations that provide up to 15% material economy are discovered for some of the well-known pre-grouped benchmark problems in the second group of experiments; surprisingly, the worst member-grouping configuration discovered by the SORTED decoding for one of the problems is better than that of the pre-grouped version.

Adaptive member adding for truss topology optimization: application to elastic design

This paper provides a rigorous and computationally efficient means of identifying compliance-based optimal truss topologies from high-resolution ground structures—problems involving over 30 million potential elements can be solved in under 1 h on a typical laptop. The adaptive ‘member adding’ approach is shown to provide significant savings in computational time and memory usage compared to directly solving the full optimization problem, whilst obtaining the same optimal solution; this paper presents the first application of this powerful principle to the well-known linear-elastic design problem. The computational advantages are particularly notable for multiple load-case problems, as the numerical structure of these cannot be effectively exploited without understanding of the physical nature of the problem. For such cases, the member adding process reduces the computational time required from approximately O(m2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(m^2)$$\\end{document} to O(m), where m is the number of potential elements; here, the time required is reduced by a factor of up to 60 for the relatively small problems that could be solved with both approaches. By using the member adding approach, compliance-optimized structures are obtained at a significantly higher resolution than has previously been possible. The findings of this paper have the potential to deliver a step change in the size of problems that can be solved in compliance-based truss topology optimization, and an accompanying Python code is provided to facilitate this.

Structural Optimization of Trusses in Building Information Modeling (BIM) Projects Using Visual Programming, Evolutionary Algorithms, and Life Cycle Assessment (LCA) Tools

The optimal structural design is imperative in order to minimize material consumption and reduce the environmental impacts of construction. Given the complexity in the formulation of structural design problems, the process of optimization is commonly performed using artificial intelligence (AI) global optimization, such as the genetic algorithm (GA). However, the integration of AI-based optimization, together with visual programming (VP), in building information modeling (BIM) projects warrants further investigation. This study proposes a workflow by combining structure analysis, VP, BIM, and GA to optimize trusses. The methodology encompasses several steps, including the following: (i) generation of parametric trusses in Dynamo VP; (ii) performing finite element modeling (FEM) using Robot Structural Analysis (RSA); (iii) retrieving and evaluating the FEM results interchangeably between Dynamo and RSA; (iv) finding the best solution using GA; and (v) importing the optimized model into Revit, enabling the user to perform simulations and engineering analysis, such as life cycle assessment (LCA) and quantity surveying. This methodology provides a new interoperable framework with minimal interference with existing supply-chain processes, and it will be flexible to technology literacy and allow architectural, engineering and construction (AEC) professionals to employ VP, global optimization, and FEM in BIM-based projects by leveraging open-sourced software and tools, together with commonly used design software. The feasibility of the proposed workflow was tested on benchmark problems and compared with the open literature. The outcomes of this study offer insight into the opportunities and limitations of combining VP, GA, FEA, and BIM for structural optimization applications, particularly to enhance structural efficiency and sustainability in construction. Despite the success of this study in developing a workable, user-friendly, and interoperable framework for the utilization of VP, GA, FEM, and BIM for structural optimization, the results obtained could be improved by (i) increasing the callback function speed between Dynamo and RSA through specialized application programming interface (API); and (ii) fine-tuning the GA parameters or utilizing other advanced global optimization and supervised learning techniques for the optimization.

Enhanced differential evolution-Rao optimization with distance comparison method and its application in optimal sizing of truss structures

A new decision-making approach based on distance measures is established in this study to effectively reduce unnecessary structural analyses in performing truss optimization by metaheuristic algorithms. This approach termed distance comparison (DiC) judges a new design candidate as worth evaluating by using its distance from the best solution. The new candidate solution will be omitted without evaluating it if it is not closer to the best solution than the one being compared. The DiC method is integrated with a novel hybrid metaheuristic based on differential evolution (DE) and the Rao algorithm. In the proposed hybrid strategy, a modified Rao algorithm and an enhanced DE are applied adaptively based on the population diversity to utilize the advantage of each one for a specific stage of the optimization process. Six truss sizing examples with continuous variables, including the 10-bar and 200-bar planar trusses and the 25-bar, 72-bar, 120-bar, and 942-bar spatial trusses, are examined to evaluate the effectiveness of the proposed method. Numerical results demonstrate that DiC significantly reduces the number of structural analyses. Moreover, the performance of the proposed hybrid metaheuristic algorithm conducted on the examples is better than that of some state-of-the-art metaheuristic algorithms.

Efficient design of sandwich panels with cellular truss cores and large phononic band gaps using surrogate modeling and global optimization

Recent advancements in additive manufacturing technologies and topology optimization techniques have catalyzed a transformative shift in the design of architected materials, enabling increasingly complex and customized configurations. This study delves into the realm of engineered cellular materials, spotlighting their capacity to modulate the propagation of mechanical waves through the strategic creation of phononic band gaps. Focusing on the design of sandwich panels with cellular truss cores, we aim to harness these band gaps to achieve pronounced wave suppression within specific frequency ranges. Our methodology combines surrogate modeling with a comprehensive global optimization strategy, employing three machine learning algorithms—k-Nearest Neighbors (kNN), Random Forest Regression (RFR), and Artificial Neural Networks (ANN)—to construct predictive models from parameterized finite element (FE) analyses. These models, once trained, are integrated with Particle Swarm Optimization (PSO) to refine the panel designs. This approach not only facilitates the discovery of optimal truss core configurations for targeted phononic band gaps but also showcases a marked increase in computational efficiency over traditional optimization methods, particularly in the context of designing for diverse target frequencies.

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.

Research on Economic Optimization Scheme of Pratt Truss Bridge

Economy is an important factor in bridge construction. The economic optimization of truss bridge is of great significance to improving the economic benefit of bridge construction. However, the safety and stability in bridge construction are often valued in traditional truss Bridges, and its economy is often ignored. The purpose of this paper is to study the economic optimization of Pratt truss bridge with 120 m span, 8m and node length of 6m, 10m and 12m respectively. The study of establishing two-dimensional model using structural mechanics solver shows that when the total length of the Pratt truss node is 12m, the total volume of the truss is the smallest, that is, the least materials are used, and the linear relationship between the bridge span and the node length is established to a certain extent. The results of this study provide an effective reference for the economic optimization of similar truss bridge structures.

System-reliability-based sizing and shape optimization of trusses considering millions of failure sequences

System-Reliability-Based Design Optimization (S-RBDO) of structures considering progressive collapse is a complex problem, as the number of potential failure sequences increases geometrically with the degree of static indeterminacy of the structure. Existing methods for identifying failure sequences in structural systems are computationally expensive and prone to missing some critical failure sequences, especially within an optimization framework. In this context, identifying the most critical failure sequences to simplify the problem is fundamental. Herein, we propose a novel system-reliability-based framework for sizing and shape optimization of trusses. The procedure identifies minimal cut sets using the recently developed null space method, which has been proven more efficient than traditional failure path-based methods. The most probable failure sequence is selected from each identified minimal cut set. System reliability is estimated using the dominant failure sequences for the whole structure, selected based on their correlations using the Probabilistic Network Evaluation Technique (PNET). Craziness-Based Particle Swarm Optimization (CRPSO) is employed as the optimization algorithm. Numerical examples involving hundreds to millions of failure sequences demonstrate applicability and efficiency of the proposed framework on truss optimization problems with different material post-failure behaviors. Results suggest that, in a system-reliability analysis considering progressive collapse, the most critical failure sequences are those obtained from minimal cut sets. Furthermore, results show that the procedure proposed herein can outperform other frameworks based on traditional failure path-based methods. Simple truss sizing and shape optimization is considered herein, but the conclusions have immediate relevance to the optimal design of realistic structures considering progressive collapse.

Non-parametric data-driven approach to reliability-based topology optimization of trusses under uncertainty of material constitutive law

Non-parametric data-driven approach to reliability-based topology optimization of trusses under uncertainty of material constitutive law

Differential Evolution with perturbation mechanism and covariance matrix based stagnation indicator for numerical optimization

Differential Evolution (DE), as a promising population-based stochastic optimization algorithm, has drawn attention from researchers of various fields owing to its simple operation, strong robustness and few control parameters. However, classic DE suffers from drawbacks such as premature convergence and stagnation resulted from reduced population diversity when tackling complicated optimization problems with high dimensions. To mitigate these deficiencies, Differential Evolution with Perturbation mechanism and Covariance Matrix based stagnation indicator (PCM-DE) is proposed in this paper. There are three main modifications in the algorithm. First, a two-phase parameter adaptation strategy based on fitness value is proposed to guide the search towards promising direction according to different stages of evolution. Second, a perturbation mechanism for archived population is proposed, where a new weight coefficient is defined by exploiting information of fitness value and position in archived individuals. Third, a stagnation indicator based on covariance matrix is proposed to assess the population diversity and the information of variance is employed to perturb stagnant individuals. To validate the effectiveness of PCM-DE, it is compared with several state-of-the-art DE variants and non-DE based algorithms under a large test suite containing 100 benchmark functions. Besides, three truss optimization problems are also employed to verify the feasibility and scalability of the algorithm. The experiment results confirm its highly competitive performance in terms of solution accuracy and convergence speed.

Improved Sine-cosine Algorithm for the Optimization Design of Truss Structures

The sine cosine algorithm (SCA) is a new meta-heuristic algorithm. It has been proven to be very competitive compared with other meta-heuristic algorithms and has attracted significant attention from researchers in different fields. At present, there is no research on the application of SCA in the truss structure. In order to solve the truss optimization problem, the following improvements are made to SCA in this paper. Firstly, a non-linear conversion parameter is set to replace the linear conversion parameter, so that the exploration area is better in line with the characteristics of the actual optimization situation. Secondly, the Lévy flight is employed to enhance the algorithm's global search ability. Thirdly, a novel elite guidance strategy taking advantage of memory data is proposed to strengthen the local search ability. Finally, a greedy selection strategy is adopted for the selection of the candidate. Combining the finite element method, we apply ISCA to optimize the size, shape and topology of truss structures. The examples show that ISCA can use less calculation time, get better results, and also better stability. So, the ISCA is effective to solve the size, shape and topology optimization problems of truss structures.

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.

A standard benchmarking suite for structural optimization algorithms: ISCSO 2016–2022

Benchmarking is an essential part of developing efficient structural optimization techniques. Despite the advent of numerous metaheuristic techniques for solving truss optimization problems, benchmarking new algorithms is often carried out using a selection of classic test examples which are indeed unchallenging for contemporary sophisticated optimization algorithms. Furthermore, the limited optimization results available in the literature on new test examples are usually not accurately comparable. This is typically due to the lack of infromation about the performance of the investigated algorithms and the inconsistencies between the studies in terms of adopted test examples for benchmarking, optimization problem formulation, maximum number of objective function evaluations and other similar issues. Accordingly, there exists a need for developing new standard test suites composed of easily reproducible challenging test examples with rigorous and comparable performance evaluation results of algorithms on these test suites. To this end, the present work aims to propose a new baseline for benchmarking structural optimization algorithms, using a set of challenging sizing and shape optimization problems of truss structures selected from the international student competition in structural optimization (ISCSO) instances. The most recent six structural optimization examples from the ISCSO are tackled using a representative metaheuristic structural optimization algorithm. The statistical results of all the optimization runs using the proposed benchmarking suite are provided to pave the way for more rigorous benchmarking of structural optimization algorithms.

Design of optimal truss components for fabrication via multi-axis additive manufacturing

Additive manufacturing (AM) has developed rapidly in recent years and has the potential to enable fabrication of structurally optimized components that have hitherto been impossible to manufacture. When the degree of design freedom is high it can be observed that structurally optimized components are often truss-like in form, such that truss topology (or ‘layout’) optimization methods can be used to rapidly and directly identify optimal forms. However, these forms are often geometrically complex, and the presence of overhanging elements means that they generally need to be manufactured with support structures when traditional 3-axis AM machines are employed. To reduce, or even completely eliminate, the need for support structures, multi-axis AM machines with 5 or more axes can instead be used. In this contribution a novel process-aware truss layout optimization strategy tailored for multi-axis AM machines is proposed, which involves combining curved printing surface identification with truss layout and geometry optimization. Due to the non-linear and non-convex nature of the resulting optimization formulation, two strategies are proposed: (i) performance-based, to obtain highly materially-efficient structures, though which have as little need for support structures as possible; (ii) printability-based, to obtain fully self-supportable structures, though which consume as little material as possible. Several examples are presented to demonstrate the effectiveness of the proposed approach. It is shown that fully self-supporting optimized structures can often be identified, with little or no sacrifice in terms of structural performance.

Optimization procedure for the Strut-and-Tie method considering the stiffness of concrete in compression

An optimization procedure is proposed for finding an optimal truss for the Strut-and-Tie method used to design the steel reinforcement in concrete structural elements. The basis of the procedure is to maximize the global stiffness of the element by optimizing the reinforcement layout but considering the stiffness of concrete in the compressed zones of the element. The hydrostatic stress is used to determine those zones, which changes along the maximization.Three examples from the literature are used to test the procedure, finding very good results in terms of higher ratios of ultimate load over the weight of steel, and also in terms of spreading more evenly the cracks in the damaged zones of the element.

Medalist learning algorithm for configuration optimization of trusses

Truss configuration optimization, involving discrete sizing variables and continuous layout variables, is crucial for various practical applications. This paper introduces a highly efficient metaheuristic algorithm known as the Medalist Learning Algorithm (MLA) to address this optimization problem. Inspired by the learning behavior observed in group dynamics, the MLA offers a concise implementation procedure with two key operations: identifying medalists and facilitating individual learning. By leveraging the learning efficiency derived from a Logistic function, the MLA strikingly balances exploration and exploitation capacities throughout the learning period. To demonstrate its effectiveness, four classical truss structures with up to 44 design variables under multiple loading conditions are utilized to evaluate the MLA's performance in solving sizing and shape optimization problems of varying scales. Comparative analysis between the MLA's results and previously reported findings establishes its superiority in achieving the final feasible best weight. Statistical evidence further illustrates the MLA's consistent ability to deliver competitive solutions for a wide range of truss configuration optimization problems. The MLA's simplicity in implementation ensures its widespread applicability and potential for practical usage in the field of structural optimization.