Sizing Optimization Of Trusses Research Articles

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

AbstractThis 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.

Integration of Excel VBA with professional software for the structural analysis and design of civil structures

AbstractA feasible combined approach between structural analysis program (SAP) 2000 and Excel software is proposed in this article to develop customized numerical tools for the analysis of civil engineering structures. For such scope, the Open Application Programming Interface from SAP 2000 software is linked to the Visual Basic for Application (VBA) environment embedded within Excel. Three computer applications resembling industrial situations related to size optimization of trusses, soil−structure interaction in buildings, and automatic design of reinforced concrete slabs are presented. As the tools are parameterized, students can observe the effects of the various parameters on the output response of the structures because geometry, loading, and material properties can be easily varied. As the main concern is the educational aspect, the novelty of this research is to present the proposed combined approach in a stepwise manner with explained codes. The source codes of the developed tools are made freely available so that the applicants can modify them according to their priorities. The tools present a friendly user interface that made them attractive to use in daily design tasks at the office, but certainly, they are the result of the integration of student knowledge as part of a bachelor's dissertation in an undergraduate civil engineering educational program. The tools have been preliminarily introduced into a reinforced concrete course at the Federal University of Rio Grande do Sul (Brazil), searching for a better understanding of theoretical concepts, while integrating technology into the classroom and reducing time constraints as new configurations for the studied structures can be easily explored during class.

The MINLP Approach to Topology, Shape and Discrete Sizing Optimization of Trusses

The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.

Meta-heuristic algorithms to truss optimization: Literature mapping and application

Truss optimization is an important class of engineering problems, with better solutions allowing for reduced material use and reduced construction costs. Due to its complexity, meta-heuristic algorithms are often applied to this problem, since these algorithms require no prior knowledge of the search space, being built upon stochastic rules. The present work has two main objectives: the elaboration of a systematic literature mapping on meta-heuristic algorithms applied to truss optimization, and the application of EB-A-SHADE, a self-adaptive algorithm based on Differential Evolution, to truss size optimization with continuous variables. The systematic mapping was made based on 179 articles published between 2010 and 2020 and analyzed the categories of truss optimization, the algorithms used, and parameter self-adaptation techniques. This mapping provided a snapshot of the current state of truss optimization research, showing that it is an active field, with an increasing number of publications each year, but that also includes gaps for potential future works. For the truss size optimization application, seven benchmark structures were used to evaluate the EB-A-SHADE algorithm, and the results obtained were compared to those of state-of-the-art algorithms with the use of statistical analysis. Convergence, constraints, and diversity plots were also employed to analyze the algorithm behavior on the problems studied, showing a stable convergence. The experiments showed that EB-A-SHADE achieved competitive results, having the statistical best results in most structures, and with the lowest standard deviation values. These results show that the algorithm can be applied to more complex approaches to the problem at hand.

Enhanced versions of the shuffled shepherd optimization algorithm for the optimal design of skeletal structures

This paper consists of two main parts. The first part is devoted to developing a parameter-free variant of the shuffled shepherd optimization algorithm (SSOA), named as a parameter-free shuffled shepherd optimization algorithm (PF-SSOA). Next, a set-theoretical multi-phase framework is proposed for the population-based metaheuristic algorithms. The proposed framework's main idea is based on dividing the population of candidate solutions into some number of well-arranged sub-populations. The number of sub-populations gradually changes during the optimization process. The framework is applied to the PF-SSOA, leading to a set-theoretical multi-phase variant of PF-SSOA named STMP-SSOA. The STMP-SSOA stands for a set-theoretical multi-phase shuffled shepherd optimization algorithm. Some skeletal structures are optimized to verify the validity and efficiency of the proposed algorithms. The optimization problems include two truss size optimization problems with multiple frequency constraints and two planar frame structures with strength and displacement constraints. The results indicate that the developed algorithms perform better than the standard version of the SSOA, especially in terms of robustness and convergence characteristics.

Shape and size optimization of trusses with dynamic constraints using a metaheuristic algorithm

Metaheuristic algorithm is used to solve the weight minimization problem of truss structures considering shape, and sizing design variables. The cross-sectional areas of the line element in trusses are the design variables for size optimization and the changeable joint coordinates are the shape optimization used in this study. The design of plane and spatial truss structures are optimized by metaheuristic technique named Teaching-Learning-Based Optimization (TLBO). Finite element analyses of structures and optimization process are carried out by the computer program visually developed by the authors coded in MATLAB. The four benchmark problems (trusses 2D ten-bar, 3D thirty-seven-bar, 3D seventy-two-bar and 2D two-hundred-bar) taken from literature are optimized and the optimal solution compared the results given by previous studies.

Truss Size Optimization with Frequency Constraints using ACO Algorithm

Truss Size Optimization with Frequency Constraints using ACO Algorithm

Truss Size Optimization by Using Ratio-Extremum Method: Considering Self-weight Loads, Static and Dynamic Constraints

For structural self-weight loads being important component in the loads, ignoring self-weight loads cannot be considered as reasonable approximation. In addition, the constraints of stresses, displacements and frequencies must be simultaneously considered to satisfy the requirements of engineering structures. According to the saddle point theory, Ratio-Extremum method is firstly proposed to solve the size optimization problem of the truss simultaneously considering self-weight loads, static and dynamic constraints. It is a great advantage that the step-size factors can be directly determined. Two cases of 72-bar special truss are used to show the effectivity and rationality.

Singular solutions of truss size optimization for considering fundamental frequency constraints

For engineering structures, the limits of internal stresses, nodal displacements and fundamental frequencies must be simultaneously considered. This had been paid attention in the theory of structural optimization. Actually, most examples of only considering static constraints or only considering dynamic constraints were presented for simultaneously considering static and dynamic constraints. A few examples of considering both static and dynamic constraints were presented, but the advantage could not be presented. It is the reason that the singularity of structural optimization for considering dynamic constraints has not been discussed. To discover the singularity, an optimization model to simultaneously consider static and dynamic constraints is used for the truss size optimization. And according to the extremum conditions of the optimization problem, Ratio-Extremum method is proposed to solve the optimization problems of considering both static and dynamic constraints and only considering dynamic constraints, in which a new searching direction of design variables is to be discussed. Particularly, the step-size factors can be determined by formulas to iteratively solve Lagrangian multipliers and design variables. Numerical examples of 15-bar planar and 72-bar spatial trusses are used to show the singular solutions. On the convergent points, the optimization weights of only considering dynamic constraints are about 66.17% and 71.14% more than the weights of considering both static and dynamic constraints, respectively. The convergent solutions of only considering dynamic constraints are not the best results. However, additional static constraints can be helpful to obtain better results for considering dynamic constraints.

Simultaneous topology, shape, and size optimization of trusses, taking account of uncertainties using multi-objective evolutionary algorithms

This paper proposes the design of trusses using simultaneous topology, shape, and size design variables and reliability optimization. Objective functions consist of structural mass and reliability, while the probability of failure is set as a design constraint. Design variables are treated to simultaneously determine structural topology, shape, and sizes. Six test problems are posed and solved by a number of multi-objective evolutionary algorithms, and it is found that Hybridized Real-Code Population-Based Incremental Learning and Differential Evolution is the best performer. This work is considered an initial study for the combination of reliability optimization and simultaneous topology, shape, and sizing optimization of trusses.

Comparison of gradient and nongradient algorithms in the structural optimization course

Gradient and nongradient optimization algorithms are currently available for structural design in structural optimization course. Despite the successful application of gradient algorithm in structural optimization, nongradient algorithm is also extensively adopted to solve the structural optimization problem. However, the efficiency of nongradient algorithm has caused a heated debate recently. To clarify this issue for the graduate students, sequential linear programming and genetic algorithm are, respectively, chosen as the representatives of gradient and nongradient algorithms to solve truss size optimization problem. Firstly, the size optimization formulations of truss structure for sequential linear programming and genetic algorithm are summarized, respectively. Secondly, an educational finite element software for truss structure is developed by using the object-oriented programming to create the software framework. This study aims to provide an open-source, extensible, and benchmarking software, which do assist the students to understand the structural optimization process in engineering education. Finally, two benchmarking examples are introduced to compare the efficiency and accuracy of sequential linear programming and genetic algorithm.

Kafes Sistemlerin BB-BC Algoritması ile Boyut Optimizasyonu Üzerine bir Çalışma: İnceleme ve Sayısal Deneyler

In the last decades, great attention has been paid to structural optimization with stochastic methods. The applications of metaheuristic algorithms have become popular, which mostly provide solutions with adequate precision for the structural optimization problems from an engineering point of view. However, these algorithms should be specifically tuned for the considered problem to obtain satisfactory results. Big Bang - Big Crunch is one of the efficient metaheuristic optimization algorithms that is based on the famous theory on the evolution of the universe. A considerable number of researchers presented applications of the Big Bang - Big Crunch algorithm for the size optimization of trusses, which is an inviting challenge in the structural optimization field. This study revisits the size optimization of trusses with continuous variables using the Big Bang - Big Crunch algorithm, discusses the previously introduced improvements and presents the results of a few experimental modifications.

Topology and Size Optimization of Trusses with Static and Dynamic Bounds by Modified Symbiotic Organisms Search

AbstractIn this study, a modified version of the symbiotic organisms search (SOS) is proposed for topology and sizing of two-dimensional (2D) and three-dimensional (3D) trusses with static and dyna...

A hybrid algorithm coupling genetic programming and Nelder–Mead for topology and size optimization of trusses with static and dynamic constraints

Truss optimization aims to provide the lightest truss to gain the maximum benefit out of available resources. Truss optimization may subject to static and dynamic constraints. Static constraints include structural kinematic stability, maximum allowable stress in truss members, maximum allowable deflection in the truss nodes and critical buckling load. However, dynamic constraints impose limits on the natural frequency of the desired truss to avoid the destructive resonance phenomenon. Taking both static and dynamic constraints into account may lead to growth in the search space but dwindling its feasible region; the search space becomes very non-convex and may subterfuge the solver to trap in a local optimum. Another design consideration may include fabricational constraints to present design variables from a set of available cross-sections to satisfy the design codes. This paper proposes a hybrid genetic programming algorithm to deal with the barriers of this complex problem. It looks for the optimum connectivity table (among the truss nodes) and optimal cross-sectional areas for its members subject to design constraints. It also benefits from a Nelder–Mead local search operator to improve the competence and true convergence of the algorithm. Our algorithm has been applied to some numerical examples considering both types of continuous and discrete design variables; It proved its efficiency to find better solutions (lighter trusses) in comparison with other methods in the literature for most of the cases.

Sizing, shape and topology optimization of trusses with energy approach

The main objective of this research is to present the procedures of combining topology, shape & sizing optimization for truss structure by employing strain energy as objective function under the constraints of volume fractions which yield more general solution than that of total weight approach. Genetic Algorithm (GA) is used as searching engine for the convergence solution. A number of algorithms from previous research are used for evaluating the feasibility and stability of candidate to accelerate convergence and reduce the computational effort. It is followed by solving problem for topology & shape optimization and topology, shape & sizing optimization of truss structure to illustrate the feasibility of applying the objective function of strain energy throughout optimization stages.

Subspace search mechanism and cuckoo search algorithm for size optimization of space trusses

This study presents a strategy so-called Subspace Search Mechanism (SSM) for reducing the computational time for convergence of population based metaheusristic algorithms. The selected metaheuristic for this study is the Cuckoo Search algorithm (CS) dealing with size optimization of trusses. The complexity of structural optimization problems can be partially due to the presence of high-dimensional design variables. SSM approach aims to reduce dimension of the problem. Design variables are categorized to predefined groups (subspaces). SSM focuses on the multiple use of the metaheuristic at hand for each subspace. Optimizer updates the design variables for each subspace independently. Updating rules require candidate designs evaluation. Each candidate design is the assemblage of responsible set of design variables that define the subspace of interest. SSM is incorporated to the Cuckoo Search algorithm for size optimizing of three small, moderate and large space trusses. Optimization results indicate that SSM enables the CS to work with less number of population (42%), as a result reducing the time of convergence, in exchange for some accuracy (1.5%). It is shown that the loss of accuracy can be lessened with increasing the order of complexity. This suggests its applicability to other algorithms and other complex finite element-based engineering design problems.

Simultaneous Topology and Size Optimization of 2D and 3D Trusses Using Evolutionary Structural Optimization with regard to Commonly Used Topologies

One of many optimization techniques is the evolutionary structural optimization (ESO), based on the idea that an optimal structure can be achieved by gradually removing ineffectively used materials from the design domain. Production of a multistage optimization is often proposed to reach the best overall solution. In the first stage, the structure is optimized according to a topology criterion, and, in the second stage, sizing optimization is carried out. The efficiency of such an approach is questionable as a fixed topology, for the second stage optimization may not be the most favorable before sizing optimization is carried out. In this paper, the simultaneous topology and size optimization of trusses using the ESO algorithm are discussed. A number of numerical examples are presented to research capacity to achieve optimal solutions for a structural problem. The topology design of the initial design domain is based on commonly used designs for multistorey trusses constructed from straight members. Therefore, the cases are of a slender shape and made from a combination of presented internal designs. The case studies will present an evaluation to show whether the described optimization approach can be beneficial in structural design for the purpose of steel framework designs.

Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm

In this paper, size and shape optimization of truss structures is performed using an efficient hybrid method. This algorithm uses a particle swarm strategy and ray optimizer, and utilizes additional harmony search for a better exploitation. Here, multiple frequency constraints are considered making the optimization a highly nonlinear problem. Some basic benchmark problems are solved by this hybrid method, and the numerical results demonstrate the efficiency and robustness of this method compared to other mathematical and heuristic algorithms.

Evaluation of crossover techniques in genetic algorithm based optimum structural design

Crossover is one of the three basic operators in any genetic algorithm (GA). Several crossover techniques have been proposed and their relative merits are currently under investigation. This paper starts with a brief discussion of the working scheme of the GAs and the crossover techniques commonly used in previous GA applications. Next, these techniques are tested on two truss size optimization problems, and are evaluated with respect to exploration and exploitation aspects of the search process. Finally, the paper proposes two newly developed crossover techniques, through which a better efficiency of GAs can be obtained. Comparative studies are carried out between the proposed and the common crossover techniques, and the results are fully discussed.

Optimization of trusses using genetic algorithms for discrete and continuous variables

This paper demonstrates the use of genetic algorithms (GAs) for size optimization of trusses. The concept of rebirthing is shown to be considerably effective for problems involving continuous design variables. Some benchmark examples are studied involving 4‐bar, 10‐bar, 64‐bar, 200‐bar and 940‐bar two‐dimensional trusses. Both continuous and discrete variables are considered.