Optimization Of Truss Structures Research Articles

Sizing Optimization of Truss Structures by an Efficient Constraint-Handling Strategy in TLBO

In this paper, an efficient constraint-handling strategy is developed as a teaching–learning–based optimization (TLBO) algorithm for sizing optimization of truss structures. The basic idea is to map the whole population of candidate designs onto the boundary of the feasible space. This technique dramatically enhances the search for the optimal structure. The proposed algorithm is capable of converging to fully feasible optimal designs. Furthermore, the number of structural analyses required in the optimization process is substantially reduced. The proposed TLBO-MS algorithm is tested in four classical truss-weight minimization problems and a real-life truss-bridge optimization problem. Besides comparison with the results reported in the literature, for the sake of completeness TLBO with two other constraint-handling techniques—namely, penalty function (TLBO-PF) and fly-back mechanism (TLBO-FB)—are studied. It is shown that the proposed method is very efficient and robust, always leads to very light structures, and fully satisfies all design constraints with low computational effort compared with other techniques.

Design Optimization and Structural Analysis of Multi-Material Truss Structure

Design Optimization and Structural Analysis of Multi-Material Truss Structure

Enhanced particle swarm optimization for size and shape optimization of truss structures

ABSTRACTThis article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.

Optimal design of truss structures using a new optimization algorithm based on global sensitivity analysis

Global sensitivity analysis (GSA) has been widely used to investigate the sensitivity of the model output with respect to its input parameters. In this paper a new single-solution search optimization algorithm is developed based on the GSA, and applied to the size optimization of truss structures. In this method the search space of the optimization is determined using the sensitivity indicator of variables. Unlike the common meta-heuristic algorithms, where all the variables are simultaneously changed in the optimization process, in this approach the sensitive variables of solution are iteratively changed more rapidly than the less sensitive ones in the search space. Comparisons of the present results with those of some previous population-based meta-heuristic algorithms demonstrate its capability, especially for decreasing the number of fitness functions evaluations, in solving the presented benchmark problems.

An approach of topology optimization of multi-rigid-body mechanism

Topology synthesis of multi-rigid-body mechanisms has always been a very important stage in the mechanism design process. In most cases, the topology of the multi-rigid-body mechanism for particular task is obtained by designers’ experience and ingenuity, rather than automatic approach. In this work, an approach of topology optimization of multi-rigid-body mechanisms is investigated. The core process of the approach is an automatic optimization design process. In this approach, we construct kinematics mapping from truss structures to the joint-linked mechanisms, which transforms the topology optimization problem of multi-body system into the truss structure optimization problem. We also develop a new strategy for topology optimization of statically determinate truss, the advantage of which lies in the ability dealing with statically determinate truss topology optimization problem compared to the existing methods. By automatically optimizing the topology of the truss structure, the topology of the multi-rigid-body mechanism is optimized automatically, accordingly. Here, we utilize the investigated approach to design suitable layout for multi-rigid-body micro-displacement amplifying mechanisms (MMAMs) with a large amplification ratio (>50). The layout consists of not only the topology information of the mechanism, but also the dimension parameters of the mechanism. The procedure of the approach is carried out in steps, and a human–computer interaction program has been developed for it. Using the developed program, different MMAMs are achieved. Meanwhile, the direct kinematics analysis of the MMAMs is achieved automatically, the existence of dead point position in the mechanism within movement range is checked and the micro-displacement amplification ratio is calculated out. The computing results are validated by the ADAMS® motion simulation, which proves that the achieved MMAMs fully fulfill the functional requirement. Along with two of the achieved MMAMs, the approach is explained, its functionality is shown, its advantages, limitations, some open problems and future works are discussed.

Cyclical parthenogenesis algorithm for layout optimization of truss structures with frequency constraints

ABSTRACTStructural optimization with frequency constraints is seen as a challenging problem because it is associated with highly nonlinear, discontinuous and non-convex search spaces consisting of several local optima. Therefore, competent optimization algorithms are essential for addressing these problems. In this article, a newly developed metaheuristic method called the cyclical parthenogenesis algorithm (CPA) is used for layout optimization of truss structures subjected to frequency constraints. CPA is a nature-inspired, population-based metaheuristic algorithm, which imitates the reproductive and social behaviour of some animal species such as aphids, which alternate between sexual and asexual reproduction. The efficiency of the CPA is validated using four numerical examples.

An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints

Structural optimization with frequency constraints is well known as a highly nonlinear and complex optimization problem with many local optimum solutions. Therefore, to solve such problems effectively, designers need to use adequate optimization methods which can make a good balance between the computational cost and the quality of solutions. In this work, a novel differential evolution (DE) is proposed to solve the shape and size optimization problems for truss structures with frequency constraints. The proposed method, called ReDE, is a new version of the DE algorithm with two improvements. Firstly, the roulette wheel selection is employed to choose members for the mutation phase instead of random selection as in the conventional DE. Secondly, an elitist selection technique is applied to the selection phase instead of basic selection to improve the convergence speed of the method. The efficiency and reliability of the proposed method are demonstrated through five numerical examples. Numerical results reveal that the proposed algorithm outperforms many optimization methods in the literature.

Optimization of Truss Structure Using Genetic Algorithm Performed on GPU

Modern Graphics Processing Units (GPU), offer a tremendous computing power, that is frequently an order of magnitude larger than even the most modern multi-core CPUs, making them an attractive platform for high performance computing due to their relative cheapness compared with conventional PC clusters. General purpose computing on GPUs (GPGPU) is becoming popular in High Performance Computing (HPC) because of its high peak performance. In this paper, a typical two-dimensional truss structure optimization problem is solved using Binary Genetic Algorithm (BGA) on both CPU and GPU. The kernel inside the GPU code computes the nodal displacements and elemental stresses by Finite Element Analysis (FEA) to evaluate the objective function and the constraints while making use of the Single Instruction Multiple Data (SIMD) structure of GPU to attain parallelization. The results are assessed for different values of parameters, such as complexity of the problem, number of elements, population size, maximum allowable generations and number of threads etc. to demonstrate how the value of speedup varies with these parameters and to provide a basic guideline for choosing the parameters for a different problem. The results clearly establish that calculations are performed considerably faster through the GPU than through the CPU in general.

Enhanced Biogeography-based Optimization: A New Method for Size and Shape Optimization of Truss Structures with Natural Frequency Constraints

The current study presents an enhanced biogeography-based optimization (EBBO) algorithm for size and shape optimization of truss structures with natural frequency constraints. The BBO algorithm is one of the recently developed meta-heuristic algorithms inspired by the mathematical models in biogeography science and is based on the migration behavior of species among the habitats in the nature. In this study, the overall performance of the standard BBO algorithm is enhanced by new migration and mutation operators. The efficiency of the proposed algorithm is demonstrated by utilizing four benchmark truss design examples with frequency constraints. Numerical results show that the proposed EBBO algorithm not only significantly improves the performance of the standard BBO algorithm, but also finds competitive results compared with recently developed optimization methods.

A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure

This paper presents a new variant of the Harmony Search (HS) algorithm. This Hybrid Harmony Search (HHS) algorithm follows a new approach to improvisation: while retaining HS algorithm Harmony Memory and pitch adjustment functions, it replaces the HS algorithm randomization function with Global-best Particle Swarm Optimization (PSO) search and neighbourhood search. HHS algorithm performance is tested on six discrete truss structure optimization problems under multiple loading conditions. Optimization results demonstrate the excellent performance of the HHS algorithm in terms of both optimum solution and the convergence behaviour in comparison with various alternative optimization methods.

Reliability-Based Design Optimization of Trusses with Linked-Discrete Design Variables using the Improved Firefly Algorithm

In this paper, an approach for conducting a Reliability-Based Design Optimization (RBDO) of truss structures with linked-discrete design variables is proposed. The sections of the truss members are selected from the AISC standard tables and thus the design variables that represent the properties of each section are linked. Latin hypercube sampling is used in the evaluation of the structural reliability. The improved firefly algorithm is used for the optimization solution process. It was found that in order to use the improved firefly algorithm for efficiently solving problems of reliability-based design optimization with linked-discrete design variables; it needs to be modified as proposed in this paper to accelerate its convergence.

Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer

The current investigation deals with the weight minimization of truss structures accomplishing the simultaneous shape, size, and topology optimization. In this regard, this study presents an effect...

General Approach for Topology-Finding of Tensegrity Structures

AbstractThis paper proposes a general approach for topology-finding of tensegrity structures. The ground structure method that is widely used in topology optimization of truss structures is employed. An optimization model, using the member connections and the internal forces of members as variables, is developed to find self-stressed tensegrities under given constraints on member distribution, configuration symmetry, and node stability. Mixed integer linear/quadratic programming is used to solve the optimization problem. Numerical examples are carried out to verify the proposed approach. Compared to previous approaches, the proposed approach is able to find a wider scope of tensegrity structures that have a maximum of k (k≥1) struts connecting to a single node and is able to deal with objective functions in quadratic form.

Structural Optimization by Spherical Interpolation of Objective Function and Constraints

A new method for structural optimization is presented for successive approximation of the objective function and constraints in conjunction with Lagrange Multipliers Approach. The focus is on presenting the methodology with simple examples. The basis of the iterative algorithm is that after each iteration it brings the approximate location of the estimated minimum closer to the exact location gradually. In other words, instead of the linear or parabolic term used in Taylor expansion which works based on a short step length, an arc is used that has a constant curvature but a longer step length. Using this approximation, the equations of optimization involve the Lagrange multipliers as the only unknown variables. The equations which depend on the design variables are decoupled linearly as these variables are directly obtained. One mathematical example is solved to explain in details how the method works. Next the method is applied to the optimization of a simple truss structure to explain how the method can be used in structural optimization. The same problems have been solved by penalty method and compared. The results from both methods have been the same. However because of the long step length and reduction in the number of variables, the speed of convergence has been higher in the presented method.

A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algo­rithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical exam­ples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications.

Proposed Algorithms for an Efficient System Reliability-Based Design Optimization of Truss Structures

AbstractThe design optimization considering the system reliability of a structural system is a computationally challenging task. This is especially the case in an indeterminate structure that has many possible modes or paths to complete failure. Accomplishing this task efficiently requires using enhanced and powerful techniques for the structural analysis, the reliability analysis, and the optimization solution. In a simulation-based reliability analysis, the actual value of the performance functions is irrelevant to the calculated probability of failure. The actual value of the performance function is merely calculated to determine whether the system failed or not. In this paper, nonlinear analysis algorithms for truss structures are proposed. These algorithms are used for determining whether the structural system failure occurs during the simulation-based system reliability analysis in a computationally efficient manner. Using these algorithms, a simulation-based system reliability design optimization o...

An adaptive elitist differential evolution for optimization of truss structures with discrete design variables

This paper proposes an adaptive elitist differential evolution (aeDE) for optimization of truss structures with discrete design variables. The aeDE algorithm is a newly improved version of the differential evolution (DE) algorithm with three modifications. Firstly, in the mutation phase, an adaptive technique based on the deviation of objective function between the best individual and the whole population in the previous generation is proposed to select a suitable mutation operator. This technique helps preserve the balance between global and local searching abilities in the DE. Secondly, in the selection phase, an elitist selection technique which helps choose the best individuals for the next generation is utilized to increase the convergence rate. Finally, a rounding technique is integrated into the aeDE for solving optimization problems with discrete design variables. The efficiency and reliability of the proposed method are demonstrated through six optimization problems of truss structures with discrete design variables. Numerical results reveal that in most of the test cases, the aeDE is more efficient than the DE and some other methods in the literature in terms of the quality of solution and convergence rate.

An improved fully stressed design evolution strategy for layout optimization of truss structures

During the recent decade, truss optimization by meta-heuristics has gradually replaced deterministic and optimality criteria-based methods. While they may provide some advantages regarding their robustness and ability to avoid local minima, the required evaluation budget grows fast when the number of design variables is increased. This practically limits the size of the problems to which they can be applied. Furthermore, many recent stochastic optimization methods handle the size optimization only, the potential saving from which is highly limited, when compared to the most sophisticated, and obviously the most challenging scenario, simultaneous topology, shape and size (TSS) optimization. In a recent study by the authors, a method based on combination of optimality criteria and evolution strategies, called fully stressed design based on evolution strategies (FSD-ES), was proposed for TSS optimization of truss structures. FSD-ES outperformed available truss optimizers in the literature, both in efficiency and robustness. The contribution of this study is twofold. First, an improved version of FSD-ES method, called FSD-ES-II, is proposed. In comparison with the earlier version, it takes the displacement constraints in the resizing step into account and can handle constraints governed by practically used specifications. Update of strategy parameters is also revised following contemporary and new developments in evolution strategies. Second, a test suite involving a number of complicated TSS optimization problems is chosen to overcome usual shortcomings in the available benchmark problems. For each problem, performance of FSD-ES-II is compared with the best results available in the literature, often showing a significant superiority of the proposed approach.

An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures

Recently, a Sequential Optimization and Reliability Assessment (SORA) method was proposed and proven to be effective for solving reliability-based design optimization (RBDO) problems. In the SORA, the optimization loop and the reliability assessment loop are decoupled from each other. This helps improve the efficiency of the SORA significantly. However, the SORA still exists two main drawbacks: (1) the optimal solutions are easily trapped within local extremes and (2) the optimal results depend on the initial trial points. To overcome these drawbacks, this paper integrates the SORA with the Improved Constrained Differential Evolution algorithm (ICDE) to give a so-called SORA-ICDE for solving RBDO problems. Due to the global search mechanism, the SORA-ICDE can easily obtain global solutions regardless of initial points. The numerical results obtained in the paper are compared with available results in the literature to illustrate the efficiency, applicability and precision of the SORA-ICDE in solving the RBDO problems for truss structures.

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.