Structural Optimization Algorithm Research Articles

Seeding the initial population with feasible solutions in metaheuristic optimization of steel trusses

In spite of considerable research work on the development of efficient algorithms for discrete sizing optimization of steel truss structures, only a few studies have addressed non-algorithmic issues affecting the general performance of algorithms. For instance, an important question is whether starting the design optimization from a feasible solution is fruitful or not. This study is an attempt to investigate the effect of seeding the initial population with feasible solutions on the general performance of metaheuristic techniques. To this end, the sensitivity of recently proposed metaheuristic algorithms to the feasibility of initial candidate designs is evaluated through practical discrete sizing of real-size steel truss structures. The numerical experiments indicate that seeding the initial population with feasible solutions can improve the computational efficiency of metaheuristic structural optimization algorithms, especially in the early stages of the optimization. This paves the way for efficient metaheuristic optimization of large-scale structural systems.

Hierarchical remeshing strategies with mesh mapping for topology optimisation

SummaryThis work investigates the use of hierarchical mesh decomposition strategies for topology optimisation using bi‐directional evolutionary structural optimisation algorithm. The proposed method uses a dual mesh system that decouples the design variables from the finite element analysis mesh. The investigation focuses on previously unexplored areas of these techniques to investigate the effect of five meshing parameters on the analysis solving time (i.e. computational effort) and the analysis quality (i.e. solution optimality). The foreground mesh parameters, including adjacency ratio and minimum and maximum element size, were varied independently across solid and void domain regions. Within the topology optimisation, strategies for controlling the mesh parameters were investigated. The differing effects of these parameters on the efficiency and efficacy of the analysis and optimisation stages are discussed, and recommendations are made for parameter combinations. Some of the key findings were that increasing the adjacency ratio increased the efficiency only modestly – the largest effect was for the minimum and maximum element size parameters – and that the most dramatic reduction in solve time can be achieved by not setting the minimum element size too low, assuming mapping onto a background mesh with a minimum element size of 1. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.

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.

Formation of Rh islands on Pd-supported α-Fe2O3(0001)

A rhodium ultra-thin film was deposited on a Pd-supported α-Fe2O3 (0001) film by molecular beam epitaxy (MBE). The surface atomic and electronic structures were studied using X-ray photoelectron diffraction (XPD), X-ray photoelectron spectroscopy (XPS), and low energy electron diffraction (LEED). For an oxide thin film (∼16.5 A), an ordered (√3 × √3)R30° structure was observed. The multiple scattering calculation approach combined with a genetic algorithm for surface structure optimization was used to investigate precisely the atomic structure of the oxide support as well as the Rh nanoislands or nanoparticles (NPs). Rh exhibited 3D growth on an α-Fe2O3 thin film forming NPs with a lattice constant expanded by 5.26% relative to the Rh bulk value. The coexistence of 60° rotated domains and also evidence of Fe termination at the surface of α-Fe2O3 were observed.

Feasibility Study of Using Artificial Neural Networks for Approximation of n-dimensional Objective Functions in Memetic Algorithms for Structural Optimization

Evaluation of objective function for problems of structural optimization is generally considered as computationally expensive and can take from few seconds to hours or even days. After certain number of solutions has been evaluated during optimization, artificial neural networks (ANNs) can be trained and used to approximate the objective function. The number of training points depends on the character and topology of objective function, but the most important factor is the dimensionality of objective function. Similarly as the performance of optimization algorithms, requirements on training data for ANNs are affected by so called “curse of dimensionality”. To achieve the same precision of ANN approximation over n-dimensional space, the number of training points grows exponentially with the number of dimensions. This paper presents a feasibility study of using ANNs for approximation of objective function for problems solved by structural optimization with respect to the number of optimization variables. The goal of this study was to find the maximum number of dimensions, where it is feasible to use ANNs for approximation of objective function. Test problem with varying number of optimization variables was used to assess the feasibility of using ANN.

A two-stage model for time series prediction based on fuzzy cognitive maps and neural networks

This paper proposes a two-stage prediction model, for multivariate time series prediction based on the efficient capabilities of evolutionary fuzzy cognitive maps (FCMs) enhanced by structure optimization algorithms and artificial neural networks (ANNs). In the first-stage, an evolutionary FCM is constructed automatically from historical time series data using the previously proposed structure optimization genetic algorithm, while in the second stage, the produced FCM defines the inputs in an ANN which next is trained by the back propagation method with momentum and Levenberg-Marquardt algorithm on the basis of available data. The structure optimization genetic algorithm for automatic construction of FCM is implemented for modeling complexity based on historical time series data, selecting the most important nodes (attributes) and interconnections among them thus providing a less complex and efficient FCM-based model. This model is used next as input in an ANN. ANNs are used at the final process for making time series prediction considering as inputs the concepts defined by the produced FCM. The previously proposed structure optimization genetic algorithm for FCM construction by historical data as well as the ANN have been already proved their efficacy on time series forecasting. The performance of the proposed approach is presented through the analysis of multivariate historical data of benchmark datasets for making predictions. The multivariate analysis of historical data is held for a large number of input variables, like season, month, day or week, holiday, mean and high temperature, etc. The whole approach was implemented in an intelligent software tool initially deployed for FCM prediction. Through the experimental analysis, the usefulness of the new two-stage approach in time series prediction is demonstrated, by calculating seven prediction performance indicators which are well known from the literature.

MULTI-OBJECTIVE OPTIMIZATION OF REINFORCED CONCRETE FRAMES USING NSGA-II ALGORITHM

In recent decades, the use of genetic algorithm (GA) for optimization of structures has been highly attractive in the study of concrete and steel structures aiming at weight optimization. However, it has been challenging for multi-objective optimization to determine the trade-off between objective functions and to obtain the Pareto-front for reinforced concrete (RC) and steel structures. Among different methods introduced for multi-objective optimization based on genetic algorithms, Non-Dominated Sorting Genetic Algorithm II (NSGA II) is one of the most popular algorithms. In this paper, multi-objective optimization of RC moment resisting frame structures considering two objective functions of cost and displacement are introduced and examined. Three design models are optimized using the NSGA-II algorithm. Evaluation of optimal solutions and the algorithm process are discussed in details. Sections of beams and columns are considered as design variables and the specifications of the American Concrete Institute (ACI) are employed as the design constraints. Pareto-fronts for the objective space have been obtained for RC frame models of four, eight and twelve floors. The results indicate smooth Pareto-fronts and prove the speed and accuracy of the method.

Research on Straight Line Stability Control Strategy of Four Wheel Drive Vehicle Based on the Sliding Mode Variable Structure Control and Optimization Algorithm

Abstract After the reference of straight line stability control strategy of four-wheel drive vehicle, this paper proposes a control algorithm combining the sliding mode variable structure and optimization control method. The control algorithm is mainly divided into the upper generalized moment calculation based on the sliding mode variable structure controller and the lower torque distribution controller based on the optimization algorithm, also including the slip rates controller based on PID algorithm to ensure the straight line stability control. This paper establishes the combined model based on the CarSim and MATLAB, and tests to verify the validation of the control strategy through the four-wheel drive vehicle test-bed based on RT_LAB. The simulation and experimental results show that when the tire-road friction coefficient is low, the control strategy can not only make the vehicle tire slip rates stay near the optimal slip ratio, at the same time through the yawing moment adjustment, ensure the yaw angle of vehicle not beyond 0.5 deg/s, so the method can effectively ensure the straight line stability of four wheel drive vehicle.

Optimal structural topology of materials with micro-scale tension-compression asymmetry simulated using granular micromechanics

Material systems derived from particulate precursor exhibit significant micro-scale tension-compression asymmetry under loading which leads to macro-scale material anisotropy. Topology optimization of structures composed of such materials could suggest new unique topologies as well as material anisotropy distribution. This paper utilizes the granular micromechanics method that relates the micro-scale interactions to the macro-scale for defining material constitutive relationship. The resultant constitutive relationship is implemented in the evolutionary structure optimization algorithm based upon finite element analysis. Benchmark problems are simulated to investigate the influences of degrees of asymmetry on structure topologies and to illustrate how material anisotropy evolves under given boundary conditions.

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.

Concurrent topological design of composite structures and the underlying multi-phase materials

This paper presents a concurrent topology optimization approach for simultaneous design of composite structures and their periodic material microstructures with three or more phases. The effective properties of multi-phase materials are obtained via homogenization technique which serves as a bridge of the finite element models of the macrostructure and the material microstructure. The base materials of periodic microstructures used in each phase of the macrostructure are divided into several groups and sensitivity analysis are carried out on them one by one. Meanwhile, the sensitivity number at the macrostructure is derived which is coupled with the designed material properties. Then, the composite configurations of material microstructures and macrostructures are inversely optimized concurrently based on the bi-directional evolutionary structural optimization (BESO) algorithm. Several 2D and 3D numerical examples are presented to demonstrate the effectiveness of proposed design approach.

Elimination of the Effects of Low Density Elements in Topology Optimization of Buckling Structures

This paper presents an algorithm for structural topology optimization involving linear buckling. In this algorithm, finite element analysis (FEA) is conducted only in a domain with solid and gray elements, eliminating the contribution of low density elements; and the response function is constructed in the full design domain accounting the contribution of removed low density elements. The errors induced by removing void elements in FEA on eigenvalue and eigenvectors are analyzed. By introducing a dynamic low bound of the first eigenvalue and a load-path coefficient, the algorithm allows converged, nondisjointed and accurate solutions for topology optimization of structures involving buckling. Numerical results are presented for plate and column-beam structures against linear buckling to illustrate the efficiency and effectiveness of the present algorithm. Buckling experiments of the plates manufactured from the obtained topologies further verify the present algorithm.

재귀적 소자 교환 방식을 이용한 능동위상배열안테나 부배열 구조 최적화 알고리즘

재귀적 소자 교환 방식을 이용한 능동위상배열안테나 부배열 구조 최적화 알고리즘

Rule extraction from an optimized neural network for traffic crash frequency modeling

This study develops a neural network (NN) model to explore the nonlinear relationship between crash frequency and risk factors. To eliminate the possibility of over-fitting and to deal with the black-box characteristic, a network structure optimization algorithm and a rule extraction method are proposed. A case study compares the performance of the trained and modified NN models with that of the traditional negative binomial (NB) model for analyzing crash frequency on road segments in Hong Kong. The results indicate that the optimized NNs have somewhat better fitting and predictive performance than the NB models. Moreover, the smaller training/testing errors in the optimized NNs with pruned input and hidden nodes demonstrate the ability of the structure optimization algorithm to identify the insignificant factors and to improve the model generalization capacity. Furthermore, the rule-set extracted from the optimized NN model can reveal the effect of each explanatory variable on the crash frequency under different conditions, and implies the existence of nonlinear relationship between factors and crash frequency. With the structure optimization algorithm and rule extraction method, the modified NN model has great potential for modeling crash frequency, and may be considered as a good alternative for road safety analysis.

Experimental evaluation of optimized strut‐and‐tie models for a dapped beam

AbstractStrut‐and‐tie modelling constitutes a powerful tool for the design of complex structural reinforced concrete elements. It has been proved numerically that strut‐and‐tie (ST) models obtained using structural optimization methods produce designs that are more efficient. However, to the best of the authors' knowledge, no experimental evidence of such results has been published. This paper presents experimental results for nine test specimens; five of them were designed using optimal models derived from a full homogenization structural optimization algorithm, and the remaining four using conventional ST models for comparison purposes. Although all specimens carry loads higher than the factored design load, specimens based on ST models derived using full homogenization with reinforcement parallel to the ties exhibit better structural performance regarding crack growth control, more ductile modes of failure and a greater increase in load capacity.

A multi-populations multi-strategies differential evolution algorithm for structural optimization of metal nanoclusters

Theoretically, the determination of the structure of a cluster is to search the global minimum on its potential energy surface. The global minimization problem is often nondeterministic-polynomial-time (NP) hard and the number of local minima grows exponentially with the cluster size. In this article, a multi-populations multi-strategies differential evolution algorithm has been proposed to search the globally stable structure of Fe and Cr nanoclusters. The algorithm combines a multi-populations differential evolution with an elite pool scheme to keep the diversity of the solutions and avoid prematurely trapping into local optima. Moreover, multi-strategies such as growing method in initialization and three differential strategies in mutation are introduced to improve the convergence speed and lower the computational cost. The accuracy and effectiveness of our algorithm have been verified by comparing the results of Fe clusters with Cambridge Cluster Database. Meanwhile, the performance of our algorithm has been analyzed by comparing the convergence rate and energy evaluations with the classical DE algorithm. The multi-populations, multi-strategies mutation and growing method in initialization in our algorithm have been considered respectively. Furthermore, the structural growth pattern of Cr clusters has been predicted by this algorithm. The results show that the lowest-energy structure of Cr clusters contains many icosahedra, and the number of the icosahedral rings rises with increasing size.

Topology optimization of stamping die components using evolutionary structural optimization method

Today, die design standards are used to design the structure of die components. These standards are usually based on high safety factors. So, the die components are often heavier and larger than required. In this article, a software package is developed which can design an appropriate topology of body structure of stamping die components with a reduced weight. This is done by implementing the evolutionary structural optimization algorithm. The proposed structure can also be modified by the designer to accommodate for a simpler casting method. This software package is developed in Microsoft Visual C# programming environment with a link to Abaqus software to analyze the finite element simulation of the process. The operation of the software is demonstrated by an example where the die for a sheet metal part is studied. The die components are initially designed, analyzed and compared with the standard die (the die which is in general use today). The final results show a reduction of 37% of volume and 8% of maximum displacement, respectively.

On the importance of viscoelastic response consideration in structural design optimization

In this paper we present a series of mathematical proofs that demonstrate the importance of accounting for viscoelastic effects in structural optimization algorithms. Focusing specifically on mass minimization problems with stiffness and deflection constraints, we show that standard techniques based on linear elastic analysis overestimate the long-term stiffness of the structure, leading to designs that become infeasible after sustained loading due to viscoelastic creep. Conversely, assuming maximum creep deflection, which also allows for linear analysis, leads to an overly conservative design that is unnecessarily heavy and therefore suboptimal. We prove both propositions for both constant and time-varying load histories. We also present proofs for generalized continuum mechanics problems as well as for a finite element formulation, which can be applied to any arbitrary geometry. Lastly, we present two numerical examples in which the conclusions derived in the proofs are verified empirically.

Eigenfrequecy-based damage identification method for non-destructive testing based on topology optimization

ABSTRACTNon-destructive testing (NDT) detects damage according to a difference in a physical phenomenon between a normal structure and damaged structure. As a solution avoiding human errors in NDT, a numerical method based on a dynamical numerical analysis model and a structural optimization algorithm was proposed. This method automatically derives a structure with a response that is equal to that of a damaged structure through an optimization procedure. Among structural optimization methods, topology optimization can optimize the structure fundamentally by changing the topology and not just the shape of a structure. Thus, topology optimization is employed together with eigenfrequency analysis, which is the most fundamental methodology of NDT. The proposed method derives a structure that has the same eigenfrequencies as a damaged structure employing topology optimization. The shape and location of damage can be identified through the optimal shape obtained.

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.