An enhanced genetic algorithm for structural topology optimization

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Topology optimization is the procedure of determining the connectivity, shape and location of voids inside a given design domain. This chapter proposes a quantum-inspired evolutionary algorithm (QEA) for structural topology optimization. It reviews the formulation of the continuum structural topology optimization model and the characteristics of quantum computing. The chapter also proposes the detailed implementation of a QEA-based topology optimization. It discusses two issues: the density-based continuum structural topology optimization formulation and the characteristics of quantum computing, which may be conducive to reducing the computational expense of topology optimization. The entire theoretical procedure of quantum-inspired topology optimization, which mainly combines FEM analysis, design sensitivity solution and quantum-inspired search, is accomplished for continuum structures. As the experimental implementation of quantum computation needs initialization, coherent manipulation, control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult.

Isogeometric analysis (IGA) connects CAE with standard CAD design tools and has been utilized for a decade in structural optimization. FEA has a number of drawbacks, including a lack of linkage between analytic and geometric models, a shortage of continuity between components, and a lack of accuracy for high-order elements. Isogeometric analysis effectively overcomes these obstacles. This paper proposes the isogeometric topological optimization mathematical model depending on the asymmetric constitutive relationship of tension and compression microscopic materials. We provide a new density-based topology optimization formulation in which the design domain is limited to the B-spline space. A rectangular domain with a tensor-product is embedded in a design domain that is arbitrarily shaped. The density field is represented using B-splines. The intrinsic filter provided by the B-spline representation for topology optimization is governed by the degrees of B-spline and the knot spans. This B-spline effectively removes numerical artifacts and controls the minimum feature-length in; when the B-spline basis functions span many analysis elements. Benchmark problems in structural topology optimization are computed through Evolutionary Structural Optimization (ESO) algorithm. Comparisons of the optimal structure topologies using finite element analysis and isogeometric collocation methods are analyzed. The influence of different tension-compression stiffness ratios on the final structure topologies is listed and analyzed. The numerical results show the reliability and performance of the proposed mathematical formulation and asymmetry of natural structure.

In this study, the binary bat algorithm (BBA) for structural topology optimization is implemented. The problem is to find the stiffest structure using a certain amount of material and some constraints using the bit-array representation method. A new filtering algorithm is proposed to make BBA find designs with no separated objects, no checkerboard patterns, less unusable material, and higher structural performance. A volition penalty function for topology optimization is also proposed to accelerate the convergence toward the optimal design. The main effect of using the BBA lies in the fact that the BBA is able to handle a large number of design variables in comparison with other well-known metaheuristic algorithms. Based on the numerical results of four benchmark problems in structural topology optimization for minimum compliance, the following conclusions are made: (1) The BBA with the proposed filtering algorithm and penalty function are effective in solving large-scale numerical topology optimization problems (fine finite elements mesh). (2) The proposed algorithm produces solid-void designs without gray areas, which makes them practical solutions that are applicable in manufacturing.

This article proposes an efficient parameterized level set method (PLSM) for structural topology optimization design with minimum compliance as the objective function and volume fraction as the constraint condition. In the stage of establishing the optimization model, the level set function (LSF) is interpolated using compactly-supported radial basis functions (CS-RBFs) to transform the Hamilton-Jacobi partial differential equation (PDE) into ordinary differential equations (ODEs), thereby making the evolution of the LSF more convenient and efficient, and ensuring the smoothness of the optimization result boundary. The method of moving asymptotes (MMA) is used for solving the established optimization model, and meanwhile the shape sensitivity constraint factor is added to improve computational efficiency. During the evolution of the LSF, an approximate re-initialization scheme is employed to prevent the gradient of the LSF boundary from being too large or too small, thereby improving the numerical stability and the convergence speed of structural topology optimization process. Furthermore, the proposed method is also extensible and applicable to topology optimization of multi-material structures. The feasibility and effectiveness of this method have been verified through several typical numerical examples involving topology optimization of single-material structures and multi-material structures within the framework of minimum compliance design. HIGHLIGHTS An efficient parameterized level set method using the approximate re-initialization scheme is proposed for structural topology optimization. The approximate re-initialization scheme is employed when solving the parameterized level set function via the MMA algorithm. This scheme can prevents the gradient of the level set function boundary from being too large or too small, making the level set function update more stable and accelerating the convergence speed of structural topology optimization. The effectiveness and feasibility of the proposed method are demonstrated through examples of single-material and multi-material structural topology optimization.

This paper will give a short survey about topology optimization of structures. It is particularly focused on topological shape optimization of structures using level-set methods, including the level-set based standard methods and the level-set based alternative methods. The former often directly solve the Hamilton-Jacobi partial differential equation (H-J PDE) to obtain the boundary velocity field using Finite Differential Methods (FDM), and the later commonly employ parametric or equivalent methods to evaluate the velocity field without directly solving the H-J PDE. The unique characteristics of the level-set based topology optimization methods are discussed, and a future perspective and prospects in this research area is also included. A benchmark numerical example is used to showcase the effectiveness of the level-set based methods.

In this thesis numerical methods combining evolutionary optimization algorithms and finite element analysis are developed and applied to problems in cardiac mechanics and structural optimization. In the first application finite element analysis is combined with a real encoded genetic algorithm to determine unknown material parameters in constitutive model for ventricular myocardium using an inverse approach. As a second application suppression of global instabilities in minimum-weight Michell structures is investigated. A real encoded genetic algorithm is combined with a finite element eigenvalue buckling analysis for suppressing global buckling associated with minimum-weight structures. A novel finite element based evolutionary algorithm is developed to determine optimal structural topologies for a 2D continuum. Finally, the topology optimization algorithm described above is modified to determine optimal structural topology for design domains composed of materials having different strengths in tension and compression (dual strength materials). Optimal topologies evolve through successive removal and admission of material based on the current strain energy distribution. Illustrative examples demonstrate the ability to determine optimal structural configuration for a dual strength material domain. Optimal topologies obtained using current scheme are shown to agree with minimum-volume layouts generated using analytic methods based on dual strength material optimality criteria.

Structural topology optimization has gained widespread attention due to more possibilities of innovative structural design. The current research focus/hotspots, application areas, main research scholars, institutions and the countries involved in structural topology optimization are visually presented through clustering and visual analysis based on CiteSpace. The four metric dimensions of the literatures in this paper are as follows: annual quantity of papers and core countries, core authors and co-authors’ institutions, hotspots and burst terms, and the highly co-cited papers. The results show the research hotspots in this field are concentrated on keywords such as "level set method", "sensitivity analysis", "homogenization", "genetic algorithm", etc. Regarding the research frontier, “moving morphable component (MMC)”, “additive manufacturing (AM)” and “deep learning” are hot topics. In addition, Y. Sui, Z. Kang and O. Sigmund, etc. have high publications. M. Bendsøe and O. Sigmund have high citations. Dalian University of Technology, Technical University of Denmark, etc. are prominent institutions. Moreover, China accounts for more than 34% in the terms of original WOS literatures following by the USA and Australia. This paper could identify structural topology optimization development patterns for the scholars concerned with this field, especially novices, to quickly focus and track the research priorities.

The present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms (GA), in developing near-optimal topologies of load bearing truss structures. The problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space. The development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness. The approach is an adaptation of the ground-structure method of topology optimization, and is implemented in a two-level GA based search. In this process, the kinematic stability constraints are imposed at one level, followed by the treatment of response constraints at a second level of optimization. Singular value decomposition is used to assess the kinematic stability constraint at the first level of design, and results in the creation of a finite number of increasing weight, stable topologies. Member sizing is then introduced at a second level of design, where minimal weight and response constraints are simultaneously considered. At this level, the only admissible topologies are those identified during the first stage and any stable combinations thereof. The design variable representation scheme allows for both the removal and addition of structural members during optimization.

Structural topology optimization seeks to identify the most efficient way to allocate material within a given domain to achieve a specific design objective. This research area has broad applications in various fields, including mechanical design and other physical disciplines. Over the past two decades, a great variety of applications and diverse research papers on structural topology optimization have been undertaken and published in the last two decades to highlight its acceptance and advantages. This paper presents a scientometric analysis of 5713 papers published between 2000 and 2022 to provide an overview and visualization of the development of structural topology optimization. While there are numerous approaches to topology optimization, this study focuses on presenting a quantitative analysis of the most popular and influential methods. The method used in this paper involved data collection and analysis through CiteSpace, one of the most popular software tools in this field. This paper provides a comprehensive overview of the latest developments of research in structural topology optimization and identifies key directions for future research. The analysis of the top 10 co-cited articles revealed four main approaches that have been developed for structural topology optimization.

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

The production of complex functional structures becomes possible using Additive Manufacturing (AM) technology. Topology optimization allows to obtain lightweight and high-performance parts. In this study, the combining of topology optimization with additive manufacturing is proposed. This combination is mainly motivated by two principal reasons. Firstly, topology optimization generates complex structures that cannot be achieved by conventional processes. Secondly, a great flexibility in part design is provided by additive manufacturing. Indeed, an automated algorithm for the topology optimization of structures obtained by additive manufacturing is presented. The proposed methodology is based on the generation of the geometry and the mesh of the studied structure using ANSYS software that uses finite element analysis (FEA). Then, the topology optimization algorithm is implemented in MATLAB. The developed algorithm is illustrated by a numerical example involving the minimization of the compliance of 3D beam structure.

Having many attractive advantages, genetic algorithms (GAs) have been applied to many design optimization problems. However, the practical application of GAs to realistic tall building design is still rather limited, since GAs require a large number of structural reanalyses and perform poorly in local searching. While the Optimality Criteria (OC) method can be applied effectively to the element sizing optimization of tall buildings, there is no guarantee that the OC method can always lead to the global optimum. In this paper, the so-called hybrid OC-GA method is presented to fully exploit the merits of both OC and GA for topology and element sizing optimization of braced tall steel frameworks. While the GA is particularly useful in the global exploration for optimal topologies, the OC technique serves as an efficient local optimizer for resizing elements of selected topologies. The effect of population size and the importance of the local OC search operator have been investigated. The applicability and efficiency of the hybrid OC-GA method were tested with two braced steel building examples. Results indicate that the incorporation of the OC operator into the GA has remarkably improved the efficiency and robustness of the evolutionary algorithm and thus make the hybrid method particularly useful for topology optimization of practical tall building structures involving a large number of structural elements and the use of numerous structural forms.

PurposeThe purpose of this paper is to report the design of a lightweight tree-shaped support structure for fused deposition modeling (FDM) three-dimensional (3D) printed models when the printing path is considered as a constraint. Design/methodology/approachA hybrid of genetic algorithm (GA) and particle swarm optimization (PSO) is proposed to address the topology optimization of the tree-shaped support structures, where GA optimizes the topologies of the trees and PSO optimizes the geometry of a fixed tree-topology. Creatively, this study transforms each tree into an approximate binary tree such that GA can be applied to evolve its topology efficiently. Unlike FEM-based methods, the growth of tree branches is based on a large set of FDM 3D printing experiments. FindingsThe hybrid of GA and PSO is effective in reducing the volume of the tree supports. It is shown that the results of the proposed method lead to up to 46.71% material savings in comparison with the state-of-the-art approaches. Research limitations/implicationsThe proposed approach requires a large number of printing experiments to determine the function of the yield length of a branch in terms of a set of critical parameters. For brevity, one can print a small set of tree branches (e.g. 30) on a single platform and evaluate the function, which can be used all the time after that. The steps of GA for topology optimization and those of PSO for geometry optimization are presented in detail. Originality/valueThe proposed approach is useful for the designers and manufacturers to save materials and printing time in fabricating complex models using the FDM technique. It can be adapted to the design of support structures for other additive manufacturing techniques such as Stereolithography and selective laser melting.