An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

基于测量的网络生成树拓扑优化

提出一种基于测量的网络生成树拓扑优化算法，可以根据网络上的流量分布动态地调整网络拓扑。仿真结果表明，在网络输入相同时，这种算法可以显著降低网络资源的占用，并可以有效地消除网络上短期流量波动对拓扑稳定性的影响，防止网络拓扑频繁变化。     

A Multi-Criteria Topology Optimization for Systematic Design of Compliant Mechanisms

This paper attempts to present a new multi-criteria topological optimization methodology for the systematic design of compliant micro-mechanisms. Instead of employing only the strain energy (SE) or the functional specifications such as mechanical efficiency (ME), in this study an alternative formulation representing multiple design requirements is included in the optimization to describe the performance of compliant mechanisms. In most conventional designs, SE is used to only measure the design requirement from the point of view of structures, while ME is usually applied to describe the mechanical performance of mechanisms. However, the design of a compliant mechanism is required to comprehensively consider both the structural and mechanical performance quantities. Displacement, material usage and dynamic response are imposed as three external constraints to narrow the searching domain. In doing so, the multi-criteria optimization problem involving the SE and ME can reasonably embody the mechanical structural characteristics of compliant mechanisms. A sequential convex programming, the method of moving asymptotes (MMA), is applied to solve the topological optimization problem, which can not only ensure numerical accuracy but also both the monotonous and non-monotonous structural behaviors. SIMP model (solid isotropic material with penalization) is used to indicate the dependence of elastic modulus upon regularized element densities. Several typical numerical examples are used to demonstrate the effectiveness of the proposed methodology, and the prototype of a resulting mechanism has also been manufactured to validate the design of the compliant mechanism.     

Quantum-Inspired Evolutionary Algorithm for Topology Optimization of Modular Cabled-Trusses

This article proposes an alternative optimization framework applied to topology optimization of modular lightweight cabled-truss structures. These structures are described as a system of intrinsically positioned cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimized topologies are determined through a stochastic discrete optimization procedure that uses ground structure approach, nonlinear finite element analysis, and quantum-inspired evolutionary algorithms. The optimization searches for optimal mass reduction with minimal losses in stiffness, such relation, is expressed by the stiffness-to-mass ratio parameter. Nonlinear finite element analysis is used to evaluate the static structural response. In order to decrease computation time, kinematically instable and structurally invalid individuals are filtered before evaluation. Modular design approach is taken into consideration to reduce the number of design variables and increase the productibility of cabled-trusses. Symmetric structural response is desired since in several mechanical applications forces can assume different directions during the working cycle. A modular ground structure with 300 elements is optimized, and optimal truss and cabled-truss topologies are compared. Complementary analyses comprise the investigation of the structural performance under different number of modules and slenderness ratios. The results indicate that the proposed optimization framework leads to optimized structures. In addition, it was observed that cabled trusses presented significant improvements in structural performance when compared with trusses.     

Topology optimization for submerged buoyant structures

This paper presents an evolutionary structural topology optimization method for the design of completely submerged buoyant modules with design-dependent fluid pressure loading. This type of structure is used to support offshore rig installation and pipeline transportation at all water depths. The proposed optimization method seeks to identify the buoy design that has the highest stiffness, allowing it to withstand deepwater pressure, uses the least material and has a minimum prescribed buoyancy. Laplace's equation is used to simulate underwater fluid pressure, and a polymer buoyancy module is considered to be linearly elastic. Both domains are solved with the finite element method. Using an extended bi-directional evolutionary structural optimization (BESO) method, the design-dependent pressure loads are modelled in a straightforward manner without any need for pressure surface parametrization. A new buoyancy inequality constraint sets a minimum required buoyancy effect, measured by the joint volume of the structure and its interior voids. Solid elements with low strain energy are iteratively removed from the initial design domain until a certain prescribed volume fraction. A test case is described to validate the optimization problem, and a buoy design problem is used to explore the features of the proposed method.     

Topology optimization of continuum structures for natural frequencies considering casting constraints

A method for the topology optimization on the natural frequency of continuum structures with casting constraints is proposed. The objective is to maximize the natural frequency of vibrating continuum structures subject to casting constraints. When the natural frequencies of the considered structures are maximized using the solid isotropic material with penalization (SIMP) model, artificial localized modes may occur in areas where elements are assigned with lower density values. In this article, the topology optimization is performed by the bi-directional evolutionary structural optimization (BESO) method. The effects of different locations of concentrated lump mass, different volume fractions and meshing sizes on the final topologies are compared. Both two and four parting directions are investigated. Several two- and three-dimensional numerical examples show that the proposed BESO method is effective in achieving convergent solid–void optimal solutions for a variety of frequency optimization problems of continuum structures.     

Lightweight Frame Topology Optimization Method Based on Multi-objective

The application of new materials is an important direction for automotive lightweighting.On the basis of ensuring the comprehensive performance of components,th...     

基于等几何裁剪分析的拓扑与形状集成优化

提出了将设计和分析、拓扑与形状优化集成的思想,探索了基于等几何裁剪分析的拓扑与形状集成优化设计算法,该方法统一了结构优化的计算机辅助设计、计算机辅助工程分析和优化设计的模型,基于B样条的等几何裁剪分析既能准确表达几何形状,又可以用裁剪面分析方便处理任意复杂拓扑优化问题,由裁剪选择标准确定合理的拓扑结构变动方向,结构变动时无需重新划分网格,设计结果突破初始设计空间的限制,还可方便优化形状。建立了等几何裁剪灵敏度分析的计算方法,给出了等几何裁剪分析拓扑与形状集成优化算法,通过典型实例表明所用方法的正确性和有效性。     

Capacitance Characteristic Optimization of Germanium MOSFETs with Aluminum Oxide by Using a Semiconductor-Device-Simulation-Based Multi-Objective Evolutionary Algorithm Method

This paper, for the first time, optimizes the characteristics of capacitance–voltage (C–V) of germanium (Ge) metal-oxide-semiconductor field effect transistors (MOSFETs) with aluminum oxide (Al₂O₃) by using a semiconductor-device-simulation-based multi-objective evolutionary algorithm (MOEA) technique. By solving a set of 2D semiconductor device transport equations, numerical simulation is intensively performed for the optimization of the C–V curve of Ge MOSFET devices. To optimize the capacitance of Ge MOSFETs with respect to the applied voltage, by minimizing the total errors of the C–V curve between the device simulation and a given specification (and experimentally measured data), the thicknesses of Al₂O₃ and GeO₂, the work function of gate electrodes, the distribution range of channel doping, the dielectric constants of Al₂O₃ and GeO₂, and the source/drain doping concentration are considered in the process of optimization. The semiconductor device simulation and the MOEA method are integrated and performed based on a unified optimization framework. According to the sharp variation characteristics of the C–V curve, except for using a residual sum of squares (RSS) (i.e., the sum of squares of residuals) as an objective function, physical key parts of the curve are also considered in the optimization problem. The engineering results of this study indicate that the semiconductor-device-simulation-based MOEA method shows great performance to optimize the parameters, which not only minimize the objective values but also match the curve shape.     

拓扑优化方法在复合材料设计中的研究进展

按照设计变量,叙述了连续变量和离散变量拓扑优化设计的一些常用算法,其中包括均匀化方法、变密度法、变厚度法、移动渐进算法、模拟退火法、遗传算法、相对差商法和Tabu搜索法,并对各种方法的优缺点进行了比较;对二维和三维复合材料的拓扑学优化设计研究现状和方法进行了阐述;提出了拓扑优化设计复合材料的未来研究方向.     

The Application of Reliability Based Optimization of Tophat Stiffened Composite Panels Subject to Bi-Directional Buckling Loads

Stiffened composite panels are used within many applications, from aerospace to marine applications. Stiffened panels are utilized for their high strength to weight ratio and flexibility of layups while counteracting the low stiffness exhibited by composites. Complications arise when attempting to utilize the full variability of layups in conjunction with reliability constraints creating a complex design problem when constrained by both buckling and material strength. To aid the process of optimizing the design of composite structures and layups, while ensuring a low mass, this paper presents a bi-level optimization scheme for minimization of the weight oftophat stiffened composite panels with probabilistic deflection constraints. To improve the computational efficiency, an energy based grillage method is formulated and applied for the investigation of buckling problems under bi-directional in-plane loads The method is validated by comparing the results obtained from FE model calculations. The variables that have a large impact on the structural safety have been identified by both safety index and COV based reliability analysis. A parametric study of plate dimensions and loading ratios is conducted to investigate the coupling effects on critical buckling load. The method presented in this paper, makes it possible for engineers to improve their designs, at an early stage, with an integrated consideration between product performance and design parameters.     

拓扑优化方法及其在微型柔性结构设计中的应用

介绍了连续体结构拓扑优化设计中常用的均匀化方法和渐进结构优化法的原理，对拓扑优化中出现的数值不稳定现象——棋盘格式、网格依赖性和局部极值——进行了分析，通过典型实例和笔者最近的研究工作说明了拓扑优化在微型柔性机构设计中的应用，最后对拓扑优化技术的发展进行了展望。     

Evolutionary Design of Nickel-Based Superalloys Using Data-Driven Genetic Algorithms and Related Strategies

Data-driven models were constructed for the mechanical properties of multi-component Ni-based superalloys, based on systematically planned, limited experimental data using a number of evolutionary approaches. Novel alloy design was carried out by optimizing two conflicting requirements of maximizing tensile stress and time-to-rupture using a genetic algorithm-based multi-objective optimization method. The procedure resulted in a number of optimized alloys having superior properties. The results were corroborated by a rigorous thermodynamic analysis and the alloys found were further classified in terms of their expected levels of hardenabilty, creep, and corrosion resistances along with the two original objectives that were optimized. A number of hitherto unknown alloys with potential superior properties in terms of all the attributes ultimately emerged through these analyses. This work is focused on providing the experimentalists with linear correlations among the design variables and between the design variables and the desired properties, non-linear correlations (qualitative) between the design variables and the desired properties, and a quantitative measure of the effect of design variables on the desired properties. Pareto-optimized predictions obtained from various data-driven approaches were screened for thermodynamic equilibrium. The results were further classified for additional properties.     

基于分析的空调系统运行控制的多目标优化

针对空调系统运行效率低下,且运行过程中子系统之间相互影响、相互制约的问题,本文基于分析方法提出一种空调系统多目标运行优化方法,以提高空调系统整体的运行效率。以某机场航站楼空调系统为研究对象,采用分析方法建立了空调系统的生产结构图,并根据生产结构将空调系统划分为3个子系统。在建立子系统分析模型的基础上,以3个子系统的最小损为优化目标,采用多目标粒子群优化算法(MOPSO)对空调系统的运行参数进行优化。针对某一典型日的运行工况对空调系统进行多目标优化,结果表明:相对于空调系统的原始控制方式,采用多目标运行优化方法可以有效减小空调各个子系统以及整个系统的损,使空调系统的运行效率明显提高,达到了节能的目的。     

Chance-Constrained Optimization of Pumping in Coastal Aquifers by Stochastic Boundary Element Method and Genetic Algorithm

In this paper the optimization of groundwater pumping in coastal aquifers under the threat of saltwater intrusion is investigated. The aquifer is inhomogeneous and contains several hydraulic conductivities zones. The aquifer data such as the hydraulic conductivities are uncertain, but with their expected mean and standard deviation values given. A stochastic boundary element method based on the perturbation technique is employed as the simulation tool. The stochastic optimization is handled by the chance-constrained programming. Genetic algorithm is selected as the optimization tool. Numerical examples of deterministic and stochastic problems are provided to demonstrate the feasibility of the proposed schemes.     

Chemical Composition Design of Superalloys for Maximum Stress, Temperature, and Time-to-Rupture Using Self-Adapting Response Surface Optimization

We have adapted an advanced semistochastic evolutionary algorithm for constrained multiobjective optimization and combined it with experimental testing and verification to determine optimum concentrations of alloying elements in heat-resistant austenitic stainless steel alloys and superalloys that will simultaneously maximize a number of the alloy's mechanical properties. The optimization algorithm allows for a finite number of ingredients in the alloy to be optimized so that a finite number of physical properties of the alloy are either minimized or maximized, while satisfying a finite number of equality and inequality constraints. Alternatively, an inverse design method was developed, which uses the same optimization algorithm to determine chemical compositions of alloys that will be able to sustain a specified level of stress at a given temperature for a specified length of time. The main benefits of the self-adapting response surface optimization algorithm are its outstanding reliability in avoiding local minimums, its computational speed, ability to work with realistic nonsmooth variations of experimentally obtained data and for accurate interpolation of such data, and a significantly reduced number of required experimentally evaluated alloy samples compared with more traditional gradient-based and genetic optimization algorithms. Experimentally preparing samples of the optimized alloys and testing them have verified the superior performance of alloy compositions determined by this multiobjective optimization.     

压缩感知中非凸优化的极大熵方法

压缩感知可由少量观测重构K-稀疏信号.本文提出的极大熵方法克服了压缩感知中lp(0＜p＜1)最优化问题的非光滑性.极大熵方法构造一条同伦曲线以获得全局最优稀疏解.数值实验表明极大熵方法的信号重构性能优于l1最优化和AST算法.     

SoftFEM: The Soft Finite Element Method

While the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a “black box” approach to FEM-based optimization remains elusive. To this end, we propose here an integrated finite element-soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient-based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population-based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.     

Estimation of Density as a Function of Temperature and Pressure for Imidazolium-Based Ionic Liquids Using a Multilayer Net with Particle Swarm Optimization

The liquid density of imidazolium-based ionic liquids has been estimated using a combined method that includes an artificial neural network and a simple group contribution method. A total of 1736 data points of density at several temperatures and pressures, corresponding to 131 ionic liquids, have been used to train the neural network developed with particle swarm optimization. To discriminate among the different substances, the molar mass and the structure of the molecule were given as input variables. Then, new values of density as a function of temperature and pressure for 33 other ionic liquids (426 data points) have been predicted and the results compared to experimental data from the literature. The results show that the chosen artificial neural network with particle swarm optimization and the group contribution method represent an excellent alternative for the estimation of the liquid density of imidazolium-based ionic liquids with acceptable accuracy (AARD=0.44; R ² = 0.9934), for a wide range of temperatures and pressures (258 K to 393K and 99kPa to 206,940kPa).