离散变量结构拓扑优化设计综合算法的进一步探讨

本文对离散变量结构拓扑优化设计的综合设计方法作了进一步的研究。通过对离散变量结构拓扑优化设计综合算法的数学模型与传统的拓扑估化模型所作的比较,指出因为综合算法的拓扑优化模型中既所含了截面变量又包含拓扑变量,它反击了结构拓扑优化的本质,从而能有效地避免“奇异拓扑”的问题。由于模型的目标函数和约束函数的单调性,从而可以高效地利用相对差商法进行求解。通过数值实验对综合算法的数值稳定性进行了讨论,为应用于     

非线性最优化问题的一种混合解法

把BFGS方法与混沌优化方法相结合,基于混沌变量提出一种求解具有变量边界约束非线性最优化问题的混合优化方法。混合算法兼顾了混沌优化全局搜索能力强和BFGS方法收敛速度快的优点,成为一种求解非凸优化问题全局最优的有效方法。算例表明,当混沌搜索的次数达到一定数量时,混合优化方法可以保证算法收敛到全局最优解,且计算效率比混沌优化方法有很大提高。     

基于遗传算法的离散型结构拓扑优化设计

采用遗传算法求解包括桁架结构和框架结构的离散型结构拓扑优化问题。在遗传算法的基础上,通过引入拓扑变量并修改被删除杆件的材料弹性模量,提出了一个受多工况荷载作用,能同时考虑应力、稳定及位移等约束的离散型结构拓扑优化问题统一数学模型。该模型不但能同时适用于桁架结构和框架结构等离散型结构拓扑优化问题,而且还能解决奇异最优解问题。结合上述统一数学模型和遗传算法,给出了求解离散型结构拓扑优化问题的优化方法。算例结果表明,采用该文提出的拓扑优化方法可有效、方便地对桁架结构、框架结构等离散型结构进行拓扑优化设计。     

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.     

基于并行混沌和复合形法的桁架结构形状优化

针对多工况下受应力、位移和局部稳定性约束的桁架形状优化问题,提出了基于并行混沌优化算法和复合形法的混合优化算法。该算法综合利用了并行混沌的全局搜索能力,复合形法的快速局部搜索能力和混沌细搜索。首先,利用并行混沌优化算法快速搜索到全局最优解附近,然后应用改进复合形法以并行混沌的优化解为初始复形进行搜索,提高了最优解的搜索速度,最后应用混沌细搜索策略提高最优解的精度。两个典型数值算例验证了该混合优化方法对桁架形状优化问题的有效性和稳定性。     

遗传算法在桁架结构优化设计中的应用

本文提出桁架结构系统优化设计的新方法—遗传算法。它与常规化算法的不同之处在于从多个初始点开始寻优，并采用交迭和变异算子避免过早地收敛到局部最优解，可获得全局最优解，且不受初始值影响。该算法不必求导计算，编程简单、快捷，尤其适用于具有离散变量的结构优化设计问题。     

基于融合禁忌搜索粒子群算法的配电网无功优化

从数学角度分析,配电网无功优化是一个非线性、多变量、多约束的混合规划问题。粒子群优化搜索算法被广泛应用于求解配电网无功优化问题。由于粒子群算法粒子群在进化过程易趋向同一化,失去多样性,从而使算法陷入局部最优解。本文在分析配电网无功优化的特性基础上,提出一种改进的紧融合禁忌搜索-粒子群算法用于配电网无功优化问题的求解。通过将禁忌搜索功能融合到粒子历史最优解和全局最优解寻优过程中,避免了粒子群算法寻优过程中出现的局部最优问题,从而提高粒子群算法的全局搜索能力。通过IEEE14节点系统的仿真计算结果表明,改进的算法能取得良好的效果。     

给水管网管径优化设计的遗传算法

给水管网管径设计是离散变量的非线性优化问题，常规的数学规划方法采用连续变量求解，其最优解受初始值影响大。本文提出一种新方法－－遗传算法，它的特点在于：从多个初始点开始寻优，并采用交迭和变异算子避免过早地收敛到局部最优解，可获得全局最优解，且不受初始值影响。该算法不必求导计算，编程简单。     

求解VRP问题的混沌模拟退火萤火虫算法

目的使萤火虫优化算法(GSO)能够适用于车辆路径问题(VRP)的求解,同时提高该算法的求解性能。方法通过对GSO算法的改进,提出求解VRP问题的混沌模拟退火萤火虫优化算法(CSAGSO)。首先,设计改进的GSO算法(IGSO)使IGSO算法能够适应VRP问题的求解;其次,在IGSO算法中引入模拟退火机制,提出模拟退火萤火虫优化算法(SAGSO),使IGSO算法可有效避免陷入局部极小并最终趋于全局最优。然后,在SAGSO算法中引入混沌机制,提出CSAGSO算法,对SAGSO算法的荧光素浓度值进行混沌初始化和混沌扰动;最后,对标准算例集进行仿真测试。结果与遗传算法、蚁群算法和粒子群算法相比,CSAGSO算法的全局寻优能力、收敛速度及稳定性均改善了50%以上。结论对GSO算法的改进是合理的,且CSAGSO算法的全局优化能力、收敛速度和稳定性均优于遗传算法、蚁群算法和粒子群算法。     

TSCOA算法在梯1级水电站日优化调度中的应用

本文将混沌优化算法与禁忌搜索法相结合,提出一种既可全局寻优又具有“记忆”能力的优化算法——TSCOA,并将这种算法引用到梯级水电站日优化调度问题中。该方法原理简单,易编程实现,能以较快速度收敛到全局最优解,从而为分时电价环境下水电站日优化调度问题提供一种新的解决途径。     

An optimization technique using the characteristics of genetic algorithm

Optimization problems could happen often in discrete or discontinuous search space. Therefore, the traditional gradient‐based methods are not able to apply to this kind of problems. The discrete design variables are considered reasonably and the heuristic techniques are generally adopted to solve this problem, and the genetic algorithm based on stochastic search technique is one of these. The genetic algorithm method with discrete variables can be applied to structural optimization problems, such as composite laminated structures or trusses. However, the discrete optimization adopted in genetic algorithm gives rise to a troublesome task that is a mapping between each strings and discrete variables. And also, its solution quality could be restricted in some cases. In this study, a technique using the genetic algorithm characteristics is developed to utilize continuous design variables instead of discrete design variables in discontinuous solution spaces. Additionally, the proposed algorithm, which is manipulating a fitness function artificially, is applied to example problems and its results are compared with the general discrete genetic algorithm. The example problems are to optimize support positions of an unstable structure with discontinuous solution spaces.     

An engineering method for complex structural optimization involving both size and topology design variables

This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second-level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second-level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.     

Simultaneous partial topology and size optimization of a wing structure using ant colony and gradient based methods

This article presents a methodology and process for a combined wing configuration partial topology and structure size optimization. It is aimed at achieving a minimum structural weight by optimizing the structure layout and structural component size simultaneously. This design optimization process contains two types of design variables and hence was divided into two sub-problems. One is structure layout topology to obtain an optimal number and location of spars with discrete integer design variables. Another is component size optimization with continuous design variables in the structure FE model. A multi city-layer ant colony optimization (MCLACO) method is proposed and applied to the topology sub-problem. A gradient based optimization method (GBOM) built in the MSC.NASTRAN SOL-200 module was employed in the component size optimization sub-problem. For each selected layout of the wing structure, a size optimization process is performed to obtain the optimum result and feedback to the layout topology process. The numerical example shows that the proposed MCLACO method and a combination with the GBOM are effective for solving such a wing structure optimization problem. The results also indicate that significant structural weight saving can be achieved.     

基于SA算法的行星齿轮减速器离散变量优化设计

考虑制造工艺要求,将所有设计变量均视为离散变量,包括一般离散变量和伪离散变量,并就这两种情况下状态产生函数的设计原理进行深入研究,解决了将模拟退火算法用于离散变量函数优化的关键技术问题,介绍了一种基于模拟退火算法的离散变量函数优化的新方法。行星齿轮传动中各齿轮的齿数受传动比条件、同轴条件和装配条件的限制而不能任意取值,齿轮的模数也要受国家标准的制约只能取一些离散值,用以数学规划理论为基础的经典约束优化方法求解效果很差,用基于模拟退火算法的离散变量优化设计方法则可以方便快捷地获得满足各方面要求的最优设计方案。     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题。通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法。算例表明:这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率。     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

Robust topology optimization of phononic crystals with random field uncertainty

The uncertain spatial variation of material properties can remarkably affect the band gap characteristics of phononic crystals (PnCs). It is necessary to consider this issue when designing and manufacturing PnC materials/structures. This paper investigates a robust topology optimization method for designing the microstructures of PnCs by considering random‐field material properties. Herein, the spatial distribution of the material properties is first represented by a random field and then discretized into uncorrelated stochastic variables with the expansion optimal linear estimation method; stochastic band gap analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of PnCs is proposed on the basis of the relative elemental density, where a weighted objective function handles the compromise of the mean value and standard deviation of the PnC band gap. The band gap response is analyzed, employing the finite element method for each sample of polynomial chaos expansion. In this context, the sensitivities of the stochastic band gap behaviors to the design variables are also derived. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of PnCs with a relatively large width and less sensitive band gap. Additionally, the effects of the weight factors in the objective function and the variation coefficient of material properties are discussed.     

A robust dual algorithm for topology design of structures in discrete variables

Dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since, in topology design problems, the number of constraints is small in comparison to the number of design variables. Good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint. However, when the perimeter constraint is relaxed, the dual algorithm tends to give bad results, even with the use of higher‐order finite element models as we demonstrate in this work. Since, a priori, one does not know what a good value of the perimeter to be specified is, it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint. We show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint. In particular, we show that the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. Copyright © 2001 John Wiley & Sons, Ltd.