离散变量结构优化的拟满应力设计方法

本文以满应力设计思想为基础,提出了适用于离散变量结构优化设计计算的拟满应力设计方法。该方法能直接计算具有应力约束和截面尺寸约柬的离散变量结构优化设计问题,也能处理同时具有稳定性约束和位移约束的多工况、多约束、多变量的离散变量结构优化设计问题。算例结果表明,拟满应力设计方法对于离散变量结构优化计算是非常有效的。     

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。     

先进复合材料格栅圆柱壳优化设计的混合遗传算法

复合材料格栅加筋结构优化设计是一个属于多工况、多约束、连续变量和非连续变量混合的优化问题。对遗传算法与单纯形法作了相应的改进, 利用外罚函数法将受稳定性约束和应变约束的多约束优化问题转化为无约束优化。在此基础上, 提出了一种遗传算法与单纯形法相结合的混合遗传算法, 通过与其它文献结果和传统遗传算法结果对比, 证实了混合遗传算法的有效性。以受均匀侧压时复合材料格栅圆柱壳优化设计为例,分别讨论了不同格栅类型和有、无强度约束时的优化结果。分析表明, 整体稳定性是控制该结构安全度的最主要约束因素。本算法具有高效和方便的特点。     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。     

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     

离散复合形法的改进及应用研究

在工程设计中,复合形法是求解约束非线性规划的一种直接方法.它计算简单、适用性强,是解决工程技术问题的常用方法.通常情况下,复合形法多用于连续变量优化设计问题的求解,但在工程实际中还存在大量的离散变量优化问题.为此,我们在连续变量复合形算法的基础上,采用平均值舍入法获取离散点,并改进了复合形迭代过程和停机准则,使之成为一种能直接求解离散变量优化解的方法.几个典型工程离散变量优化设计算例的计算结果表明,我们提出的方法十分有效.     

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。     

基于Newmark法敏度计算的刚架结构动力优化

提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。     

输电塔结构离散变量优化设计方法

鉴于格构式输电塔结构具有杆件众多、型式复杂等显著特点,所以建设和发展既安全可靠,又经济合理的此类结构一直是工程界的研究热点和难点。因此,该文提出了一套完整的基于蚁群优化算法的输电塔结构离散变量优化设计方法。该方法是在结构的截面、拓扑和形状变量统一转化为离散变量的基础上,将4类不同层次的优化问题统一为不同规模的标准化旅行商问题,并最终采用蚁群算法实现输电塔结构的优化设计。通过对某一实际输电塔结构的优化设计表明:该文方法不仅可以简单高效的求解输电塔结构的截面、拓扑、形状和布局优化问题,而且清晰明确的阐述了不同优化内容的物理意义和优化准则,实现了优化方法和思路的统一。此外,基于蚁群算法的输电塔结构离散变量优化方法通用性强、易于程序化,而且具有非常好的工程应用前景。     

基于敏度分析的框架抗震优化

针对目前结构抗震优化设计方法存在优化效率低下的问题,提出一种高效的框架抗震优化设计方法。在有限元法和Newmark法基础上导出一种高效的层间相对位移对设计变量一阶和二阶导数的算法,建立显含时间参数,以结构质量最小化为目标,同时满足层间相对位移和设计变量约束的优化数学模型,通过积分型内点罚函数将显含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题,利用层间相对位移对设计变量一阶和二阶导数的信息计算罚函数的梯度和海森矩阵,然后利用梯度和海森矩阵构造求解优化设计问题高效有效的优化算法。算例表明本文的抗震优化方法能获得结构的最优设计,具有简单、下降速度快、不需要进行一维搜索等特点。是一种有效和高效的框架抗震二阶优化方法。     

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.     

混合离散变量模拟退火方法及其应用

基于海洋工程中存在的设计变量为离散型和连续型的混合离散变量的情况,探讨了一种优化设计问题的方法———混合离散模拟退火法.该方法相对常规模拟退火方法有一定改进并且针对混合离散变量进行了特定处理.实际算例计算表明,该方法可用于海洋工程优化设计中,其结果不需圆整,而且其解题可靠性和效率相当高.     

Engineering optimization using a real-parameter genetic-algorithm-based hybrid method

A hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is proposed. The proposed algorithm incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators such that its hill-climbing ability towards the optimum solution is improved. The algorithm is used to optimize the weight of four planar or space truss structures and the results are compared with those obtained using other well-known optimization schemes. The evaluation trials investigate the performance of the algorithm in optimizing over discrete sizing variables only and over both discrete sizing variables and continuous configuration variables. The results show that the proposed algorithm consistently outperforms the other optimization methods in terms of its weight-saving capabilities. It is also shown that the global searching ability and convergence speed of the proposed algorithm are significantly improved by the inclusion of adaptive mechanisms to adjust the values of the genetic operators. Hence the hybrid algorithm provides an efficient and robust technique for solving engineering design optimization problems.     

Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

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。     

离散变量桁架结构拓扑优化设计的混合算法

将相对差商法和混沌优化结合起来,形成求解离散变量桁架结构拓扑优化设计的混合算法。利用相对差商法可以对离散变量快速寻优的特点,及混沌变量的全局遍历性,可以有效地跳出局部最优解,达到拓扑优化全局寻优的目的。通过采用和准最优解的对比及几何稳定性的判断等辅助性技术,降低了重分析次数。同时,高效的重分析方法的结合,提高了求解的效率,也避免了拓扑优化问题中求解的一些困难。算例表明,该算法对于离散变量的拓扑优化设计问题是快速有效的。     

Design optimization of cold-formed steel portal frames taking into account the effect of building topology

Cold-formed steel portal frames are a popular form of construction for low-rise commercial, light industrial and agricultural buildings with spans of up to 20 m. In this article, a real-coded genetic algorithm is described that is used to minimize the cost of the main frame of such buildings. The key decision variables considered in this proposed algorithm consist of both the spacing and pitch of the frame as continuous variables, as well as the discrete section sizes. A routine taking the structural analysis and frame design for cold-formed steel sections is embedded into a genetic algorithm. The results show that the real-coded genetic algorithm handles effectively the mixture of design variables, with high robustness and consistency in achieving the optimum solution. All wind load combinations according to Australian code are considered in this research. Results for frames with knee braces are also included, for which the optimization achieved even larger savings in cost.     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.