多目标优化的求解方法与发展

本文首先介绍了传统多目标优化求解方法和改进;对遗传算法,模糊优化,神经网络等算法在多目标优化中的应用做了介绍;最后介绍了满意度.     

60MN力标准机承压板结构多目标拓扑优化研究

针对60 MN力标准机承压板结构轻量化拓扑优化时,既要求结构的刚度最大化又要求结构的低阶固有频率最大化的多目标拓扑优化问题,提出了针对多个目标采用加权平均的方法把多目标优化问题转化为单目标优化问题。通过对选定的多个低阶固有频率目标函数采用加权求平均频率的方法实现了承压板结构的动态特性优化;采用加权平均的方法确定了刚度和频率的综合目标函数,实现了承压板结构的多目标拓扑优化,最终设计出了一种新的承压板结构。研究结果表明,优化后的承压板结构的最大变形量减少了25.5%,最大应力减少了14.1%,前五阶固有频率增加了5.7%~13.2%;可以看出新的承压板结构的前五阶固有频率和静态刚度均得到显著提高,从而验证了该优化方法的可行性。     

龙门导轨磨床立柱的多目标拓扑优化

以多工况下的应变能和结构振动固有频率为优化目标函数,对龙门导轨磨床立柱进行多目标拓扑优化。将质量小于1.3t做为约束函数,得到最佳质量分布云图,根据质量分布云图重新对立柱部件进行结构设计,再对新立柱做进一步的多目标参数优化,采用同样的约束函数和目标函数完成尺寸优化。优化结果表明,质量减少18%,最大总位移减少6.7%,第一阶固有频率提高11%。实现了在减少材料使用的情况下提高立柱动静态特性的轻量化设计目标。     

超精密机械结构多目标拓扑优化设计

为满足超精密工件台结构极高的静动性能要求,提出了一种基于目标分层的多目标结构拓扑优化方法,并将其应用于超精密工件台关键件的结构优化设计中。基于ANSYS的仿真实验结果表明,多目标结构拓扑优化方法能够有效地提高结构的静动性能和设计效率,满足超精密结构极高的性能要求,为现代工程结构的多目标优化设计和改进提供了理论依据和方法。     

基于折衷规划的车架结构多目标拓扑优化设计

为避免单目标拓扑优化无法考虑其他因素的缺点,笔者提出了一种车架结构的多目标拓扑优化研究方法.采用折衷规划法建立了车架结构多目标拓扑优化的数学模型,其中多刚度拓扑优化目标函数采用折衷规划法定义,振动频率拓扑优化目标函数采用平均频率法定义.以某越野车车架为例,通过优化得到了同时满足刚度和振动频率要求的车架拓扑结构.理论分析...     

控制臂多目标拓扑优化研究

以控制臂为对象,研究了结构材料的多目标拓扑优化问题。应用加权特征值倒数法和折中规划法相结合的方法建立静动态多目标优化数学模型。在连续体结构变密度拓扑优化方法的基础上,建立了控制臂拓扑优化的有限元模型,确定子目标权重系数,进行了多目标拓扑优化。优化结果得到了材料的理想分布,提高了结构固有频率,减低了结构质量,实现多目标的同步优化。     

汽车车架结构多目标拓扑优化方法研究

为了研究以静态多工况下刚度和动态振动频率为目标函数的车架拓扑结构,提出了一种结构的多目标拓扑优化研究方法。基于实体各向同性材料惩罚函数的拓扑优化方法,采用折衷规划法定义多目标拓扑优化和多刚度拓扑优化的目标函数,而振动固有频率拓扑优化的目标函数则采用平均频率法定义。通过优化得到了同时满足静态刚度和振动低阶频率要求的汽车车架结构拓扑。该方法避免了单目标拓扑优化无法考虑其他因素的缺点,适合连续体结构的多目标拓扑优化。     

利用双向渐进结构优化法对结构固有振型的优化

利用双向渐进结构优化法研究结构的固有振型优化问题，双向渐进结构优化法(bi—directional evolutionary struetural optimization，简称BESO)是一种拓扑优化方法，它基于这样一个简单的优化程序：从结构中一步步地删去对结构目标性能低效或无效的材料，同时增加对结构目标性能高效的材料，从而使材料布局趋于优化。文中分别采用近似重分析思路的方法和基于变分法推导的公式计算单元特征向量灵敏度，并简单阐述BESO法对结构固有振型(特征向量)进行拓扑优化的一般过程。数值算例表明，用该方法对结构固有振型的优化是行之有效的，且用变分法计算特征向量灵敏度进行优化较之近似重分析法效率更高。     

结构多目标拓扑优化设计

为了研究结构多目标拓扑优化设计方法,引入了数学规划法的相关理论,分别采用最短距离法、平方加权法、规范目标法、线性加权法和折衷规划法建立了五种不同的目标函数,将多目标拓扑优化问题转化为单目标拓扑优化问题。通过在一个优化实例中验证这五种方法,结果表明五种方法均能解决多目标拓扑优化问题,其中线性加权法在提高结构刚度方面贡献比较大,而折衷规划法更能提高结构的固有频率。     

应用响应面法的电机支架多目标优化设计

针对汽车电机支架在增大载荷力条件下的结构优化问题,利用响应面法和多目标优化算法相结合,对电机支架进行有限元分析和多目标结构优化设计.以应力值和支架质量为优化目标,通过表面中心复合实验设计和响应面方法构建响应面模型,并在此基础上应用Hammersley筛选法对其进行多目标优化求解.优化结果表明在载荷力增大8.3％的情况下,优化后电机支架的最大应力降低9.7％,质量降低3％,满足预期结构优化目标.     

Evolutionary bi-criteria optimum design of robots based on task specifications

The optimum robot structure design problem based on task specifications is an important one, since it has greater influence on manipulator workspace design, vibrations of the manipulator during operation, manipulator efficiency in the work environment and power consumption. In this paper, an optimization robot structure problem is formulated with the objective of determining the optimal geometric dimensions of the robot manipulators considering the task specifications (pick and place operation). The aim is to minimize torque required for motion and maximize manipulability measure of the robot subject to dynamic, kinematic, deflection and structural constraints with link physical characteristics (length and cross-sectional area parameters) as design variables. In this work, five different cross-sections (hollow circle, hollow square, hollow rectangle, C-channel and I-channel) have been experimented for the link. Three evolutionary optimization algorithms namely multi-objective genetic algorithm (MOGA), elitist nondominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) are used for the optimum structural design of 2-link and 3-link planar robots. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best optimal solution. Two multiobjective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the Pareto optimal fronts. Two more multiobjective performance measures namely optimiser overhead and algorithm effort, are used to find computational effort of optimization algorithm. The results obtained from various techniques are compared and analyzed.     

NEW MULTIOBJECTIVE SIMULATED ANNEALING ALGORITHM AND ITS APPLICATION TO TURBINE CASCADES’ DESIGN

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非稳态罚函数遗传算法及其用于机械/结构系统的健壮性设计

在机械 /结构的优化设计中 ,普遍存在约束的作用 ,且最优解往往位于可行域的边界上。由于外界环境的变化或人为因素造成设计变量扰动 ,可能使设计成为不可行。本文提出了一种基于设计变量敏感性的健壮性设计方法 ,并用非稳态罚函数遗传算法来实现多目标优化设计。     

System reliability optimization using time value of money

In the recent years, many significant methods for evaluation of structural system reliability and its improvement have been evolved. First step for improving the longevity of system is to estimate the system reliability. After that, improving actions can be employed in an optimized way. This paper tries to evaluate the reliability of system during function period. Also, the optimization model has been developed to make a best decision on component's number and improving actions' level. To achieve this goal, reliability value and engineering economic tools have been useful to model a multiobjective problem. At last, an illustrative example is presented, and genetic algorithm, as the most applicable meta-heuristic method in the field of reliability optimization, has been used.     

NEW MULTIOBJECTIVE SIMULATED ANNEALING ALGORITHM AND ITS APPLICATION TO TURBINE CASCADES' DESIGN

A new kind of multiobjective simulated annealing algorithm is proposed,in which the concept of non-dominate d character is introduced and a new multiobjective acceptance criterion is set u p.The optimization example of a typical mathematical problem with two minimum ob jective functions indicates that all of the solutions contract to the set of the non-dominated points,and the variation trend of the optimal solutions is verif ied to be identical with that obtained using Genetic Algor thms.The ne w developed algorithm is then applied to the multiobjective optimization design of turbine cascades,in which it is coupled with the aerodynamics computation of the cascade flow fields and performance and the calculated loss coefficient and work potential of the cascade are considered as the objective functions,thus set ting up a technique to the engineering optimization design for the cascades.The optimization results,by the view of a group of optimal solutions,show that the a lgorithm is superior to the traditional technique of multiobjective optimization design and can be applied to more than two objective optimization cascade desig n problem or other engineering multiobjective optimization designs.     

压电智能桁架作动器配置的优化设计

利用优化设计的思路来探讨作动器的优化配置,并将优化模型分为两类:待控模态数目固定前提下优化作动器的数目和位置;固定作动器的数目,优化作动器的位置以控制更多的模态数目。并根据该类优化问题为多目标优化的性质,提出了一种基于模糊逻辑推理的多目标遗传算法,构造了一个能与适应度相对应的评价个体优劣的评价体系,以引导处理多目标问题的遗传算法的进化过程。数值算例结果表明了所提方法是正确的和有效的。     

Pareto多目标遗传算法及其在机械健壮设计中的应用

在机械或结构的优化设计中 ,普遍存在约束的作用 ,且最优解往往位于可行域的边界上。由于外界环境的变化或人为因素造成设计变量扰动 ,可能使设计成为不可行。本文提出了一种的基于设计变量敏感性的健壮性设计方法 ,并提出了一种用 Pareto遗传算法来实施的带约束的多目标优化方法以求解健壮性问题。 Pareto遗传算法可得到 Pareto最优解集 ,从中可选出满足设计需要的解。本文提出的算法包括 5个基本算子 :选择、变异、交叉、小生境技术、Pareto集合过滤器。文中用算例说明该方法的应用     

Comparison of nongradient methods with hybrid Taguchi-based epsilon constraint method for multiobjective optimization of cylindrical fin heat sink

The primary aim of the paper is to compare the different nongradient methods of multiobjective optimization for optimizing the geometry parameters of a cylindrical fin heat sink. The methods studied for comparison are Taguchi-based grey relational analysis, ε (epsilon) constraint method and genetic algorithm. The various responses that have been studied are electromagnetic emitted radiations, thermal resistance and mass of the heat sink. Since the responses are obtained using complex simulation softwares (HFSS—Ansoft for emitted radiations and CFD—Flotherm for thermal resistance), there is no way of calculating the derivates of the objective functions. Hence, the Taguchi design of experiments design is used to derive the linear regression equations for the responses studied, which are then taken as the objective functions to be optimized. A new hybrid method known as Taguchi-based epsilon constraint method has been proposed in this paper for obtaining nondominated Pareto solution set. The results obtained using the proposed method show that the Pareto optimal set is competitive in terms of diversity of the solutions obtained. It is not likely that there exists a solution, which simultaneously minimizes all the objectives using any of the multiobjective techniques implemented. The value path analysis has been done to compare the trade-off among the design alternatives for the chosen multiple objective parameter optimization problem.     

水平型制造协作联盟订单分配多目标优化模型研究

针对水平型制造协作联盟的订单分配问题,引入了生产负荷参数,建立了最小化综合成本与生产负荷均衡的多目标优化模型。应用改进的非支配排序遗传算法对多目标优化模型进行求解,获得了Pareto最优解集。仿真计算结果表明,所提出的模型和算法能够获得满意的解。     

圆锥破碎机的多目标规划设计

为研制符合新型层压破碎工作原理的圆锥破碎机,基于总体平衡模型和散体物料运动学特性,提出圆锥破碎机破碎腔型分层研究模型和腔型优化设计新方法.提出破碎机生产率计算新方法和圆锥破碎机操作模型,建立破碎机腔型优化、生产率优化和破碎产品粒度分布优化的计算模型.研究分析基于层压破碎原理的破碎腔型、生产率和破碎产品粒度之间的相互耦合关系模型,建立圆锥破碎机的多目标规划模型,能够为自主研制开发新型、高效、节能的现代高能圆锥破碎机奠定理论基础.