Application of the Genetic Algorithm to the Multi-Objective Optimization of Air Bearings

A feasible solution must be obtained in a reasonable time with high probability of global optimum for a complex tribological design problem. To meet this decisive requirement in a multi-objective optimization problem, the popular and powerful genetic algorithms (GAs) are adopted in an illustrated air bearing design. In this study, the goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selection of mating groups in the GAs. In the illustrated example the diversity of group members in the evolution process is much better maintained by using Pareto ranking method than that with the roulette wheel selection scheme. The final selection of the optimal point of the points satisfied the Pareto optimality is based on the minimum–maximum objective deviation criterion. It is shown that the application of the GA with the Pareto ranking is especially useful in dealing with multi-objective optimizations. A hybrid selection scheme combining the Pareto ranking and roulette wheel selections is also presented to deal with a problem with a combined single objective. With the early generations running the Pareto ranking criterion, the resultant divergence preserved in the population benefits the overall GA's performance. The presented procedure is readily adoptable for parallel computing, which deserves further study in tribological designs to improve the computational efficiency.     

基于改进粒子群算法的供应商参与可靠性设计优化

研究供应商参与下的汽车产品子系统可靠性设计的优化问题,考虑供应商参与产品设计的可信度因素,建立以最大化系统的可靠度和供应商的可信度为优化目标的多目标数学规划模型。通过加权的方法把多目标优化模型转化为单目标非线性整数规划模型。采用粒子群(Particle swarm optimization,PSO)算法进行求解,提出适用于“零部件—供应商”关系的离散粒子编码方法。设计带有自适应动态惩罚项的适应度函数,把优化问题转化为无约束优化问题,并将粒子的搜索范围扩展到近可行解空间,进而较好地改进了算法的搜索速度和收敛性能。以某中级轿车传动系统零部件可靠性设计的优化问题为实例,进行仿真研究,应用质量功能展开和模糊评判的方法生成了零部件的权重和供应商可信度初始数据值,仿真结果验证了所提出PSO算法的实用性和有效性。     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

多目标结构模糊优化的分层序列法

提出了多目标结构模糊优化的分层序列法,首先把原多目标模糊优化问题分解为一系列单目标（ 或多目标） 模糊优化子问题,该子问题用最大最小法求解。最后可以按着目标函数的重要程度给出原问题模糊最优解。最后用一个三杆桁架的最小重量与变形的模糊多目标优化设计问题证明了该方法的正确性     

结构多目标拓扑优化目标函数构建方法的研究

为实现结构材料的多目标拓扑优化设计,基于数学规划法提出一种广义的平均距离法,用以研究多目标拓扑优化目标函数的构建方法。介绍了运用平均距离法演变的将多目标转化为单目标的多种方法,并以汽车悬架控制臂为实例,应用演变的多种方法进行拓扑优化仿真研究。研究表明：运用平均距离法演变的多种方法可以灵活地构建多目标优化目标函数,基于所构建的目标函数可以寻找较优的构建方法,更好地将平均距离理念应用于多目标结构优化设计。     

基于自适应代理模型的翼型气动隐身多目标优化*

针对翼型气动隐身多目标优化设计存在的计算量大与权重难以选取的问题,提出基于自适应径向基函数代理模型与物理规划的高效多目标优化策略(Multi-objective optimization strategy using adaptive radial basis function and physical programming, ARBF-PP)。利用物理规划法通过非线性加权的方式将多目标优化问题转化为直接反映设计偏好的单目标优化问题,然后分别对综合偏好函数和约束条件构造径向基函数代理模型,采用增广Lagrange乘子法处理约束,并用遗传算法(Genetic algorithm, GA)进行求解。优化迭代过程中,在当前可能最优解附近增加样本点,更新代理模型,提高代理模型在最优解附近的近似精度,引导搜索过程快速收敛。使用数值多目标优化算例与翼型气动隐身多目标优化实例验证了本文所提出优化策略的有效性。翼型气动隐身多目标优化结果表明：相比于初始翼型,优化翼型的升阻比提高了34.28%,重点方位角的雷达散射截面(Radar cross section, RCS)均值减小了24.19%。此外,在相同样本规模的情况下,本文方法所得最优翼型的气动隐身性能比静态径向基函数代理模型方法的优化结果分别提高了11%与25.6%;与遗传算法相比,本文方法所需的分析模型调用次数(Number of evaluation function, Nfe)降低了93.5%。     

基于模糊多目标免疫算法的概念设计

针对概念设计中方案设计的组合优化问题,如何避免组合爆炸、快速有效地产生一些可行方案的难题,提出多模糊集代数和定理以及模糊集比较定理,根据产品功能与功能载体、功能载体与功能载体之间的相互关系,利用模糊集理论建立了产品模糊矩阵和模糊多目标优化数学模型,并根据免疫细胞进化原理提出一种有效的多目标免疫优化算法.以带式输送机的传动方案设计为例进行验证,试验结果显示这种方法能够快速产生可行方案集,实现方案的自动化设计.     

多目标优化设计在机构运动学综合中的应用

基于杆长约束,机构综合问题可以转化为非线性方程组的求解问题,再将非线性方程组转化为多目标无约束优化问题,应用多目标优化方法求解.应用多目标优化原理,首次提出了机构综合问题非线性方程组求解的新方法,并用Matlab语言的优化工具箱实现求解.机构运动学综合的实例表明该方法的正确性与有效性.     

Optimal clustering of MGs based on droop controller for improving reliability using a hybrid of harmony search and genetic algorithms

This paper proposes a novel method to address reliability and technical problems of microgrids (MGs) based on designing a number of self-adequate autonomous sub-MGs via adopting MGs clustering thinking. In doing so, a multi-objective optimization problem is developed where power losses reduction, voltage profile improvement and reliability enhancement are considered as the objective functions. To solve the optimization problem a hybrid algorithm, named HS-GA, is provided, based on genetic and harmony search algorithms, and a load flow method is given to model different types of DGs as droop controller. The performance of the proposed method is evaluated in two case studies. The results provide support for the performance of the proposed method.     

基于混合元胞自动机的柔顺机构多目标拓扑优化方法

采用无梯度优化方法——混合元胞自动机方法进行体积约束下柔顺机构多目标拓扑优化设计。以应变能最小化和互应变能最大化为目标,以结构体积为约束,采用标准化方法定义多目标拓扑优化的目标函数,消除不同性质目标函数在数量级上的差异。将混合元胞自动机方法用于多目标优化问题的求解,以比例控制作为局部控制规律。数值算例结果表明,该方法用于柔顺机构多目标拓扑优化设计是有效的,优化迭代次数较少,且结构不易出现单节点铰链现象。