CONTINUUM TOPOLOGY OPTIMIZATION FOR MONOLITHIC COMPLIANT MECHANISMS OF MICRO-ACTUATORS

A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffness are both considered as objective functions. The compliant micro-mechanism developed in this way can not only provide sufficient output work but also have sufficient rigidity to resist reaction forces and maintain its shape when holding the work-piece. A density filtering approach is also proposed to eliminate numerical instabilities such as checkerboards, mesh-dependency and one-node connected hinges occurring in resulting mechanisms. SIMP is used as the interpolation scheme to indicate the dependence of material modulus on element-regularized densities. The sequential convex programming method, such as the method of moving asymptotes (MMA), is used to solve the optimization problem. The validation of the presented methodologies is demonstrated by a typical numerical example.     

中考最优化方案设计题解析

<正>中考试题中最优化方案设计问题倍受考官青睐.通过设置一个实际问题的情景.给出若干信息,运用数学知识设计恰当的解决方案,以求得最好的实用效果或最大的经济效益.具体解法可通过建立方程、不等式或函数等方法求解.下面从三个方面分析优选方案设计题目类型和解题方法.     

全局优化问题的一个新的无参数填充函数

求全局最优化问题的填充函数算法被提出以来,参数的选取和调整一直是制约算法有效性的因素.如何在实际的计算过程中选取合适的参数,直接影响和决定了运算速度和效率.因此,构造不含参数的填充函数就显得极为重要.提出一个新的无参数的填充函数,对其理论性质进行了分析,并给出相应的填充函数算法,数值计算验证了算法的有效性.     

基于实物期权的双源供应链柔性采购协调策略

在需求不确定下,由风险规避的供应商和占主导地位的零售商组成的二级供应链中,构建了在现货市场影响下基于实物期权的双源柔性采购协调模型,给出了实现供应链协调的最优期权参数的求解算法,探讨了现货市场价格不确定性和供应商风险规避特性对零售商采购策略和双方利润的影响。研究结果表明,在考虑现货市场影响和供应商风险规避的条件下,实物期权契约可以实现供应链协调。     

互补问题算法的新进展

互补问题是一类重要的优化问题,在最近３０多年的时间里,人们为求解它而提出了许多算法,该文主要介绍１９９０－１９９７年之间出现的某些新算法,它们大致可归类为：（１）光滑方程法;（２）非光滑方程法;（３）可微无约束优化法;（４）ＧＬＰ投影法;（５）内点法;（６）磨光与非内点连续法,文中对每类算法及相应的收敛性结果做了描述与评论,并列出有关文献。     

无需线搜索的并行非线性共轭梯度法

给出了一类无需线搜索的无约束最优化并行算法--并行非线性共轭梯度法(NLS-PNCG),用一个固定的公式来计算搜索步长,较常用的共轭梯度法计算量小.并且证明了目的的全局收敛性,给出了数值试验,结果显示NLS-PNCG优于线搜索的非线性共轭梯度法(NCG).     

一类新共轭梯度法的全局收敛性

共轭梯度法是求解无约束最优化问题的有效方法.本文在βkDY的基础上对βk引入参数,提出了一类新共轭梯度法,并证明其在强Wolfe线性搜索条件下具有充分下降性和全局收敛性.     

多背包问题的半定松驰算法

The multiple knapsack problem denoted by MKP (B,S,rn,n) can be defined as follows. A set B of n items and a set S of rn knapsacks are given such that each item j has a profit pi and weight wj,and each knapsack i has a capacity Ci. The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks. MKP (B,S,m,n) is strongly NP-Complete and no polynomial time approximation algorithm can have an approximation ratio better than 0.5. In the last ten years,semi-definite programming has been empolyed to solve some combinatorial problems successfully. This paper firstly presents a semi-definite relaxation algorithm (MKPS) for MKP (B,S,rn,n). It is proved that MKPS have a approximation ratio better than 0. 5 for a subclass of MKP (B,S,m,n) with n≤100, m≤5 and max^nj=1{wj}/min^mi=1={Ci}≤2/3.     

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ. LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part Ⅰ is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.     

Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming in Locally Convex Spaces

This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.