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Optimization solution algorithm is the most important in topology optimization.Algorithms fit for discrete structure and continuum structure are all investigated. Thecharacteristic and different using limit of both optimization criteria method andmathematics programming method are all analyzed in this paper. OC algorithm and theseries MMA algorithm based on SIMP approach are deducedand used for the topology optimization problem of continuum structure.

优化求解算法是拓扑优化问题求解的核心和关键，本文系统分析了适用于离散结构和连续体结构优化的优化求解算法，重点讨论了 OC 算法和 MP 算法，分析比较了不同算法的特点和适用范围，推导了基于 SIMP 理论的优化准则法和 MMA 系列算法，并将MMA 系列算法应用于连续体结构拓扑优化问题的求解。

Thecharacteristic and different using limit of both optimization criteria method andmathematics programming method are all analyzed in this paper. OC algorithm and theseries MMA algorithm based on SIMP approach are deducedand used for the topology optimization problem of continuum structure. MMA algorithm hasa bad convergence but it has a high computational efficiency, while GCMMA is excellent onconvergence and stability with bad calculation efficiency.

优化求解算法是拓扑优化问题求解的核心和关键，本文系统分析了适用于离散结构和连续体结构优化的优化求解算法，重点讨论了 OC 算法和 MP 算法，分析比较了不同算法的特点和适用范围，推导了基于 SIMP 理论的优化准则法和 MMA 系列算法，并将MMA 系列算法应用于连续体结构拓扑优化问题的求解。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

For its simple computational complexity, fast convergence speed and many other advantages, adaptive filer has been widely used.

分别就几种算法在算法原理，算法性能分析和计算机仿真等方面来说明各种算法的优越性。

Introduce the ideological root causes and background knowledge in detailed, give the iterative formula and the iteration step.

针对微粒群算法在求解函数优化问题时出现的一系列问题，本文提出了雁群算法，详细介绍了雁群算法的提出的思想根源和背景知识，给出了算法的迭代公式和迭代步骤，并结合具体实例与微粒群算法相比较，对于某些优化问题，其优化性能比微粒群算法有较大的提高，在一定程度上弥补了微粒群算法的不足。

The convergence of the iterative algorithm is proved, and an analysis of the computational time is given.

该算法是一种迭代算法，证明了该算法的收敛性，并分析了该算法运算量。

It is improved to solve the prematurely and stagnation problems of traditional Ant Colony Optimization in the paper. First, mean value method is used to update pheromone to avoid premature convergence which leads to non-globally optimal solution. Second, Pheromone is updated by Best Track to speed the rate of convergence which will help to avoid locally optimal solution.

本文针对基本蚁群算法比较容易陷入早熟和停滞，对现有蚁群算法的信息素更新规则进行了改进，一是采用平均值法更新信息素，避免算法过早收敛于非全局最优解；二是采用最佳路径法更新信息素，可加快收敛速度，并使算法跳出局部最优解。

It shows that the adaptive immune algorithm is superior to both genetic algorithm and normal immune algorithm at solving optimal problems.

将改进算法、遗传算法和一般免疫算法分别应用到函数优化问题中，其结果证明了该算法的有效性。

The results of numberical simutation show that the new algorithm is more effective than the other algorithms.

该算法弥补了仅用罚函数作为遗传算法的适应函数之不足，数值模拟结果表明该算法比其他算法更加有效。

And, by adding the self-adaptive temperature decay coefficient, made the SA algorithm could auto-tune the search criteria according the environment, avoid the deficiency of premature convergence.

针对微粒群优化算法在求解作业车间调度问题时存在的易早熟、搜索准确度差等缺点，在微粒群优化算法的基础上引入了模拟退火算法，从而使得算法同时具有全局搜索和跳出局部最优的能力，并且增加了对不可行解的优化，从而提高了算法的搜索效率；同时，在模拟退火算法中引入自适应温度衰变系数，使得SA算法能根据当前环境自动调整搜索条件，从而避免了微粒群优化算法易早熟的缺点。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。