优化问题

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。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

For a class of bilevel multi-objective decision,this paper converts it into the problem of equivalent single-level multi-objective decision,then makes use of the inversion property of the genetic algorithm with the ergodic property of the chaos optimization method.

针对求解一类二层多目标决策问题，首先将其转化为等价的单目标决策问题，然后利用遗传算法优化的反演性和混沌优化方法的遍历性，并结合精确不可微罚函数求解非线性约束优化问题，提出了求解此类问题的混沌遗传算法。

For a class of bilevel multi-objective decision,this paper converts it into the problem of equivalent single-level multi-objective decision,then makes use of the inversion property of the genetic algorithm with the ergodic property of the chaos optimization method.Combined with exact non-differentiable penalty function,a new chaos genetic optimization algorithm is presented.

针对求解一类二层多目标决策问题，首先将其转化为等价的单目标决策问题，然后利用遗传算法优化的反演性和混沌优化方法的遍历性，并结合精确不可微罚函数求解非线性约束优化问题，提出了求解此类问题的混沌遗传算法。

Multiobjective optimization problem has a wide range of applications in the real world. It is different from the single objective optimization. It often involves incommensurable and competing objectives, and the number of its Pareto optimal solutions is usually infinite. Therefore, it is very important to design new algorithms which can find well distributed and close-to-Pareto-optimal solutions.

在现实世界中很多问题都是多目标优化问题，不同于单目标优化，在多目标优化中，各目标之间是互相冲突的，其最优解往往有无穷多个，如何使得到的Pareto最优曲面距离真正的Pareto最优曲面最近、最优解的分布均匀且范围更广是求解多目标优化问题的关键。

For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the wholenetworks to some sub-problems in some sub-areas.

对于单目标无功电压优化，根据实际电网分区情况，采用分解协调法复制各分区的边界节点，建立分解协调模型，采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题，然后采用辅助问题原理分解变量和增广拉格朗日函数，从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。

Imitating human intelligence, a new algorithm based on heuristic sequential linear optimization for one-dimensional cutting-stock problem is presented.

针对一维下料优化问题，提出了一种基于启发式多级序列线性优化思想的新算法，即将下料优化问题转化为多级序列线性优化问题求解。

There exits several MDO algorithms. But they are in our opinion either nonefficient or complicated. So we devised an algorithm called Subspace Approximation Optimization . In the SAO algorithm, the whole system is decomposed into one system-level optimization and several disciplinary optimizations so that a large and complicated problem can be divided into several easy-solving sub-problems. The coupling relationships and the coordination among disciplines are presented by equality constraints and these equality constraints are assigned to relevant disciplines. The optimums of design variables in system level optimization are transferred to discipline level optimization. The optimums of design variables in discipline level correspond to the point that is the nearest to the optimums of design variables in system level. If the optimums of design variables in system level are out of feasible region of discipline 1eve1, linear constraints can be built in the system level optimization using the design variable optimums obtained by the discipline level optimization. The system level optimization would improve the design of the whole system with these linear constraints.

目前，国内外已经发展出了多种飞机多学科设计优化算法，本文的重点是针对协同优化算法的不足，提出了子空间近似优化算法(Subspace ApproximatingOptimization，SAO)，SAO算法中，整个系统的优化问题被分解成一个系统级优化和若干学科级优化，而各个学科之间的耦合与权衡关系则被当作等式约束，这些等式约束将被分配到各个学科级优化中去，系统级优化的任务是寻找整个系统的最优解，而学科级优化的目标函数是以系统级优化分配下来的设计点为圆心的超球半径的平方，因此，如果系统级优化分配下来的设计点在学科级优化可行域内，则学科级优化目标函数为0，反之，则学科级优化的最优点是系统级优化当前设计点距离可行域最近的点。

Traditionally, a surface is usually scatted in an array of 3D data points which are topologically connected by rows and columns to form a rectangular mesh. This method can't meet the requirement of description and measurement for some complex surfaces. On the basis of tracing border points, a new method is proposed to deliver 3D data points of surfaces, which are topologically constructed with optimum rectangular and triangular mesh. In order to measure surface efficiently and safely with NC machine, an optimization of measurement paths is proposed to avoid interference between the measuring tool and the surface with holes. The curve design is the basis of surface modeling.

数控测量技术的发展为测量自动化、集成化、智能化提供了可能，而对于复杂曲面的自动测量规划则是测量技术中的难点问题，平行截面等数目测点分布和四边拓扑测点分布规划方法，不论在测点分布的合理性上还是在网格结构的优化方面，均难以满足形状或边界较复杂曲面的离散化描述和曲面造型的要求，为了实现任意拓扑曲面的自动测量，本文对复杂曲面的合理离散化描述和自动测量问题进行了研究，提出了基于边界跟踪、优化网格的测点自动分布规划和四边、三角混合网格的生成方法：同时对具有孔洞或测量干涉凸台等非完整曲面的测量路径优化问题进行了研究，提出了路径优化方法。

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。