Aggregation in Large-Scale Optimization
Aggregation in Large-Scale Optimization
复制标题
大规模优化中的聚合
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
V. Tsurkov
中科院分区：
文献类型：
--
作者：
I. Litvinchev;V. Tsurkov
当分析具有大量参数的系统时，原始系统的锡永可能会给分析带来难以克服的困难。这样，就可以方便地用少得多的聚合变量或宏观变量来重新表述原始系统。换句话说，具有n维状态向量的原始系统被重新表述为具有比n小得多的维度向量的系统。聚合变量可以很容易地定义和处理，或者聚合系统可以被认为是原始系统的近似模型。在后一种情况下，原系统的操作可以详尽地分析框架内的聚合模型，和一个面临的问题，定义的规则，引入宏变量，指定损失的信息和准确性，恢复原始变量的聚合等，我们也考虑详细的所谓的迭代聚合方法。它构造了一个迭代过程，在每一步都解决了一个宏问题，由于其维数较低，所以比原始问题更简单。然后更新聚合权重，并且过程转到下一步骤。宏变量常用于递阶优化的协调问题。
When analyzing systems with a large number of parameters, the dimen- sion of the original system may present insurmountable difficulties for the analysis. It may then be convenient to reformulate the original system in terms of substantially fewer aggregated variables, or macrovariables. In other words, an original system with an n-dimensional vector of states is reformulated as a system with a vector of dimension much less than n. The aggregated variables are either readily defined and processed, or the aggregated system may be considered as an approximate model for the orig- inal system. In the latter case, the operation of the original system can be exhaustively analyzed within the framework of the aggregated model, and one faces the problems of defining the rules for introducing macrovariables, specifying loss of information and accuracy, recovering original variables from aggregates, etc. We consider also in detail the so-called iterative aggregation approach. It constructs an iterative process, at* every step of which a macroproblem is solved that is simpler than the original problem because of its lower dimension. Aggregation weights are then updated, and the procedure passes to the next step. Macrovariables are commonly used in coordinating problems of hierarchical optimization.