Optimization of Systems having Uncontrollable Subsystems

具有不可控子系统的系统的优化

基本信息

批准号：
14380188
负责人：
YAMAMOTO Yoshitsugu
金额：
$ 3.78万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

A conventional paradigm common to mathematical programming or optimization could be referred to as "controllability." Namely, it is taken for granted that we can freely control the variables of the system as we choose. What has been done sp far in this field is to optimize an objective function under this controllability assumption. The difficulty of putting together the different and controversial objectives of the system into a single objective function has been recognized and hence drove multi-objective optimization as well as multi-level optimization. However, the uncontrollability of variables has not been fully considered yet.Take a society as the whole system and each individual with his own preference function as a sub-system, the model we consider here leads to the social welfare function and social choice function concerning the democratic decision of society. We have shown, like the conventional impossibility theorem, negative conclusions in the society of mutual evaluation, … More however some positive conclusion about the strategy proofness. Concerning the problem of how much cost each stakeholder should pay we have given some results about the non-emptyness of core.We take a network as the whole system, which is divided into several sub-networks, and arc flows as variables to control, and considered the design problem of network by means of worst case analysis. The problem is formulated as an optimization problem over a non-convex set, for which we have proposed an algorithm. The complementarity constraint emerges as this kind of optimization problems, and we also investigate the interior point method for the problem. If the uncontrollability comes from the probabilistic nature of the system, stochastic programming that emerges as credit risk problem, portfolio selection problems comes in. Fuzzy parameters will bring fuzzy optimization.With the above viewpoint, encouraging self-discipline of members we have carried out collaboration for three years. A good many papers has been published with the support of this fellowship. Less

数学编程或优化的常规范式可以称为“可控性”。也就是说，我们可以自由地控制系统的变量是理所当然的。在此领域中所做的工作已经完成的是在此可控性假设下优化目标函数。将系统的不同和有争议的目标汇总到单个目标函数中的困难已得到认可，因此驱动了多目标优化以及多级优化。但是，变量的不可控制性尚未被充分考虑。将一个社会作为整个系统，每个人都具有自己的喜好作为子系统的偏好功能，我们在这里考虑的模型会导致社会福利的功能和社会选择功能，涉及社会民主决策。我们已经表明，就像常规的不可能定理一样，在相互评估社会中的负面结论，……关于策略证明的一些积极结论。关于每个利益相关者应支付多少成本的问题，我们就核心的非空置性给出了一些结果。我们将网络作为整个系统，将网络分为几个子网络，并将其视为可以控制的变量，并通过最坏情况分析考虑了网络的设计问题。该问题被作为在非凸集集合的优化问题中提出的，我们为此提出了一种算法。完整性约束是作为这种优化问题而出现的，我们还研究了该问题的内点方法。如果不可控制性来自系统的问题性质，那么随着信用风险问题而出现的随机编程，投资组合选择问题就会出现。模糊参数将带来模糊的优化。与上述观点，鼓励我们进行了三年协作的会员的自律。在这项奖学金的支持下，已经发表了许多论文。较少的