New Approaches to Modelling Covering Problems in Monitoring Optimization

2019 IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S&T) Pub Date : 2019-10-01 DOI:10.1109/PICST47496.2019.9061386

O. Pichugina

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引用次数: 3

Abstract

An issue of mathematical modeling in design of monitoring, diagnostic, and control systems is investigated. Mathematical models of the design problems reducible to covering of a circle object by circles are built. They are based on extracting a combinatorial structure of a new type connected with multipermutatons, on exploiting new geometric properties of objects involved, as well as on applying a continuous functional representation theory for modeling of the multipermutation set. Also, a Method of Artifical Space Dilation was used for constructing one of the mathematical models in extended space. This model is a global optimization one, which is the most promising in terms of obtaining a local optimum close to a global one. The models presented are generalized directly onto problems of covering a circular object by smaller circular objects that allows to cover a much wider class of the design problems regarding their mathematical modeling and solving by continuous and discrete optimization methods.

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涵盖监测优化问题的建模新方法

研究了监测、诊断和控制系统设计中的数学建模问题。建立了可简化为圆形物体被圆覆盖的设计问题的数学模型。它们基于提取与多置换相连接的新型组合结构，利用所涉及对象的新几何性质，以及应用连续泛函表示理论对多置换集进行建模。在此基础上，提出了一种人工空间膨胀的方法来构建扩展空间中的数学模型。该模型是一个全局优化模型，在获得接近全局最优的局部最优方面最有前途。所提出的模型可以直接推广到用较小的圆形物体覆盖圆形物体的问题上，从而可以涵盖更广泛的设计问题，包括它们的数学建模和通过连续和离散优化方法解决的问题。

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2019 IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S&T)

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