Global Optimization: Interval Analysis and Balanced Interval Arithmetic

2008 ◽  
pp. 1346-1350 ◽  
Author(s):  
Julius Žilinskas ◽  
Ian David Lockhart Bogle
Keyword(s):  
Global Optimization ◽  
Interval Analysis ◽  
Interval Arithmetic

An interval arithmetic method for global optimization

Computing ◽  
1979 ◽  
Vol 23 (1) ◽  
pp. 85-97 ◽  
Author(s):  
K. Ichida ◽  
Y. Fujii
Keyword(s):  
Global Optimization ◽  
Interval Arithmetic ◽  
Arithmetic Method

A study on global optimization and deep neural network modeling method in performance-seeking control

2019 ◽  
Vol 234 (1) ◽  
pp. 46-59 ◽  
Author(s):  
Qiangang Zheng ◽  
Dawei Fu ◽  
Yong Wang ◽  
Haoying Chen ◽  
Haibo Zhang
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Global Optimization ◽  
Interval Analysis ◽  
Sequential Quadratic Programming ◽  
Deep Neural Network ◽  
Network Modeling ◽  
Engine Performance ◽  
Neural Network Modeling ◽  
Swarm Optimization

In this article, a novel performance-seeking control method based on deep neural network and interval analysis is proposed to obtain a better engine performance. A deep neural network modeling method which has stronger representation capability than conventional neural network and can deal with big training data is adopted to establish an on-board model in the subsonic and supersonic cruising envelops. Meanwhile, a global optimization algorithm interval analysis is applied here to get a better engine performance. Finally, two simulation experiments are conducted to verify the effectiveness of the proposed methods. One is the on-board model modeling which compares the deep neural network with the conventional neural network, and the other is the performance-seeking control simulations comparing interval analysis with feasible sequential quadratic programming, particle swarm optimization, and genetic algorithm, respectively. These two experiments show that the deep neural network has much higher precision than the conventional neural network and the interval analysis gets much better engine performance than feasible sequential quadratic programming, particle swarm optimization, and genetic algorithm.

scholarly journals Interval arithmetic in calculations

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Gaziza Bairbekova ◽  
Talgat Mazakov ◽  
Sholpan Djomartova ◽  
Salima Nugmanova
Keyword(s):  
Interval Analysis ◽  
Interval Arithmetic ◽  
Mathematical Structure ◽  
Rounding Errors ◽  
Math Model ◽  
Interval Mathematics ◽  
Integral Analysis ◽  
Data Objects ◽  
Definition Of ◽  
The Given

Abstract Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.

Global Optimization Using Interval Analysis.

1994 ◽  
Vol 63 (207) ◽  
pp. 428
Author(s):  
Arnold Neumaier ◽  
Eldon Hansen
Keyword(s):  
Global Optimization ◽  
Interval Analysis
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