Nonlinear Interval Optimization for Uncertain Problems

by Chao Jiang, Xu Han, Huichao Xie

Overview

This book systematically discusses nonlinear interval optimization design theory and methods. Firstly, adopting a mathematical programming theory perspective, it develops an innovative mathematical transformation model to deal with general nonlinear interval uncertain optimization problems, which is able to equivalently convert complex interval uncertain optimization problems to simple deterministic optimization problems. This model is then used as the basis for various interval uncertain optimization algorithms for engineering applications, which address the low efficiency caused by double-layer nested optimization. Further, the book extends the nonlinear interval optimization theory to design problems associated with multiple optimization objectives, multiple disciplines, and parameter dependence, and establishes the corresponding interval optimization models and solution algorithms. Lastly, it uses the proposed interval uncertain optimization models and methods to deal with practical problems in mechanical engineering and related fields, demonstrating the effectiveness of the models and methods.

Product Details

ISBN-13:	9789811585463
Publisher:	Springer-Verlag New York, LLC
Publication date:	12/08/2020
Series:	Springer Tracts in Mechanical Engineering
Sold by:	Barnes & Noble
Format:	eBook
File size:	25 MB
Note:	This product may take a few minutes to download.

About the Author

Dr. Jiang obtained his Ph.D. in Mechanical Engineering from Hunan University in 2008. Since then, he has been working as a professional staff at the College of Mechanical and Vehicle Engineering of Hunan University. He was promoted to full professor in 2011 and was appointed executive dean of the college in 2018. His academic research is mainly focused on mechanical design, with particular interests in the scientific issues of structural reliability, optimization design, and fracture and fatigue. He has published about 120 scientific papers in peer-reviewed international journals and received more than 3,000 citations. Dr. Jiang is member of editorial board of several international and domestic journals in the field of mechanical engineering science. He also serves on the committees of several major academic societies related to mechanical engineering, and has organized a series of international academic conferences dedicated to promoting the progress of mechanical engineering science. Dr. Jiang received some reputable honors and awards in China, such as the Leading Talent in Science and Technology Innovation of “Ten Thousand Talents Program”, Holder of the National Natural Science Foundation for Distinguished Young Scholars. Moreover, he is also the principal investigator of a multidisciplinary research team at Hunan University that has established a good reputation internationally.

Table of Contents

Introduction.- Fundamentals of interval number theory.- Mathematical transformation models of nonlinear interval optimization.- Interval optimization based on hybrid optimization algorithms.- Interval optimization based on interval structural analysis.- Interval optimization based on sequential linear programming.- Interval optimization based on surrogate models.- Interval multidisciplinary optimization design.- Interval optimization based on a novel interval possibility degree model.- Interval optimization considering parameter dependences.- Interval multi-objective optimization design.- Interval optimization considering tolerance design.- Interval differential evolution algorithm.