Nonlinear Interval Optimization for Uncertain Problems

1. Front Matter

   Pages i-xii

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2. Introduction

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 1-24

3. The Basic Principles of Interval Analysis

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 25-34

4. Mathematical Transformation Models of Nonlinear Interval Optimization

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 35-59

5. Interval Optimization Based on Hybrid Optimization Algorithm

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 61-77

6. Interval Optimization Based on Interval Structural Analysis

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 79-102

7. Interval Optimization Based on Sequential Linear Programming

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 103-129

8. Interval Optimization Based on Approximation Models

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 131-177

9. Interval Multidisciplinary Design Optimization

   • Chao Jiang, Xu Han, Huichao Xie

   Pages 179-194

10. A New Type of Possibility Degree of Interval Number and Its Application in Interval Optimization

    • Chao Jiang, Xu Han, Huichao Xie

    Pages 195-217

11. Interval Optimization Considering the Correlation of Parameters

    • Chao Jiang, Xu Han, Huichao Xie

    Pages 219-234

12. Interval Multi-objective Optimization

    • Chao Jiang, Xu Han, Huichao Xie

    Pages 235-246

13. Interval Optimization Considering Tolerance Design

    • Chao Jiang, Xu Han, Huichao Xie

    Pages 247-258

14. Interval Differential Evolution Algorithm

    • Chao Jiang, Xu Han, Huichao Xie

    Pages 259-284

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.

• Uncertain optimization
• Optimization design
• Non-probabilistic
• Interval analysis
• Sequential linear programming
• Surrogate model
• Multidisciplinary optimization design
• Multi-objective optimization design
• Interval possibility degree
• Parameter dependence
• Tolerance design
• Differential evolution

• College of Mechanical and Vehicle Engineering, Hunan University, Changsha, China

  Chao Jiang

• Hebei University of Technology, Hongqiao District, China

  Xu Han

• College of Material Science and Engineering, Central South University of Forestry and Technology, Changsha, China

  Huichao Xie

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.

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