Probability-Based Multi-objective Optimization for Material Selection

Preface to the Second Edition
Preface to the First Edition
Contents
About the Authors
1 History and Current Status of Material Selection with Multi-objective Optimization
	1.1 Brief Introduction
	1.2 Evolution of Material Selections
	1.3 Evolution of Multi-objective Optimization
	1.4 Summary and Conclusions
	References
2 Introduction to Multi-objective Optimization in Material Selections
	2.1 Introduction
	2.2 Previous Approaches for Multi-objective Optimization of Material Selection
		2.2.1 Qualitative Approach
		2.2.2 Quantitative Approach
		2.2.3 Discussion and Summary of the Previous Approaches for Multi-objective Optimization of Material Selection
	2.3 Fundamental Consideration of Multiple objective Optimization for Material Selection
		2.3.1 Statement of Situation
		2.3.2 Basic Principles for Selection of Equipment Materials
		2.3.3 Basic Procedure for Material Selection
	2.4 Conclusion
	References
3 Fundamental Principle of Probability-Based Multi-objective Optimization and Applications
	3.1 Introduction
	3.2 Multi-objective Optimization in Viewpoint of System Theory
	3.3 Arithmetic of Probability Treatment
	3.4 Quantitative Approach for Material Selection in Respect to Probability Theory
		3.4.1 Concept of Preferable Probability
		3.4.2 Probability-Based Approach
	3.5 Applications of the Probability-Based Method for Multi-objective Optimization in Material Selection
	3.6 Other Applications in More Broader and General Issues
	3.7 Concluding Remarks
	References
4 Robustness Evaluation with Probability-Based Multi-objective Optimization
	4.1 Introduction
	4.2 Extension of Probability-Based Multi-objective Optimization to Contain Robustness
	4.3 Application of the Extended PMOO in Evaluation of Optimal Problems with Variance of Data in Material Engineering
	4.4 Conclusion
	References
5 Extension of Probability-Based Multi-objective Optimization in Condition of the Utility with Desirable Value
	5.1 Introduction
	5.2 Assessments of Partial and Overall Preferable Probability for Performance Response with Desirable Value in the Probability-Based Multiple Objectives Optimization
		5.2.1 One Range Desirable Value Problem
		5.2.2 One Side Desirable Value Problem
	5.3 Applications
	5.4 Concluding Remarks
	References
6 Hybrids of Probability-Based Multi-objective Optimization with Experimental Design Methodologies
	6.1 Introduction
	6.2 Hybrid of Probability-Based Multi-objective Optimization with Orthogonal Experimental Design
		6.2.1 Algorithm of the Hybrid for PMOO with Orthogonal Experimental Design
		6.2.2 Application of the Hybrid of PMOO with Orthogonal Experimental Design in Material Selection
	6.3 Hybrid of Probability-Based Multi-objective Optimization with Response Surface Methodology Design
		6.3.1 Algorithm of the Hybrid for PMOO with Response Surface Methodology (RSM)
		6.3.2 Application of the Hybrid of PMOO with Response Surface Methodology Design in Material Selection
	6.4 Hybrid of Probability-Based Multi-objective Optimization with Uniform Experimental Design Methodology
		6.4.1 Algorithm of the Hybrid for PMOO with Uniform Experimental Design Methodology (UED)
		6.4.2 Application of the Hybrid of PMOO with Uniform Experimental Design Methodology in Material Selection
	6.5 Conclusion
	References
7 Discretization of Simplified Evaluation in Probability-Based Multi-objective Optimization by Means of GLP and Uniform Experimental Design
	7.1 Introduction
	7.2 Fundamental Characteristics of Uniform Experimental Design
		7.2.1 Main Features of Uniform Experimental Design
		7.2.2 Fundamental Principle of Uniform Experimental Design
	7.3 Feature Analysis of the Periodic Function in a Single Period
	7.4 Typical Examples for the Efficient Approach of Numerical Integration for a Single Peak Function Based on Rules of GLD and Uniform Design Method
	7.5 Typical Examples of Applications of the Finite Sampling Point Method in Assessment of Probability-Based Multi-objective Optimization
	7.6 Conclusive Remarks
	References
8 Fuzzy-Based Probabilistic Multi-objective Optimization for Material Selection
	8.1 Introduction
	8.2 Formulation of Fuzzy Probability-Based Multi-objective Optimization (FPMOO)
		8.2.1 Membership Value of Material Performance in Fuzzy Language
		8.2.2 Fuzzy Probability-Based Multi-objective Optimization (FPMOO)
	8.3 Illustrative Example
	8.4 Concluding Remarks
	References
9 Cluster Analysis of Separation of “Independent Objective” for Probability-Based Multi-objective Optimization
	9.1 Introduction
	9.2 Characterization of Similarity Between Performances or Samples
	9.3 Application of Clustering Analysis in Separation of “Independent Objective” for Multi-objective Optimization
	9.4 Conclusion
	References
10 Applications of Probability-Based Multi-objective Optimization Beyond Material Selection
	10.1 Introduction
	10.2 Application of the Multi-objective Optimization in Drug Design and Extraction
		10.2.1 Optimal Preparation of Encapsulation Composite of Water-Soluble Chitosan/Poly-Gamma-Glutamic Acid-Tanshinone IIA with Response Surface Methodology Design
		10.2.2 Optimal Preparation of Glycerosomes–Triptolide as an Encapsulation Composite with Orthogonal Experimental Design
		10.2.3 Optimization of Compatibility of the Traditional Chinese Medicine Drug by Using Orthogonal Experimental Design
		10.2.4 Optimization of Multi-objective Drug Extraction Conditions Based on Uniform Experimental Designs
	10.3 Application of the Probability-Based Multi-objective Optimization in Military Engineering Project with Weighting Factor
		10.3.1 Decision Making of Multi-objective Military Engineering Investment
		10.3.2 Flexible Ability Assessment of Antiaircraft Weapon System
	10.4 Comparative Analysis of Scheme Selection for Water Purification Treatment by Using PMOO with the Traditional MCDM
	10.5 Application of the Probability-Based Multi-objective Optimization in Power Equipment
	10.6 Conclusion
	References
11 Treatment of Portfolio Investment by Means of Probability-Based Multi-objective Optimization
	11.1 Introduction
	11.2 Solution of Portfolio Problem by Means of Probability-Based Multi-objective Optimization
	11.3 Example of Case with Four Securities
	11.4 Conclusion
	References
12 Treatment of Multi-objective Shortest Path Problem by Means of Probability-Based Multi-objective Optimization
	12.1 Introduction
	12.2 Approach for Multi-objective Shortest Path Problem Based on Probability Theory
		12.2.1 Probabilistic Model of Multi-objective Optimization Problem
		12.2.2 Assessment Procedure of Simultaneous Optimization of Multi-objective Shortest Path Problem in Respect of Probability Theory
	12.3 Application of the Probability-Based Approach of Multi-objective Shortest Path Problem
		12.3.1 Application in Hazardous Materials Transportation Path Problem
		12.3.2 Application in Multi-objective Inter-Model Transportation of Grain from Northern China to the South Considering Weather Factor
	12.4 Conclusion
	References
13 Discussion on Preferable Probability, Discretization, Error Analysis, and Hybrid of Sequential Uniform Design with PMOO
	13.1 On Preferable Probability
	13.2 On the Assessments of Robustness of Performance Utility with Uncertainty
	13.3 On the Number of Discretized Sampling Points of Evaluation in Probability-Based Multi-objective Optimization by Means of GLP and Uniform Experimental Design
	13.4 Error Analysis
	13.5 Hybrid of Sequential Uniform Design with Probability-Based Multi-objective Optimization
	13.6 On Weighting Factor
	13.7 Conclusion
	References
14 General Conclusions
Correction to: Probability-Based Multi-objective Optimization for Material Selection
	Correction to:  M. Zheng et al., Probability-Based Multi-objective Optimization for Material Selection, https://doi.org/10.1007/978-981-99-3939-8