
Parameter Space Investigation Method Toolkit
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Content
- The Parameter Space Investigation Method Toolkit
- Contents
- Acknowledgments
- Preface
- Part I The Parameter Space Investigation Method Toolkit
- 1 Introduction
- 1.1 Some Basic Features of Real-Life Optimization Problems
- 1.2 Generalized Formulation of Multicriteria Optimization Problems
- 1.2.1 Definition
- 1.3 Applying Single-Criterion Methods for Solving Multicriteria Problems
- 1.3.1 Substitution of a Multitude of Criteria by a Single One
- 1.3.2 Optimization of the Most Important Criterion
- 1.4 Systematic Search in Multidimensional Domains by Using Uniformly Distributed Sequences
- 1.4.1 Quantitative Characteristics of Uniformity
- References
- 2 Parameter Space Investigation Method as a Tool for Formulation and Solution of Real-Life Problems
- 2.1 The Parameter Space Investigation Method
- 2.1.1 The Complexity of the Investigation
- 2.1.2 Definition of the Feasible Solution in Parallel Mode
- 2.1.3 Number Generators for Systematic Search in the Design Variable Space
- 2.2 "Soft" Functional Constraints and Pseudo-Criteria
- 2.3 More About Applying Single-Criterion Methods for Solving Multicriteria Problems
- 2.4 An Example of Optimization Problem Statement and Significant Challenge That It Presents
- 2.4.1 Expert's Difficulties
- References
- 3 Using the PSI Method and MOVI Software System for Multicriteria Analysis and Visualization
- 3.1 Performing Tests
- 3.2 Construction of Feasible and Pareto Optimal Sets
- 3.2.1 Constructing Test Tables
- 3.2.2 Constructing the Feasible Solution Set: Dialogues of an Expert with a Computer
- 3.2.3 Tables of Feasible and Pareto Optimal Solutions
- 3.2.4 Selecting the Most Preferable Solution
- 3.3 Histograms and Graphs
- 3.3.1 Design Variable Histograms: Histograms of the Distribution of Feasible Solutions
- 3.3.2 Criteria Histograms: Visualization of Contradictory Criteria
- 3.3.3 Graphs "Criterion Versus Design Variable II"
- 3.3.4 Graphs "Criterion Versus Criterion"
- 3.3.5 Graphs "Criterion Versus Design Variable I"
- 3.4 Weakening Functional Constraints
- 3.4.1 Tables of Functional Failures
- References
- 4 Improving Optimal Solutions
- 4.1 Solving a New Optimization Problem
- 4.1.1 New Design Variable Constraints
- 4.1.2 Tables of Feasible and Pareto Optimal Solutions
- 4.1.3 Histograms of the Distribution of the Feasible Solutions
- 4.1.4 Graphs of Criterion Versus Design Variable II
- 4.1.5 Graphs Criterion Versus Criterion
- 4.2 Construction of the Combined Pareto Optimal Set
- 4.2.1 Basic Principles
- 4.2.2 Tables of Combined Pareto Optimal Solutions
- 4.2.3 Analysis of the Combined Pareto Optimal Set
- 4.2.4 Conclusions for Chapters 2 Through 4
- References
- Part II Applications to Real-Life Problems
- 5 Multicriteria Design
- 5.1 Multicriteria Analysis of the Ship Design Prototype
- 5.1.1 Improvement Problem
- 5.2 Problem with the High Dimensionality of the Design Variable Vector
- 5.3 Rear Axle Housing for a Truck: PSI Method with the FiniteElement Method
- 5.3.1 General Statement of the Problem
- 5.3.2 Solution of the Problem and Analysis of the Results
- 5.3.3 Conclusions
- 5.4 Improving the Truck Frame Prototype
- 5.4.1 History of This Project
- 5.4.2 Finite Element Model of a Truck Frame
- 5.4.3 Criteria and Pseudo-Criteria
- 5.4.4 Design Variables
- 5.5 Multicriteria Optimization of Orthotropic Bridges
- 5.5.1 Introduction and Purposes
- 5.5.2 Mathematical Model and Parameters
- 5.5.3 Results of Optimization
- 5.5.4 Conclusion
- References
- 6 Multicriteria Identification
- 6.1 Adequacy of Mathematical Models
- 6.2 Multicriteria Identification and Operational Development
- 6.2.1 The PSI Method in Multicriteria Identification Problems
- 6.2.2 The Search for the Identified Solutions
- 6.2.3 Operational Development of Prototypes
- 6.2.4 Conclusion
- 6.3 Vector Identification of a Spindle Unit for Metal-Cutting Machines
- 6.3.1 Introduction
- 6.3.2 Experimental Determination of the Characteristics of a Spindle Unit
- 6.3.3 Construction of Mathematical Models
- 6.3.4 The Identified Parameters of the Models
- 6.3.5 Adequacy Criteria
- 6.3.6 Solution of the Identification Problems
- 6.3.7 Solution of the Optimization Problem
- 6.3.8 Conclusion
- References
- 7 Other Multicriteria Problems and Related Issues
- 7.1 Search for the Compromise Solution When the Desired Solution Is Unattainable
- 7.1.1 Definition of the Solution That Is the Closest to the Unattainable Solution
- 7.1.2 Conclusion
- 7.2 Design of Controlled Engineering Systems
- 7.2.1 Multistage Axial Flow Compressor for an Aircraft Engine
- 7.2.2 Conclusion
- 7.3 Multicriteria Analysis from Observational Data
- 7.3.1 Example
- 7.4 Multicriteria Optimization of Large-Scale Systems in Parallel Mode
- 7.4.1 Computationally Expensive Problems
- 7.4.2 First Example
- 7.4.3 Second Example
- 7.4.4 Conclusion
- 7.5 On the Number of Trails in the Real-Life Problems
- References
- 8 Adopting the PSI Method for Database Search
- 8.1 Introduction
- 8.1.1 Characteristics of Alternatives: Criteria and Pseudo-Criteria
- 8.1.2 General Statement of the Problem and Solution Approach
- 8.1.3 Motivation of the Problem Statement
- 8.2 DBS-PSI Method
- 8.2.1 DBS-PSI Method as a New Paradigm of a Database Search
- 8.3 Searching for a Matching Partner
- 8.3.1 Conclusions of the Example
- 8.4 Summary
- References
- 9 Multicriteria Analysis of L1 Adaptive Flight Control System
- 9.1 Objective of the Research
- 9.2 Prototype: Criteria and Design Variables
- 9.2.1 Design Variables
- 9.2.2 List of Criteria and Pseudo-Criteria
- 9.2.3 Criteria Addressing FQ and PIO Characteristics
- 9.2.4 Criteria Constraints
- 9.3 Solutions and Analysis
- 9.3.1 First Iteration
- 9.3.2 Second Iteration
- 9.3.3 Conclusion
- References
- Conclusions
- Appendix Examples of Calculation of the Approximate Compromise Curves
- Analytical Approach
- Example A.1
- Example A.2
- References
- About the AUthors
- Index
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