دانلود کتاب Nonlinear Interval Optimization for Uncertain Problems

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Contents Abbreviations 1 Introduction 1.1 The Research Significance of Uncertain Optimization 1.2 Stochastic Programming and Fuzzy Programming 1.2.1 Stochastic Programming 1.2.2 Fuzzy Programming 1.2.3 Troubles and Difficulties in Stochastic Programming and Fuzzy Programming 1.3 Uncertain Optimization Based on Non-probabilistic Modeling 1.3.1 Convex Model Optimization 1.3.2 Interval Optimization 1.4 Current Problems in Interval Optimization 1.5 The Research Target and Framework of This Book References 2 The Basic Principles of Interval Analysis 2.1 The Origin of Interval Number 2.2 The Basic Conceptions of Interval Mathematics 2.3 The Basic Arithmetic Operations of Interval Number 2.4 The Overestimation Problem in Interval Arithmetic 2.5 Summary References 3 Mathematical Transformation Models of Nonlinear Interval Optimization 3.1 The Description of a General Nonlinear Interval Optimization Problem 3.2 Possibility Degree of Interval Number and Transformation of Uncertain Constraints 3.2.1 An Improved Possibility Degree of Interval Number 3.2.2 Transformation of Uncertain Constraints Based on Possibility Degree of Interval Number 3.3 The Mathematic Transformation Model Based on Order Relation of Interval Number 3.3.1 Order Relation of Interval Number and Transformation of Uncertain Objective Function 3.3.2 The Transformed Deterministic Optimization 3.4 The Mathematic Transformation Model Based on Possibility Degree of Interval Number 3.5 A Two-Layer Optimization Algorithm Based on IP-GA 3.5.1 A Brief Introduction of IP-GA 3.5.2 Procedure of the Algorithm 3.6 Numerical Example and Discussions 3.6.1 By Using the Mathematic Transformation Model Based on Order Relation of Interval Number 3.6.2 By Using the Mathematic Transformation Model Based on Possibility Degree of Interval Number 3.7 Summary References 4 Interval Optimization Based on Hybrid Optimization Algorithm 4.1 The Nonlinear Interval Optimization with Uniformly Expressed Constraints 4.2 The ANN Model 4.3 Construction of the Hybrid Optimization Algorithms 4.3.1 The Hybrid Optimization Algorithm with Multiple Networks 4.3.2 The Hybrid Optimization Algorithm with a Single Network 4.4 Engineering Applications 4.4.1 The Variable Binder Force Optimization in U-Shaped Forming 4.4.2 The Locator Optimization in Welding Fixture 4.5 Summary References 5 Interval Optimization Based on Interval Structural Analysis 5.1 Interval Set Theory and Interval Extension 5.2 The Interval Structural Analysis Method 5.2.1 Interval Structural Analysis for Small Uncertainties 5.2.2 Interval Structural Analysis for Large Uncertainties 5.2.3 Numerical Example and Discussions 5.3 An Efficient Interval Optimization Method 5.3.1 Algorithm Description 5.3.2 Engineering Applications 5.4 Summary References 6 Interval Optimization Based on Sequential Linear Programming 6.1 Formulation of the Algorithm 6.1.1 Solution of the Linear Interval Optimization Problems 6.1.2 Iteration Mechanism 6.1.3 Calculation of the Intervals of the Actual Objective Function and Constraints in Each Iteration 6.2 Testing of the Proposed Method 6.2.1 Test Function 1 6.2.2 Test Function 2 6.3 Discussions on Convergence of the Proposed Method 6.4 Application to the Design of a Vehicle Occupant Restraint System 6.5 Summary References 7 Interval Optimization Based on Approximation Models 7.1 Nonlinear Interval Optimization Based on the Approximation Model Management Strategy 7.1.1 Quadratic Polynomial Response Surface 7.1.2 Design of Experiment Method 7.1.3 The Method by Using the Transformation Model Based on Order Relation of Interval Number 7.1.4 The Method by Using the Transformation Model Based on Possibility Degree of Interval Number 7.1.5 Test Functions 7.1.6 Discussions on the Convergence 7.1.7 Engineering Applications 7.2 Nonlinear Interval Optimization Based on the Local-Densifying Approximation Technique 7.2.1 Radial Basis Function 7.2.2 Algorithm Flow 7.2.3 Test Functions 7.2.4 Application to the Crashworthiness Design of a Thin-Walled Beam of Vehicle Body 7.3 Summary References 8 Interval Multidisciplinary Design Optimization 8.1 An Interval MDO Model 8.2 Decoupling the Multidisciplinary Analysis 8.3 Transformation of the Interval Optimization Problem 8.4 Numerical Example and Engineering Application 8.4.1 Numerical Example 8.4.2 Application to the Aerial Camera Design 8.5 Summary References 9 A New Type of Possibility Degree of Interval Number and Its Application in Interval Optimization 9.1 Three Existing Possibility Degree Models of Interval Number and Their Disadvantages 9.2 The Reliability-Based Possibility Degree of Interval Number 9.3 Interval Optimization Based on RPDI 9.3.1 Linear Interval Optimization 9.3.2 Nonlinear Interval Optimization 9.4 Numerical Example and Engineering Applications 9.4.1 Numerical Example 9.4.2 Application to a 10-bar Truss 9.4.3 Application to the Design of an Automobile Frame 9.5 Summary References 10 Interval Optimization Considering the Correlation of Parameters 10.1 Multidimensional Parallelepiped Interval Model 10.1.1 Two-Dimensional Problem 10.1.2 Multidimensional Problem 10.1.3 Construction of the Uncertainty Domain 10.2 Interval Optimization Based on the Multidimensional Parallelepiped Interval Model 10.2.1 Affine Coordinate Transformation 10.2.2 Conversion to a Deterministic Optimization 10.3 Numerical Example and Engineering Applications 10.3.1 Numerical Example 10.3.2 Application to a 25-bar Truss 10.3.3 Application to the Crashworthiness Design of Vehicle Side Impact 10.4 Summary References 11 Interval Multi-objective Optimization 11.1 An Interval Multi-objective Optimization Model 11.2 Conversion to a Deterministic Multi-objective Optimization 11.3 Algorithm Flow 11.4 Numerical Example and Engineering Application 11.4.1 Numerical Example 11.4.2 Application to the Design of an Automobile Frame 11.5 Summary References 12 Interval Optimization Considering Tolerance Design 12.1 An Interval Optimization Model Considering Tolerance Design 12.2 Conversion to a Deterministic Optimization 12.3 Numerical Example and Engineering Applications 12.3.1 Numerical Example 12.3.2 Application to a Cantilever Beam 12.3.3 Application to the Crashworthiness Design of Vehicle Side Impact 12.4 Summary References 13 Interval Differential Evolution Algorithm 13.1 Fundamentals of the Differential Evolution Algorithm 13.1.1 Initial Population Generation Strategy 13.1.2 Mutation Strategy 13.1.3 Crossover Strategy 13.1.4 Selection Strategy 13.2 Formulation of the Interval Differential Evolution Algorithm 13.2.1 Satisfaction Value of Interval Possibility Degree and Treatment of Uncertain Constraints 13.2.2 Selection Strategy Based on an Interval Preferential Rule 13.2.3 Algorithm Flow 13.3 Numerical Examples and Engineering Application 13.3.1 Numerical Examples 13.3.2 Application to the Design of Augmented Reality Glasses 13.4 Summary Appendix: Numerical Examples References