The Parameter Space Investigation Method Toolkit

The Parameter Space Investigation Method Toolkit......Page 2
Contents......Page 6
Acknowledgments......Page 12
Preface......Page 14
Part I The Parameter Space Investigation Method Toolkit......Page 26
1.1 Some Basic Features of Real-Life Optimization Problems......Page 28
1.2 Generalized Formulation of Multicriteria Optimization Problems......Page 29
1.3.1 Substitution of a Multitude of Criteria by a Single One......Page 32
1.3.2 Optimization of the Most Important Criterion......Page 33
1.4 Systematic Search in Multidimensional Domains by Using Uniformly Distributed Sequences......Page 34
1.4.1 Quantitative Characteristics of Uniformity......Page 35
References......Page 36
2.1 The Parameter Space Investigation Method......Page 38
2.1.1 The Complexity of the Investigation......Page 41
2.2 “Soft” Functional Constraints and Pseudo-Criteria......Page 42
2.3 More About Applying Single-Criterion Methods for Solving Multicriteria Problems......Page 44
2.4 An Example of Optimization Problem Statement and Significant Challenge That It Presents......Page 45
2.4.1 Expert’s Difficulties......Page 47
References......Page 48
3 Using the PSI Method and MOVI Software System for Multicriteria Analysis and Visualization......Page 50
3.2.1 Constructing Test Tables......Page 51
3.2.2 Constructing the Feasible Solution Set: Dialogues of an Expert with a Computer......Page 53
3.2.3 Tables of Feasible and Pareto Optimal Solutions......Page 55
3.2.4 Selecting the Most Preferable Solution......Page 56
3.3 Histograms and Graphs......Page 58
3.3.1 Design Variable Histograms: Histograms of the Distribution of Feasible Solutions......Page 59
3.3.3 Graphs “Criterion Versus Design Variable II”......Page 61
3.3.4 Graphs “Criterion Versus Criterion”......Page 64
3.3.5 Graphs “Criterion Versus Design Variable I”......Page 67
3.4.1 Tables of Functional Failures......Page 71
References......Page 75
4.1.1 New Design Variable Constraints......Page 76
4.1.3 Histograms of the Distribution of the Feasible Solutions......Page 77
4.1.4 Graphs of Criterion Versus Design Variable II......Page 80
4.2.1 Basic Principles......Page 83
4.2.3 Analysis of the Combined Pareto Optimal Set......Page 86
4.2.4 Conclusions for Chapters 2 Through 4......Page 87
References......Page 90
Part II Applications to Real-Life Problems......Page 92
5.1.1 Improvement Problem......Page 94
5.2 Problem with the High Dimensionality of the Design Variable Vector......Page 105
5.3.1 General Statement of the Problem......Page 113
5.3.2 Solution of the Problem and Analysis of the Results......Page 116
5.4 Improving the Truck Frame Prototype......Page 119
5.4.2 Finite Element Model of a Truck Frame......Page 120
5.4.3 Criteria and Pseudo-Criteria......Page 121
5.5.1 Introduction and Purposes......Page 122
5.5.2 Mathematical Model and Parameters......Page 124
5.5.3 Results of Optimization......Page 128
5.5.4 Conclusion......Page 129
References......Page 133
6.1 Adequacy of Mathematical Models......Page 136
6.2 Multicriteria Identification and Operational Development......Page 138
6.2.1 The PSI Method in Multicriteria Identification Problems......Page 139
6.2.2 The Search for the Identified Solutions......Page 140
6.2.3 Operational Development of Prototypes......Page 141
6.3.1 Introduction......Page 142
6.3.2 Experimental Determination of the Characteristics of a Spindle Unit......Page 143
6.3.3 Construction of Mathematical Models......Page 145
6.3.5 Adequacy Criteria......Page 147
6.3.6 Solution of the Identification Problems......Page 150
References......Page 151
7.1 Search for the Compromise Solution When the Desired Solution Is Unattainable......Page 154
7.1.1 Definition of the Solution That Is the Closest to the Unattainable Solution......Page 155
7.1.2 Conclusion......Page 156
7.2 Design of Controlled Engineering Systems......Page 157
7.2.1 Multistage Axial Flow Compressor for an Aircraft Engine......Page 160
7.2.2 Conclusion......Page 162
7.3.1 Example......Page 163
7.4.1 Computationally Expensive Problems......Page 166
7.4.2 First Example......Page 168
7.4.3 Second Example......Page 169
7.4.4 Conclusion......Page 171
7.5 On the Number of Trails in the Real-Life Problems......Page 172
References......Page 175
8.1 Introduction......Page 178
8.1.1 Characteristics of Alternatives: Criteria and Pseudo-Criteria......Page 179
8.1.2 General Statement of the Problem and Solution Approach......Page 181
8.1.3 Motivation of the Problem Statement......Page 182
8.2.1 DBS-PSI Method as a New Paradigm of a Database Search......Page 183
8.3 Searching for a Matching Partner......Page 185
8.3.1 Conclusions of the Example......Page 187
8.4 Summary......Page 188
References......Page 189
9.1 Objective of the Research......Page 190
9.2 Prototype: Criteria and Design Variables......Page 193
9.2.1 Design Variables......Page 194
9.2.2 List of Criteria and Pseudo-Criteria......Page 195
9.2.3 Criteria Addressing FQ and PIO Characteristics......Page 200
9.2.4 Criteria Constraints......Page 201
9.3.1 First Iteration......Page 202
9.3.2 Second Iteration......Page 210
9.3.3 Conclusion......Page 217
References......Page 218
Conclusions......Page 220
Analytical Approach......Page 222
Example A.1......Page 224
Example A.2......Page 225
References......Page 234
About the AUthors
......Page 236
Index......Page 238