The parameter space investigation method toolkit

The Premise is quite simple: To find the optimal solution to a problem, you need to identify the criteria that limit deasible solutions. But for engineers working on large scale technology projects, implementing this premise can be a major challenge in itself. This title helps engineers meet the challenge.

Author Notes

Roman Statnikov is a senior researcher and instructor in the Information Sciences Department at the Naval Postgraduate School in Monterey, California, and is also a professor and principal research scientist in the Optimal Design Theory and Methods Laboratory at the Mechanical Engineering Research Institute, Russian Academy of Sciences. He holds a Dr. Tech. Sci. degree in the theory of machines and mechanisms from the Mechanical Engineering Institute, Russian Academy of Sciences. He received a Ph.D. on the same subject from Moscow State University of Railways.
Alexander Statnikov is an assistant professor at the Center for Health Informatics and Bioinformatics, New York University Langone Medical Center. He holds a Ph.D. in biomedical informatics from Vanderbilt University, Nashville, Tennessee.

Acknowledgments	p. xi
Preface	p. xiii
Part I The Parameter Space Investigation Method Toolkit	p. 1
1 Introduction	p. 3
1.1 Some Basic Features of Real-Life Optimization Problems	p. 3
1.2 Generalized Formulation of Multicriteria Optimization Problems	p. 3
1.2.1 Definition	p. 7
1.3 Applying Single-Criterion Methods for Solving Multicriteria Problems	p. 7
1.3.1 Substitution of a Multitude of Criteria by a Single One	p. 7
1.3.2 Optimization of the Most Important Criterion	p. 8
1.4 Systematic Search in Multidimensional Domains by Using Uniformly Distributed Sequences	p. 9
1.4.1 Quantitative Characteristics of Uniformity	p. 10
References	p. 11
2 Parameter space investigation Method as a loot for Formulation and Solution of Real-life Problems	p. 13
2.1 The Parameter Space Investigation Method	p. 13
2.1.1 Trie Complexity of the Investigation	p. 16
2.1.2 Definition of the Feasible Solution in Parallel Mode	p. 17
2.1.3 Number Generators for Systematic Search in the Design Variable Space	p. 17
2.2 "Soft" Functional Constraints and Pseudo-Criteria	p. 17
2.3 More About Applying Single-Criterion Methods for Solving Multicriteria Problems	p. 19
2.4 An Example of Optimization Problem Statement and Significant Challenge That It Presents	p. 20
2.4.1 Expert's Difficulties	p. 22
References	p. 23
3 Using the PSI Method and MOVI Software System for Multicriteria Analysis and Visualization	p. 25
3.1 Performing Tests	p. 26
3.2 Construction of Feasible and Pareto Optimal Sets	p. 26
3.2.1 Constructing Test Tables	p. 26
3.2.2 Constructing the Feasible Solution Set: Dialogues of an Expert with a Computer	p. 28
3.2.3 Tables of Feasible and Pareto Optimal Solutions	p. 30
3.2.4 Selecting the Most Preferable Solution	p. 31
3.3 Histograms and Graphs	p. 33
3.3.1 Design Variable Histograms: Histograms of the Distribution of Feasible Solutions	p. 34
3.3.2 Criteria Histograms: Visualization of Contradictory Criteria	p. 36
3.3.3 Graphs "Criterion Versus Design Variable II"	p. 36
3.3.4 Graphs "Criterion Versus Criterion"	p. 39
3.3.5 Graphs "Criterion Versus Design Variable I"	p. 42
3.4 Weakening Functional Constraints	p. 46
3.4.1 Tables of Functional Failures	p. 46
References	p. 50
4 Improving Optimal Solutions	p. 51
4.1 Solving a New Optimization Problem	p. 51
4.1.1 New Design Variable Constraints	p. 51
4.1.2 Tables of Feasible and Pareto Optimal Solutions	p. 52
4.1.3 Histograms of die Distribution of the Feasible Solutions	p. 52
4.1.4 Graphs of Criterion Versus Design Variable II	p. 55
4.1.5 "Graphs'CriteriotrVersas Criterion	p. 58
4.2 Construction of die Combined Pareto -Optimal Set	p. 58
4.2.1 Basic Principles	p. 58
4.2.2 Tables of Combined Pareto Optimal Solutions	p. 61
4.2.3 Analysis of die Combined Pareto Optimal Set	p. 61
4.2.4 Conclusions for Chapters 2 Through 4	p. 62
References	p. 65
Part II Applications to Real-Life Problems	p. 67
5 Multicriteria Design	p. 69
5.1 Multicriteria Analysis of the Ship Design Prototype	p. 69
5.1.1 Improvement Problem	p. 69
5.2 Problem with the High Dimensionality of the Design Variable Vector	p. 80
5.3 Rear Axle Housing for a Truck: PSI Method with the Finite Element Method	p. 88
5.3.1 General Statement of the Problem	p. 88
5.3.2 Solution of the Problem and Analysis of the Results	p. 91
5.3.3 tConclusions	p. 94
5.4 Improving the Truck Frame Prototype	p. 94
5.4.1 History of This Project	p. 95
5.4.2 Finite Element Model of a Truck Frame	p. 95
5.4.3 Criteria and Pseudo-Criteria	p. 96
5.4.4 Design Variables	p. 97
5.5 Multicriteria Optimization of Orthotropic Bridges	p. 97
5.5.1 Introduction and Purposes	p. 97
5.5.2 Mathematical Model and Parameters	p. 99
5.5.3 Results of Optimization	p. 103
5.5.4 Conclusion	p. 104
References	p. 108
6 Multicriteria Identification	p. 111
6.1 Adequacy of Mathematical Model	p. 111
6.2 Multicriteria Identification and Operational Development	p. 113
6.2.1 The PSI Method in Multicriteria Identification Problems	p. 114
6.2.2 The Search for the Identified Solutions	p. 115
6.2.3 Operational Development of Prototypes	p. 116
6.2.4 Conclusion	p. 117
6.3 Vector Identification of a Spindle Unit for Metal-Cutting Machines	p. 117
6.3.1 Introduction	p. 117
6.3.2 Experimental Determination of the Characteristics of a Spindle Unit	p. 118
6.3.3 Construction of Mathematical Models	p. 120
6.3.4 The Identified Parameters of the Models	p. 122
6.3.5 Adequacy Criteria	p. 122
6.3.6 Solution of the Identification Problems	p. 125
6.3.7 Solution of the Optimization Problem	p. 126
6.3.8 Conclusion	p. 126
References	p. 126
7 Other Multicriteria Problems and Related Issues	p. 129
7.1 Search for the Compromise Solution When the Desired Solution Is Unattainable	p. 129
7.1.1 Definition of die Solution That Is the Closest to the Unattainable Solution	p. 130
7.1.2 Conclusion	p. 131
7.2 Design of Controlled Engineering Systems	p. 132
7.2.1 Multistage Axial Flow Compressor for an Aircraft Engine	p. 135
7.2.2 Conclusion	p. 137
7.3 Multicriteria Analysis from Observational Data	p. 138
7.3.1 Example	p. 138
7.4 Multicriteria Optimization of Large-Scale Systems in Parallel Mode	p. 141
7.4.1 Computationally Expensive Problems	p. 141
7.4.2 First Example	p. 143
7.4.3 Second Example	p. 144
7.4.4 Conclusion	p. 146
7.5 On the Number of Trails in the Real-Life Problems	p. 147
References	p. 150
8 Adopting the PSI Method for Database Search	p. 153
8.1 Introduction	p. 153
8.1.1 Characteristics of Alternatives: Criteria and Pseudo-Criteria	p. 154
8.1.2 General Statement of the Problem and Solution Approach	p. 156
8.1.3 Motivation of the Problem Statement	p. 157
8.2 DBS-PSI Method	p. 158
8.2.1 DBS-PSI Method as a New Paradigm of a Database Search	p. 158
8.3 Searching for a Matching Partner	p. 160
8.3.1 Conclusions of the Example	p. 163
8.4 Summary	p. 163
References	p. 164
9 Multicriteria Analysis of I, Adaptive Flight Control System	p. 165
9.1 Objective of the Research	p. 165
9.2 Prototype: Criteria and Design Variables	p. 168
9.2.1 Design Variables	p. 169
9.2.2 List of Criteria and Pseudo-Criteria	p. 170
9.2.3 Criteria Addressing FQ and PIO Characteristics	p. 175
9.2.4 Criteria Constraints	p. 176
9.3 Solutions and Analysis	p. 177
9.3.1 First Iteration	p. 177
9.3.2 Second Iteration	p. 185
9.3.3 Conclusion	p. 192
References	p. 193
Conclusions	p. 195
Appendix: Examples of Calculation of the Approximate Compromise Curves	p. 197
About the Authors	p. 211
Index	p. 213

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