Feasibility and infeasibility in optimization: algorithms and computational methods
"Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, non...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | International series in operations research & management science
118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, nonlinear, and mixed-integer programs. Connections to related work in constraint programming are shown." "A main goal of the book is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems."--BOOK JACKET. |
| Physical Description: | XXI, 270 S. Ill., graph. Darst. |
| ISBN: | 9780387749310 0387749314 9780387749327 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Dedication v
Preface vii
Table of Contents ix
List of Figures xiii
List of Tables xv
List of Algorithms xvii
Introduction xix
1. Preliminaries 1
1.1. The Optimization Model 1
1.2. Measuring Infeasibility 2
Parti: Seeking Feasibility 7
Model Reformulation 8
2. Seeking Feasibility in Linear Programs 11
2.1. The Phase 1 Algorithm 11
2.2. The Big MMethod 13
2.3. Phase 1 fromAnyBasis 13
2.4. Crash Start Heuristics 15
2.5. Crossover from an Infeasible Basis J6
2.6. Advanced Starts: Hot and Warm Starts 17
2.7. Seeking Feasibility and Optimality Simultaneously 18
2.8. Projection Methods 19
3. Seeking Feasibility in Mixed Integer Linear Programs 23
3.1. Pivot and Complement and Pivot and Shift Heuristics 25
3.2. The OCTANE Heuristic 28
3.3. The Feasibility Pump 30
3.3.1. The Feasibility Pump for Mixed Integer Nonlinear Programs. 34
3.4. Branching Variable Selection by Active Constraints Methods 37
3.5. Conflict Analysis 42
3.6. Market Split Problems 43
4. A Brief Tour of Constraint Programming 45
4.1. Branching in the Satisfiability Problem 49
x Table of Contents
5. Seeking Feasibility in Nonlinear Programs 51
5.1. Penalty Methods 52
5.2. Determining the Characteristics of anNLP 54
5.2.1. Convex Sampling Enclosures 58
5.2.2. Hit and Run Methods 59
5.2.3. Approximating Nonconvex Feasible Regions 60
5.3. Bootstrapping in a Convex Constrained Region 60
5.4. Initial Point Placement Heuristics 63
5.5. Constraint Consensus Methods for Approximate Feasibility 65
5.6. Finding a Good Sampling Box for Multistart 73
5.6.1. Tightening the Variable Bounds 73
5.6.2. Best Heuristic Sampling Box 76
5.7. Multistart Methods 77
5.7.1. MSNLP Feasibility Mode 80
5.7.2. Multistart Constraint Consensus 80
5.8. Bootstrapping Method of Debrosse and Westerberg 85
5.9. Global Optimization 87
Part II: Analyzing Infeasibility 89
6. Isolating Infeasibility 93
6.1. General Logical Methods 94
6.1.1. Logical Reduction of Models and Presolving 95
6.1.2. The Deletion Filter 97
6.1.3. The Additive Method 98
6.1.4. The Elastic Filter 101
6.1.5. Speed ups: Treating Constraints in Groups 104
6.1.6. Speed ups: Combining the Additive Method
and the Deletion Filter 109
6.1.7. Sampling Methods 110
6.2. Methods Specific to Linear Programs 112
6.2.1. The Reciprocal Filter 113
6.2.2. The Sensitivity Filter 114
6.2.3. Pivoting Methods 116
6.2.4. Interior Point Methods 118
6.2.5. Speed ups: Combining Methods 118
6.2.6. Guiding the Isolation 120
6.2.7. Finding Useful Isolations 122
6.2.8. Analyzing Infeasible Network LPs 127
6.2.9. Software 128
6.3. Methods Specific to Mixed Integer Linear Programming 130
6.3.1. A Deletion Filter for MIPs 133
6.3.2. Additive Methods for MIPs 134
6.3.3. An Additive/Deletion Method for MIPs 137
6.3.4. Using the Information in the Initial Branch
and Bound Tree 138
Table of Contents xi
6.3.5. Speed ups 140
6.3.6. Conclusions from Empirical Studies 140
6.3.7. Software Survey 143
6.4. Methods Specific to Nonlinear Programming 143
6.4.1. Deletion Filtering 144
6.4.1.1. Speeding the Isolation by Grouping Constraints 149
6.4.2. IIS Isolation by the method of Debrosse and Westerberg 150
6.4.3. Methods for Quadratic Programs 151
6.4.4. Methods for Space Covering Global Optimizers 153
6.4.5. Software Survey 154
6.5. Methods Specific to Constraint Programming 154
7. Finding the Maximum Feasible Subset of Linear Constraints 159
7.1. Exact Solutions 161
7.1.1. An Exact Solution via MIP 161
7.1.2. An Exact Formulation via Equilibrium Constraints 162
7.2. IIS Enumeration and Covering 164
7.3. Phase One Heuristics 167
7.4. Chinneck s SINF Reduction Heuristics 169
7.5. Two Phase Relaxation Based Heuristic 179
7.6. Randomized Thermal Relaxation Algorithms 181
7.7. An Interior Point Heuristic 183
7.8. Working with IIS Covers 184
7.8.1. Single Member IIS Covers 185
7.8.2. Finding Specific IISs Based on IIS Covers 186
7.9. The Minimum Number of Feasible Partitions Problem 189
7.10. Partial Constraint Satisfaction in Constraint Programming 193
8. Altering Constraints to Achieve Feasibility 197
8.1. Shifting Constraints 197
8.1.1. Using the Phase 1 Result 198
8.1.2. Minimizing the lx Norm 199
8.1.3. Least Squares Methods 199
8.1.4. Roodman s Bounds on Minimum Constraint Adjustments 200
8.1.5. A Fuzzy Approach to Constraint Shifting 202
8.1.6. A Goal Programming Approach to Constraint Shifting 202
8.1.7. Constraint Shifting in Sequential Quadratic Programming 204
8.1.8. Violating a Limited Number of Constraints by a Limited
Amount 205
8.2. Adjusting the Constraint Matrix 206
8.3. Related Research 208
xii Table of Contents
Part III: Applications 211
9. Other Model Analyses 213
9.1. Analyzing Unbounded Linear Programs 213
9.2. Analyzing the Viability of Network Models 213
9.3. Analyzing Multiple Objective Linear Programs 216
9.3.1. Interaction Analysis of the Constraints 218
9.3.2. Interaction Analysis of the Objectives 218
9.3.2.1. Generating Different Interacting Sets of Objectives 220
9.3.2.2. Which Objectives Conflict With
a Particular Objective? 221
9.3.2.3. Evaluating the Relative Amount
of Objective Interference 221
9.3.3. Summary of the Method 222
9.3.4. Example 224
10. Data Analysis 227
10.1. Classification and Neural Networks 227
10.2. Data Depth 231
10.3. Errors in Massive Data Sets 232
11. Miscellaneous Applications 235
11.1. Radiation Treatment Planning 235
11.2. Protein Folding 236
11.3. Digital Video Broadcasting 237
11.4. Automated Test Assembly 238
11.5. Buffer Overrun Detection 239
11.6. Customized Page Ranking 239
11.7. Backtracking in Tree Structured Search 240
11.8. Piecewise Linear Model Estimation 242
11.9. Finding Sparse Solutions to Systems of Linear Equations 243
11.10. Various NP Hard Problems 244
12. Epilogue 247
References 249
Index 265
|
| adam_txt |
Table of Contents
Dedication v
Preface vii
Table of Contents ix
List of Figures xiii
List of Tables xv
List of Algorithms xvii
Introduction xix
1. Preliminaries 1
1.1. The Optimization Model 1
1.2. Measuring Infeasibility 2
Parti: Seeking Feasibility 7
Model Reformulation 8
2. Seeking Feasibility in Linear Programs 11
2.1. The Phase 1 Algorithm 11
2.2. The Big MMethod 13
2.3. Phase 1 fromAnyBasis 13
2.4. Crash Start Heuristics 15
2.5. Crossover from an Infeasible Basis J6
2.6. Advanced Starts: Hot and Warm Starts 17
2.7. Seeking Feasibility and Optimality Simultaneously 18
2.8. Projection Methods 19
3. Seeking Feasibility in Mixed Integer Linear Programs 23
3.1. Pivot and Complement and Pivot and Shift Heuristics 25
3.2. The OCTANE Heuristic 28
3.3. The Feasibility Pump 30
3.3.1. The Feasibility Pump for Mixed Integer Nonlinear Programs. 34
3.4. Branching Variable Selection by Active Constraints Methods 37
3.5. Conflict Analysis 42
3.6. Market Split Problems 43
4. A Brief Tour of Constraint Programming 45
4.1. Branching in the Satisfiability Problem 49
x Table of Contents
5. Seeking Feasibility in Nonlinear Programs 51
5.1. Penalty Methods 52
5.2. Determining the Characteristics of anNLP 54
5.2.1. Convex Sampling Enclosures 58
5.2.2. Hit and Run Methods 59
5.2.3. Approximating Nonconvex Feasible Regions 60
5.3. Bootstrapping in a Convex Constrained Region 60
5.4. Initial Point Placement Heuristics 63
5.5. Constraint Consensus Methods for Approximate Feasibility 65
5.6. Finding a Good Sampling Box for Multistart 73
5.6.1. Tightening the Variable Bounds 73
5.6.2. Best Heuristic Sampling Box 76
5.7. Multistart Methods 77
5.7.1. MSNLP Feasibility Mode 80
5.7.2. Multistart Constraint Consensus 80
5.8. Bootstrapping Method of Debrosse and Westerberg 85
5.9. Global Optimization 87
Part II: Analyzing Infeasibility 89
6. Isolating Infeasibility 93
6.1. General Logical Methods 94
6.1.1. Logical Reduction of Models and Presolving 95
6.1.2. The Deletion Filter 97
6.1.3. The Additive Method 98
6.1.4. The Elastic Filter 101
6.1.5. Speed ups: Treating Constraints in Groups 104
6.1.6. Speed ups: Combining the Additive Method
and the Deletion Filter 109
6.1.7. Sampling Methods 110
6.2. Methods Specific to Linear Programs 112
6.2.1. The Reciprocal Filter 113
6.2.2. The Sensitivity Filter 114
6.2.3. Pivoting Methods 116
6.2.4. Interior Point Methods 118
6.2.5. Speed ups: Combining Methods 118
6.2.6. Guiding the Isolation 120
6.2.7. Finding Useful Isolations 122
6.2.8. Analyzing Infeasible Network LPs 127
6.2.9. Software 128
6.3. Methods Specific to Mixed Integer Linear Programming 130
6.3.1. A Deletion Filter for MIPs 133
6.3.2. Additive Methods for MIPs 134
6.3.3. An Additive/Deletion Method for MIPs 137
6.3.4. Using the Information in the Initial Branch
and Bound Tree 138
Table of Contents xi
6.3.5. Speed ups 140
6.3.6. Conclusions from Empirical Studies 140
6.3.7. Software Survey 143
6.4. Methods Specific to Nonlinear Programming 143
6.4.1. Deletion Filtering 144
6.4.1.1. Speeding the Isolation by Grouping Constraints 149
6.4.2. IIS Isolation by the method of Debrosse and Westerberg 150
6.4.3. Methods for Quadratic Programs 151
6.4.4. Methods for Space Covering Global Optimizers 153
6.4.5. Software Survey 154
6.5. Methods Specific to Constraint Programming 154
7. Finding the Maximum Feasible Subset of Linear Constraints 159
7.1. Exact Solutions 161
7.1.1. An Exact Solution via MIP 161
7.1.2. An Exact Formulation via Equilibrium Constraints 162
7.2. IIS Enumeration and Covering 164
7.3. Phase One Heuristics 167
7.4. Chinneck's SINF Reduction Heuristics 169
7.5. Two Phase Relaxation Based Heuristic 179
7.6. Randomized Thermal Relaxation Algorithms 181
7.7. An Interior Point Heuristic 183
7.8. Working with IIS Covers 184
7.8.1. Single Member IIS Covers 185
7.8.2. Finding Specific IISs Based on IIS Covers 186
7.9. The Minimum Number of Feasible Partitions Problem 189
7.10. Partial Constraint Satisfaction in Constraint Programming 193
8. Altering Constraints to Achieve Feasibility 197
8.1. Shifting Constraints 197
8.1.1. Using the Phase 1 Result 198
8.1.2. Minimizing the lx Norm 199
8.1.3. Least Squares Methods 199
8.1.4. Roodman's Bounds on Minimum Constraint Adjustments 200
8.1.5. A Fuzzy Approach to Constraint Shifting 202
8.1.6. A Goal Programming Approach to Constraint Shifting 202
8.1.7. Constraint Shifting in Sequential Quadratic Programming 204
8.1.8. Violating a Limited Number of Constraints by a Limited
Amount 205
8.2. Adjusting the Constraint Matrix 206
8.3. Related Research 208
xii Table of Contents
Part III: Applications 211
9. Other Model Analyses 213
9.1. Analyzing Unbounded Linear Programs 213
9.2. Analyzing the Viability of Network Models 213
9.3. Analyzing Multiple Objective Linear Programs 216
9.3.1. Interaction Analysis of the Constraints 218
9.3.2. Interaction Analysis of the Objectives 218
9.3.2.1. Generating Different Interacting Sets of Objectives 220
9.3.2.2. Which Objectives Conflict With
a Particular Objective? 221
9.3.2.3. Evaluating the Relative Amount
of Objective Interference 221
9.3.3. Summary of the Method 222
9.3.4. Example 224
10. Data Analysis 227
10.1. Classification and Neural Networks 227
10.2. Data Depth 231
10.3. Errors in Massive Data Sets 232
11. Miscellaneous Applications 235
11.1. Radiation Treatment Planning 235
11.2. Protein Folding 236
11.3. Digital Video Broadcasting 237
11.4. Automated Test Assembly 238
11.5. Buffer Overrun Detection 239
11.6. Customized Page Ranking 239
11.7. Backtracking in Tree Structured Search 240
11.8. Piecewise Linear Model Estimation 242
11.9. Finding Sparse Solutions to Systems of Linear Equations 243
11.10. Various NP Hard Problems 244
12. Epilogue 247
References 249
Index 265 |
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| author | Chinneck, John W. |
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| classification_rvk | SK 870 |
| classification_tum | MAT 912f MAT 900f DAT 517f |
| ctrlnum | (OCoLC)175285178 (DE-599)DNB985306203 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV023063400 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:29:44Z |
| indexdate | 2024-07-09T21:10:08Z |
| institution | BVB |
| isbn | 9780387749310 0387749314 9780387749327 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016266620 |
| oclc_num | 175285178 |
| open_access_boolean | |
| owner | DE-29T DE-824 DE-91G DE-BY-TUM DE-703 DE-11 |
| owner_facet | DE-29T DE-824 DE-91G DE-BY-TUM DE-703 DE-11 |
| physical | XXI, 270 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Chinneck, John W. Verfasser aut Feasibility and infeasibility in optimization algorithms and computational methods John W. Chinneck New York, NY Springer 2008 XXI, 270 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 118 "Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, nonlinear, and mixed-integer programs. Connections to related work in constraint programming are shown." "A main goal of the book is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems."--BOOK JACKET. Feasibility studies Mathematical optimization Feasible Algorithm (DE-588)4716213-2 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Machbarkeit (DE-588)4432424-8 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Constraint-Erfüllung (DE-588)4580374-2 gnd rswk-swf Optimierung (DE-588)4043664-0 s Feasible Algorithm (DE-588)4716213-2 s DE-604 Lineare Optimierung (DE-588)4035816-1 s Constraint-Erfüllung (DE-588)4580374-2 s Machbarkeit (DE-588)4432424-8 s 1\p DE-604 International series in operations research & management science 118 (DE-604)BV011630976 118 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016266620&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chinneck, John W. Feasibility and infeasibility in optimization algorithms and computational methods International series in operations research & management science Feasibility studies Mathematical optimization Feasible Algorithm (DE-588)4716213-2 gnd Lineare Optimierung (DE-588)4035816-1 gnd Machbarkeit (DE-588)4432424-8 gnd Optimierung (DE-588)4043664-0 gnd Constraint-Erfüllung (DE-588)4580374-2 gnd |
| subject_GND | (DE-588)4716213-2 (DE-588)4035816-1 (DE-588)4432424-8 (DE-588)4043664-0 (DE-588)4580374-2 |
| title | Feasibility and infeasibility in optimization algorithms and computational methods |
| title_auth | Feasibility and infeasibility in optimization algorithms and computational methods |
| title_exact_search | Feasibility and infeasibility in optimization algorithms and computational methods |
| title_exact_search_txtP | Feasibility and infeasibility in optimization algorithms and computational methods |
| title_full | Feasibility and infeasibility in optimization algorithms and computational methods John W. Chinneck |
| title_fullStr | Feasibility and infeasibility in optimization algorithms and computational methods John W. Chinneck |
| title_full_unstemmed | Feasibility and infeasibility in optimization algorithms and computational methods John W. Chinneck |
| title_short | Feasibility and infeasibility in optimization |
| title_sort | feasibility and infeasibility in optimization algorithms and computational methods |
| title_sub | algorithms and computational methods |
| topic | Feasibility studies Mathematical optimization Feasible Algorithm (DE-588)4716213-2 gnd Lineare Optimierung (DE-588)4035816-1 gnd Machbarkeit (DE-588)4432424-8 gnd Optimierung (DE-588)4043664-0 gnd Constraint-Erfüllung (DE-588)4580374-2 gnd |
| topic_facet | Feasibility studies Mathematical optimization Feasible Algorithm Lineare Optimierung Machbarkeit Optimierung Constraint-Erfüllung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016266620&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011630976 |
| work_keys_str_mv | AT chinneckjohnw feasibilityandinfeasibilityinoptimizationalgorithmsandcomputationalmethods |