Multicriteria optimization:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Orig. publ. as vol. 491 in the series: Lecture notes in economics and mathematical systems. - Literaturverz. S. [291] - 305 |
| Physical Description: | XIII, 323 S. graph. Darst. |
| ISBN: | 9783642059759 3540213988 9783540213987 |
Staff View
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Record in the Search Index
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| adam_text | MATTHIAS EHRGOTT MULTICRITERIA OPTIMIZATION SECOND EDITION WITH 88
FIGURES AND 12 TABLES SPRINGER CONTENTS PREFACE V NOTATION IX CONTENTS
XI 1 INTRODUCTION 1 1.1 OPTIMIZATION WITH MULTIPLE CRITERIA 1 1.2
DECISION SPACE AND OBJECTIVE (CRITERION) SPACE 4 1.3 NOTIONS OF
OPTIMALITY 7 1.4 ORDERS AND CONES 8 1.5 CLASSIFICATION OF MULTICRITERIA
OPTIMIZATION PROBLEMS 16 1.6 NOTES 19 EXERCISES 20 2 EFFLCIENCY AND
NONDOMINANCE 23 2.1 EFFICIENT SOLUTIONS AND NONDOMINATED POINTS 23 2.2
BOUNDS ON THE NONDOMINATED SET 33 2.3 WEAKLY AND STRICTLY EFFICIENT
SOLUTIONS 38 2.4 PROPER EFFICIENCY AND PROPER NONDOMINANCE 50 2.5 NOTES
59 EXERCISES 62 3 THE WEIGHTED SUM METHOD AND RELATED TOPICS 65 3.1
WEIGHTED SUM SCALARIZATION AND (WEAK) EFFICIENCY 68 3.2 WEIGHTED SUM
SCALARIZATION AND PROPER EFFICIENCY 71 3.3 OPTIMALITY CONDITIONS 80 3.4
CONNECTEDNESS OF EFFICIENT AND NONDOMINATED SETS 86 3.5 NOTES 91 XII
CONTENTS EXERCISES 93 4 SCALARIZATION TECHNIQUES 97 4.1 THE E-CONSTRAINT
METHOD 98 4.2 THE HYBRID METHOD 101 4.3 THE ELASTIC CONSTRAINT METHOD
102 4.4 BENSON S METHOD 106 4.5 COMPROMISE SOLUTIONS - APPROXIMATION OF
THE IDEAL POINT.... 111 4.6 THE ACHIEVEMENT FUNCTION METHOD 121 4.7
NOTES 122 EXERCISES 124 5 OTHER DENNITIONS OF OPTIMALITY -
NONSCALARIZING METHODS . 127 5.1 LEXICOGRAPHIC OPTIMALITY 128 5.2
MAX-ORDERING OPTIMALITY 132 5.3 LEXICOGRAPHIC MAX-ORDERING OPTIMIZATION
135 5.4 NOTES 146 EXERCISES 148 6 INTRODCUTION TO MULTICRITERIA LINEAR
PROGRAMMING 151 6.1 NOTATION AND DENNITIONS 152 6.2 THE SIMPLEX METHOD
AND BIOBJECTIVE LINEAR PROGRAMS 160 EXERCISES 170 7 A MULTIOBJECTIVE
SIMPLEX METHOD 171 7.1 ALGEBRA OF MULTIOBJECTIVE LINEAR PROGRAMMING 171
7.2 THE GEOMETRY OF MULTIOBJECTIVE LINEAR PROGRAMMING 184 7.3 NOTES 193
EXERCISES 195 8 MULTIOBJECTIVE COMBINATORIAL OPTIMIZATION 197 8.1 BASICS
198 8.2 PROBLEMS WITH EXPLICITELY GIVEN FEASIBLE SET 209 8.3
SCALARIZATION OF MULTIOBJECTIVE INTEGER PROGRAMS 214 8.4 NOTES 218
EXERCISES 220 9 MULTIOBJECTIVE VERSIONS OF POLYNOMIALLY SOLVABLE
PROBLEMS 221 9.1 ALGORITHMS FOR THE SHORTEST PATH PROBLEM 221 9.2 THE
MINIMUM SPANNING TREE PROBLEM 236 9.3 MATROIDS 247 9.4 THE ASSIGNMENT
PROBLEM AND THE TWO PHASE METHOD 253 CONTENTS XIII 9.5 NOTES 267
EXERCISES 269 10 MULTIOBJECTIVE VERSIONS OF SOME AFP-HARD PROBLEMS 271
10.1 THE KNAPSACK PROBLEM AND BRANCH AND BOUND 271 10.2 THE TRAVELLING
SALESPERSON PROBLEM AND HEURISTICS 279 10.3 NOTES 288 EXERCISES 290
BIBLIOGRAPHY 291 LIST OF FIGURES 307 LIST OF TABLES 311 AUTHOR INDEX 313
SUBJECT INDEX 315
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:55Z |
| institution | BVB |
| isbn | 9783642059759 3540213988 9783540213987 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012841979 |
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| physical | XIII, 323 S. graph. Darst. |
| publishDate | 2005 |
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| spelling | Ehrgott, Matthias 1966- Verfasser (DE-588)135907578 aut Multicriteria optimization Matthias Ehrgott 2. ed. Berlin [u.a.] Springer 2005 XIII, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Orig. publ. as vol. 491 in the series: Lecture notes in economics and mathematical systems. - Literaturverz. S. [291] - 305 Mathematical optimization Multiple criteria decision making Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s DE-604 text/html http://www.loc.gov/catdir/enhancements/fy0663/2005924730-d.html Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012841979&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ehrgott, Matthias 1966- Multicriteria optimization Mathematical optimization Multiple criteria decision making Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| subject_GND | (DE-588)4610682-0 |
| title | Multicriteria optimization |
| title_auth | Multicriteria optimization |
| title_exact_search | Multicriteria optimization |
| title_full | Multicriteria optimization Matthias Ehrgott |
| title_fullStr | Multicriteria optimization Matthias Ehrgott |
| title_full_unstemmed | Multicriteria optimization Matthias Ehrgott |
| title_short | Multicriteria optimization |
| title_sort | multicriteria optimization |
| topic | Mathematical optimization Multiple criteria decision making Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| topic_facet | Mathematical optimization Multiple criteria decision making Mehrkriterielle Optimierung |
| url | http://www.loc.gov/catdir/enhancements/fy0663/2005924730-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012841979&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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