Mathematical modeling and optimization: an essay for the design of computer based modeling tools
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1999
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| Series: | Applied optimization
31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 313 S. graph. Darst. |
| ISBN: | 0792359275 |
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| 245 | 1 | 0 | |a Mathematical modeling and optimization |b an essay for the design of computer based modeling tools |c by Tony Hürlimann |
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Record in the Search Index
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| adam_text | IMAGE 1
MATHEMATICAL MODELING AND
OPTIMIZATION AN ESSAY FOR THE DESIGN OF COMPUTER-BASED MODELING TOOLS
BY TONY HUERLIMANN
INSTITUTE FOR INFORMATICS, UNIVERSITY OF FRIBOURG, SWITZERLAND
BFL
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
TABLE OF CONTENTS
1. INTRODUCTION 1
1.1. MODELS AND THEIR FUNCTIONS 2
1.2. THE ADVENT OF THE COMPUTER 4
1.3. NEW SCIENTIFIC BRANCHES EMERGE 5
1.4. MATHEMATICAL MODELING - THE CONSEQUENCES 8 1.5. COMPUTER-BASED
MODELING MANAGEMENT 10
1.6. ABOUT THIS BOOK 12
2. WHAT IS MODELING? 17
2.1. MODEL: A DEFINITION 17
2.1. MATHEMATICAL MODELS 23
2.2. MODEL THEORY 26
2.3. MODELS AND INTERPRETATIONS 29
2.4. RELATED CONCEPTS 30
2.5. DECLARATIVE VERSUS PROCEDURAL KNOWLEDGE 3 3
3. THE MODELING LIFE CYCLE 37
3.1. STAGE 1: SPECIFICATION OF THE REAL PROBLEM 3 9 3.2. STAGE 2:
FORMULATION OF THE MATHEMATICAL MODEL 39 3.3. STAGE 3: SOLUTION OF THE
MODEL 43
3.4. STAGE 4: VALIDATION OF THE MODEL AND ITS SOLUTION 44 3.4.1. LOGICAL
CONSISTENCY 50
3.4.2. DATA TYPE CONSISTENCY 51
3.4.3. UNIT TYPE CONSISTENCY 51
3.4.4. USER DEFINED DATA CHECKING 52
3.4.5. SIMPLICITY CONSIDERATIONS 53
3.4.6. SOLVABILITY CHECKING 53
3.4.7. NUMERICAL STABILITY AND SENSITIVITY ANALYSIS 53
3.4.8. CHECKING THE CORRESPONDENCE 55
3.5. STAGE 5: WRITING A REPORT 5 7
3.6. TWO CASE STUDIES 5 8
4. MODEL PARADIGMS 67
4.1. MODEL TYPES 67
4.1.1. OPTIMIZATION MODELS 68
4.1.2. SYMBOLICAL - NUMERICAL MODELS 68
4.1.3. LINEAR - NONLINEAR MODELS 68
4.1.4. CONTINUOUS - DISCRETE MODELS 69
4.1.5. DETERMINISTIC - STOCHASTIC MODELS 69
4.1.6. ANALYTIC - SIMULATION MODELS 70
4.2. MODELS AND THEIR PURPOSES 71
4.3. MODELS IN THEIR RESEARCH COMMUNITIES 72
IMAGE 3
V L LL
4.3.1. DIFFERENTIAL EQUATION MODELS 72
4.3.2. OPERATIONS RESEARCH 73
4.3.3. ARTIFICIAL INTELLIGENCE 75
4.4. MODELING UNCERTAINTY 80
4.4.1. MATHEMATICAL MODELS AND UNCERTAINTY 80
4.4.2. GENERAL APPROACHES IN MODELING UNCERTAINTY 82
4.4.3. CLASSICAL APPROACHES IN OR 84
4.4.4. APPROACHES IN LOGICAL MODELS 86
4.4.5. FUZZY SET MODELING 92
4.4.6. OUTLOOK 96
5. PROBLEMS AND CONCEPTS 101
5.1. PRESENT SITUATION IN MMS 102
5.2. WHAT MMS IS NOT 102
5.3. MMS, WHAT FOR? 106
5.4. MODELS VERSUS PROGRAMS 108
6. AN OVERVIEW OF APPROACHES 115
6.1. SPREADSHEET 115
6.2. RELATIONAL DATABASE SYSTEMS 119
6.3. GRAPHICAL MODELING 126
6.4. CONSTRAINT LOGIC PROGRAMMING LANGUAGES (CLP) 131 6.5. ALGEBRAIC
LANGUAGES 139
6.5.1. AIMMS 140
6.5.2. AMPL 146
6.5.3. SUMMARY 148
6.6. GENERAL REMARKS 150
6.6.1. STRUCTURED MODELING 151
6.6.2. EMBEDDED LANGUAGE TECHNIQUE 152
6.6.3. MULTI-VIEW ARCHITECTURE 153
6.6.4. A MODEL CONSTRUCTION AND BROWSING TOOL 154
6.6.5. CONCLUSION 154
7. A MODELING FRAMEWORK 155
7.1. THE REQUIREMENTS C ATALOGUE 15 5
7.1.1. DECLARATIVE AND PROCEDURAL KNOWLEDGE 156
7.1.2. THE MODELING ENVIRONMENT 157
7.1.3. INFORMAL KNOWLEDGE 159
7.1.4. SUMMARY 159
7.2. THE MODELING LANGUAGE 161
7.2.1. THE ADOPTED APPROACH 162
7.2.2. THE OVERALL STRUCTURE OF THE MODELING LANGUAGE 167
7.2.3. ENTITIES AND ATTRIBUTES 172
7.2.4. INDEX-SETS 176
7.2.5. EXPRESSION 182
7.2.6. THE INSTRUCTION ENTITIES 1 84
IMAGE 4
IX
7.2.7. THE COMPLETE SYNTAX SPECIFICATION 185
7.2.8. SEMANTIC INTERPRETATION 187
7.2.8. SUMMARY 188
7.3. FOUR EXAMPLES 189
7.4. MODELING TOOLS 201
7.4.1. A TEXTUAL-BASED TOOL 202
7.4.2. A TOOL BASED ON GRAPHS 203
7.5. OUTLOOK 204
8. THE DEFINITION OF THE LANGUAGE 209
8.1.INTRODUCTION 209
8.2. AN OVERVIEW OF THE LPL-LANGUAGE 210
8.2.1. THE ENTITIES AND THE ATTRIBUTES 210
8.2.2. INDEX-SETS 212
8.2.3. DATA 213
8.2.4. EXPRESSIONS 219
8.2.5. LOGICAL MODELING 220
8.3. THE BACKUS-NAUR SPECIFICATION OF LPL 232
9. THE IMPLEMENTATION 235
9.1. THE KERNEL 235
9.2. THE ENVIRONMENT (USER INTERFACE) 236
9.3. THE TEXT BROWSER 238
9.4. THE GRAPHICAL BROWSER 243
10. SELECTED APPLICATIONS 249
10.1. GENERAL LP-, MIP-, AND QP-MODELS 249
10.2. GOAL PROGRAMMING 260
10.3. LP S WITH LOGICAL CONSTRAINTS 263
10.5. PROBLEMS WITH DISCONTINUOUS FUNCTIONS 2 81
10.6. MODELING UNCERTAINTY 284
11. CONCLUSION 289
REFERENCES 295
GLOSSARY 307
INDEX 311
|
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| indexdate | 2024-07-09T18:39:24Z |
| institution | BVB |
| isbn | 0792359275 |
| language | English |
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| physical | XXII, 313 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Kluwer Acad. Publ. |
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| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Hürlimann, Tony Verfasser aut Mathematical modeling and optimization an essay for the design of computer based modeling tools by Tony Hürlimann Dordrecht [u.a.] Kluwer Acad. Publ. 1999 XXII, 313 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 31 Datenverarbeitung Mathematisches Modell Computer simulation Mathematical models Data processing Mathematical optimization Konzeptionelle Modellierung (DE-588)4123555-1 gnd rswk-swf Konzeptionelle Modellierung (DE-588)4123555-1 s DE-604 Applied optimization 31 (DE-604)BV010841718 31 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008938615&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hürlimann, Tony Mathematical modeling and optimization an essay for the design of computer based modeling tools Applied optimization Datenverarbeitung Mathematisches Modell Computer simulation Mathematical models Data processing Mathematical optimization Konzeptionelle Modellierung (DE-588)4123555-1 gnd |
| subject_GND | (DE-588)4123555-1 |
| title | Mathematical modeling and optimization an essay for the design of computer based modeling tools |
| title_auth | Mathematical modeling and optimization an essay for the design of computer based modeling tools |
| title_exact_search | Mathematical modeling and optimization an essay for the design of computer based modeling tools |
| title_full | Mathematical modeling and optimization an essay for the design of computer based modeling tools by Tony Hürlimann |
| title_fullStr | Mathematical modeling and optimization an essay for the design of computer based modeling tools by Tony Hürlimann |
| title_full_unstemmed | Mathematical modeling and optimization an essay for the design of computer based modeling tools by Tony Hürlimann |
| title_short | Mathematical modeling and optimization |
| title_sort | mathematical modeling and optimization an essay for the design of computer based modeling tools |
| title_sub | an essay for the design of computer based modeling tools |
| topic | Datenverarbeitung Mathematisches Modell Computer simulation Mathematical models Data processing Mathematical optimization Konzeptionelle Modellierung (DE-588)4123555-1 gnd |
| topic_facet | Datenverarbeitung Mathematisches Modell Computer simulation Mathematical models Data processing Mathematical optimization Konzeptionelle Modellierung |
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