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E-raamat: Modeling Languages in Mathematical Optimization

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  • Sari: Applied Optimization 88
  • Ilmumisaeg: 01-Dec-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461302155
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  • Formaat: PDF+DRM
  • Sari: Applied Optimization 88
  • Ilmumisaeg: 01-Dec-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461302155
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This book deals with the aspects of modeling and solving real-world optimiza- tion problems in a unique combination. It treats systematically the major mod- eling languages and modeling systems used to solve mathematical optimization problems. The book is an offspring ofthe 71 st Meeting of the GOR (Gesellschaft fill Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Op- timization during April 23-25, 2003 in the German Physics Society Confer- ence Building in Bad Honnef, Germany. The modeling language providers AIMMS Johannes Bisschop, Paragon Decision Technology B. V, Haarlem, The Netherlands, AMPL Bob Fourer, Northwestern Univ.; David M. Gay, AMPL Optimization LLC. , NJ, GAMS Alexander Meeraus, GAMS Development Corporation, Washington D. C. , Mosel Bob Daniel, Dash Optimization, Blisworth, UK, MPL Bjami Krist jansson, Maximal Software, Arlington, VA, NOP-2 Hermann Schichl, Vienna University, Austria, PCOMP Klaus Schittkowski, Bayreuth University, Germany, and OPL Sofiane Oussedik, ILOG Inc. , Paris, France gave deep insight into their motivations and conceptual design features of their software, highlighted their advantages but also critically discussed their limits. The participants benefited greatly from this symposium which gave a useful overview and orientation on today's modeling languages in optimization. Roughly speaking, a modeling language serves the need to pass data and a mathematical model description to a solver in the same way that people, es- Of course, in pecially mathematicians describe those problems to each other.
List of Figures
xiii
List of Tables
xv
Preface xvii
Contributing Authors xxiii
Introduction xxix
Josef Kallrath
Part I Theoretical and Practical Concepts of Modeling Languages
Mathematical Optimization and the Role of Modeling Languages
3(22)
Josef Kallrath
Mathematical Optimization
3(3)
Classes of Problems in Mathematical Optimization
6(11)
A Deterministic Standard MINLP Problem
7(2)
Constraint Satisfaction Problems
9(1)
Multi-Objective Optimization
9(1)
Multi-Level Optimization
10(1)
Semi-Infinite Programming
11(1)
Optimization Involving Differential Equations
12(1)
Safety Programming
12(1)
Optimization Under Uncertainty
13(1)
Approaches to Optimization Under Uncertainty
13(2)
Stochastic Optimization
15(1)
Beyond Stochastic Programming
16(1)
The History of Modeling Languages in Optimization
17(7)
Conventions and Abbreviations
24(1)
Models and the History of Modeling
25(12)
Hermann Schichl
The History of Modeling
25(3)
Models
28(1)
Mathematical Models
29(2)
The Modeling Process
31(6)
The Importance of Good Modeling Practice
32(3)
Making Mathematical Models Accessible for Computers
35(2)
Mathematical Model Building
37(8)
Arnold Neumaier
Why Mathematical Modeling?
37(1)
A List of Applications
38(1)
Basic numerical tasks
39(1)
The Modeling Diagram
40(1)
General Rules
41(1)
Conflicts
42(1)
Attitudes
43(2)
Theoretical Concepts and Design of Modeling Languages
45(18)
Hermann Schichl
Modeling Languages
45(11)
Algebraic Modeling Languages
46(5)
Non-algebraic Modeling Languages
51(3)
Integrated Modeling Environments
54(1)
Model-Programming Languages
55(1)
Other Modeling Tools
55(1)
Global Optimization
56(3)
Problem Description
57(1)
Algebraic Modeling Languages and Global Optimization
58(1)
A Vision --- What the Future Needs to Bring
59(4)
Data Handling
59(1)
Solver Views
60(1)
GUI
60(1)
Object Oriented Modeling --- Derived Models
61(1)
Hierarchical Modeling
61(1)
Building Blocks
62(1)
Open Model Exchange Format
62(1)
The Importance of Modeling Languages for Solving Real-World Problems
63(8)
Josef Kallrath
Josef Liesenfeld
Modeling Languages and Real World Problems
64(1)
Requirements from Practitioners towards Modeling Languages and Modeling Systems
65(6)
Part II The Modeling Languages in Detail
The Modeling Language AIMMS
71(34)
Johannes Bisschop
Marcel Roelofs
AIMMS Design Philosophy, Features and Benefits
72(6)
AIMMS Outer Approximation (AOA) Algorithm
78(6)
Problem Statement
79(1)
Basic Algorithm
79(2)
Open Solver Approach
81(2)
Alternative Uses of the Open Approach
83(1)
Units of Measurement
84(4)
Unit Analysis
86(1)
Unit-Based Scaling
87(1)
Unit Conventions
87(1)
Time-Based Modeling
88(5)
Calendars
90(1)
Horizons
90(2)
Data Conversion of Time-Dependent Identifiers
92(1)
The AIMMS Excel Interface
93(3)
Excel as the Main Application
94(1)
AIMMS as the Main Application
94(2)
Multi-Agent Support
96(5)
Basic Agent Concepts
96(1)
Examples of Motivation
97(2)
Agent-Related Concepts in AIMMS
99(2)
Agent Construction Support
101(1)
Future Developments
101(4)
Appendix
103(1)
AIMMS Features Overview
103(1)
Language Features
103(1)
Mathematical Programming Features
103(1)
End-User Interface Features
103(1)
Connectivity and Deployment Features
104(1)
Application Examples
104(1)
Design Principles and New Developments in the AMPL Modeling Language
105(32)
Robert Fourer
David M. Gay
Brian W. Kernighan
Background and Early History
106(1)
The McDonald's Diet Problem
107(4)
The Airline Fleet Assignment Problem
111(3)
Iterative Schemes
114(4)
Flow of Control
114(1)
Named Subproblems
115(3)
Debugging
118(1)
Other Types of Models
118(10)
Piecewise-Linear Terms
119(1)
Complementarity Problems
120(3)
Combinatorial Optimization
123(3)
Stochastic Programming
126(2)
Communicating with Other Systems
128(7)
Relational Database Access
128(1)
Internet Optimization Services
129(4)
Communication with Solvers via Suffixes
133(2)
Updated AMPL Book
135(1)
Concluding Remarks
135(2)
General Algebraic Modeling System (GAMS)
137(22)
Michael R. Bussieck
Alex Meeraus
Background and Motivation
138(1)
Design Goals and Changing Focus
139(2)
A User's View of Modeling Languages
141(8)
Academic Research Models
141(4)
Domain Expert Models
145(2)
Black Box Models
147(2)
Summary and Conclusion
149(10)
Appendix
150(1)
Selected Language Features
150(1)
GAMS External Functions
151(1)
Secure Work Files
151(1)
GAMS versus Fortran Matrix Generators
152(1)
Sample GAMS Problem
153(6)
The Lingo Algebraic Modeling Language
159(14)
Kevin Cunningham
Linus Schrage
History
159(1)
Design Philosophy
160(11)
Simplified Syntax for Small Models
160(2)
Close Coupled Solvers
162(1)
Interface to Excel
163(3)
Model Class Identification
166(1)
Automatic Linearization and Global Optimization
167(1)
Debugging Models
168(2)
Programming Interface
170(1)
Future Directions
171(2)
The LPL Modeling Language
173(12)
Tony Hurlimann
History
173(2)
Some Basic Ideas
175(1)
Highlights
176(2)
The Cutting Stock Problem
178(3)
Liquid Container
181(1)
Model Documentation
182(1)
Conclusion
183(2)
The Minopt Modeling Language
185(26)
Carl A. Schweiger
Christodoulos A. Floudas
Introduction
186(3)
Motivation
186(2)
Minopt Overview
188(1)
Model Types and Solution Algorithms
189(15)
Mixed-Integer Nonlinear Program (MINLP)
190(1)
Generalized Benders Decomposition (GBD)
190(2)
Outer Approximation/Equality Relaxation/Augmented Penalty (OA/ER/AP)
192(3)
Nonlinear Program with Differential and Algebraic Constraints (NLP/DAE)
195(2)
Mixed-Integer Nonlinear Program with Differential and Algebraic Constraints (MINLP/DAE)
197(3)
Optimal Control Problem (OCP) and Mixed Integer Optimal Control
200(4)
External Solvers
204(1)
Example Problems
204(5)
Language Overview
205(1)
MINLP Problem-Nonconvex Portfolio Optimization Problem
205(2)
Optimal Control Problem--Dow Batch Reactor
207(2)
Summary
209(2)
Mosel: A Modular Environment for Modeling and Solving Optimization Problems
211(28)
Yves Colombani
Bob Daniel
Susanne Heipcke
Introduction
211(2)
Solver Modules
212(1)
Other Modules
212(1)
User Modules
213(1)
Contents of this
Chapter
213(1)
The Mosel Language
213(7)
Example Problem
214(1)
Types and Data Structures
215(2)
Initialization of Data/Data File Access
217(1)
Language Constructs
218(1)
Selections
218(1)
Loops
219(1)
Set Operations
219(1)
Subroutines
220(1)
Mosel Libraries
220(2)
Mosel Modules
222(8)
Available Modules
223(1)
QP Example with Graphical Output
224(1)
Example of a Solution Algorithm
225(5)
Writing User Modules
230(8)
Defining a New Subroutine
231(2)
Creating a New Type
233(1)
Module Context
234(1)
Type Creation and Deletion
235(1)
Type Transformation to and from String
235(1)
Overloading of Arithmetic Operators
236(2)
Summary
238(1)
The MPL Modeling System
239(28)
Bjarni Kristjansson
Denise Lee
Maximal Software and Its History
239(2)
Algebraic Modeling Languages
241(4)
Comparison of Modeling Languages
242(1)
Modeling Language
243(1)
Multiple Platforms
243(1)
Open Design
243(1)
Indexing
244(1)
Scalability
244(1)
Memory Management
244(1)
Speed
245(1)
Robustness
245(1)
Deployment
245(1)
Pricing
245(1)
MPL Modeling System
245(5)
MPL Integrated Model Development Environment
246(1)
Solve the Model
247(1)
View the Solution Results
248(1)
Display Graph of the Matrix
249(1)
Change Option Settings
250(1)
MPL Modeling Language
250(12)
Sparse Index and Data Handling
251(1)
Scalability and Speed
252(1)
Structure of the MPL Model File
252(1)
Sample Model in MPL: A Production Planning Model
253(1)
Going Through the Model File
254(3)
Connecting to Databases
257(2)
Reading Data from Text Files
259(1)
Connecting to Excel Spreadsheets
259(1)
Optimization Solvers Supported by MPL
260(2)
Deployment into Applications
262(5)
Deployment Phase: Creating End-User Applications
263(1)
OptiMax 2000 Component Library Application Building Features
263(4)
The Optimization Systems MPSX and OSL
267(12)
Kurt Spielberg
Introduction
267(1)
MPSX from its Origins to the Present
268(11)
Initial Stages Leading to MPSX/370
268(2)
The Role of the IBM Scientific Centers
270(1)
An Important Product: Airline Crew Scheduling
271(1)
MPSX Management in White Plains and Transition to Paris
272(1)
A Major Growth Period in LP and MIP: MPSX/370; 1972-1985
272(1)
MPSX as an Engine in Research and Applications
273(1)
Case A: Algorithmic Tools for Solving Difficult Models
273(1)
Case B: New Solver Programs with ECL
274(1)
Case C: Application Packages -- Precursors to Modeling
275(1)
Business Cases for MPSX
276(1)
Changes in Computing, Development and Marketing Groups
277(1)
Transition to OSL
277(2)
The NOP-2 Modeling Language
279(14)
Hermann Schichl
Arnold Neumaier
Introduction
279(1)
Concepts
280(2)
Specialties of NOP-2
282(9)
Specifying Structure --- The Element Concept
283(3)
Data and Numbers
286(1)
Sets and Lists
287(1)
Matrices and Tensors
288(2)
Stochastic and Multistage Programming
290(1)
Recursive Modeling and Other Components
291(1)
Conclusion
291(2)
The OMNI Modeling System
293(14)
Larry Haverly
OMNI Features as they Developed Historically
293(6)
Early History
293(3)
Activities Versus Equations
296(1)
Recent and Current Trends
297(2)
Omni Features to Meet Applications Needs
299(1)
OMNI Example
300(5)
Omni Features
305(1)
Summary
306(1)
The OPL Studio Modeling System
307(44)
Pascal Van Hentenryck
Laurent Michel
Frederic Paulin
Jean-Francois Puget
Introduction
308(2)
Overview of OPL
310(1)
Overview of OPL Studio
311(2)
Mathematical Programming
313(1)
Frequency Allocation
314(5)
Sport Scheduling
319(3)
Job-Shop Scheduling
322(3)
Scene Allocation
325(6)
The Trolley Application
331(7)
Visualization
338(5)
Conclusion
343(8)
Appendix: Advanced Models
344(1)
A Round-Robin Model for Sport-Scheduling
344(3)
The Complete Trolley Model
347(4)
PCOMP: A Modeling Language for Nonlinear Programs with Automatic Differentiation
351(18)
Klaus Schittkowski
Introduction
351(2)
Automatic Differentiation
353(3)
The Pcomp Language
356(4)
Program Organization
360(1)
Case Study: Interactive Data Fitting with Easy-Fit
361(6)
Summary
367(2)
The Tomlab Optimization Environment
369(10)
Kenneth Holmstrom
Marcus M. Edvall
Introduction
369(1)
Matlab as a Modeling Language
370(1)
The Tomlab Development
371(1)
The Design of Tomlab
372(4)
Structure Input and Output
372(1)
Description of the Input Problem Structure
372(2)
Defining an Optimization Problem
374(1)
Solving Optimization Problems
375(1)
A Nonlinear Programming Example
376(3)
Part III The Future of Modeling Systems
The Future of Modeling Languages and Modeling Systems
379(4)
Josef Kallrath
References 383(20)
Index 403