Modeling Languages in Mathematical Optimization (Hardcover)

I Theoretical and Practical Concepts of Modeling Languages.- 1 Mathematical Optimization and the Role of Modeling Languages.- 1.1 Mathematical Optimization.- 1.2 Classes of Problems in Mathematical Optimization.- 1.2.1 A Deterministic Standard MINLP Problem.- 1.2.2 Constraint Satisfaction Problems.- 1.2.3 Multi-Objective Optimization.- 1.2.4 Multi-Level Optimization.- 1.2.5 Semi-Infinite Programming.- 1.2.6 Optimization Involving Differential Equations.- 1.2.7 Safety Programming.- 1.2.8 Optimization Under Uncertainty.- 1.2.8.1 Approaches to Optimization Under Uncertainty.- 1.2.8.2 Stochastic Optimization.- 1.2.8.3 Beyond Stochastic Programming.- 1.3 The History of Modeling Languages in Optimization.- 1.4 Conventions and Abbreviations.- 2 Models and the History of Modeling.- 2.1 The History of Modeling.- 2.2 Models.- 2.3 Mathematical Models.- 2.4 The Modeling Process.- 2.4.1 The Importance of Good Modeling Practice.- 2.4.2 Making Mathematical Models Accessible for Computers.- 3 Mathematical Model Building.- 3.1 Why Mathematical Modeling?.- 3.2 A List of Applications.- 3.3 Basic numerical tasks.- 3.4 The Modeling Diagram.- 3.5 General Rules.- 3.6 Conflicts.- 3.7 Attitudes.- 4 Theoretical Concepts and Design of Modeling Languages.- 4.1 Modeling Languages.- 4.1.1 Algebraic Modeling Languages.- 4.1.2 Non-algebraic Modeling Languages.- 4.1.3 Integrated Modeling Environments.- 4.1.4 Model-Programming Languages.- 4.1.5 Other Modeling Tools.- 4.2 Global Optimization.- 4.2.1 Problem Description.- 4.2.2 Algebraic Modeling Languages and Global Optimization.- 4.3 A Vision - What the Future Needs to Bring.- 4.3.1 Data Handling.- 4.3.2 Solver Views.- 4.3.3 GUI.- 4.3.4 Object Oriented Modeling - Derived Models.- 4.3.5 Hierarchical Modeling.- 4.3.6 Building Blocks.- 4.3.7 Open Model Exchange Format.- 5 The Importance of Modeling Languages for Solving Real-World Problems.- 5.1 Modeling Languages and Real World Problems.- 5.2 Requirements from Practitioners towards Modeling Languages and Modeling Systems.- II The Modeling Languages in Detail.- 6 The Modeling Language AIMMS.- 6.1 AIMMS Design Philosophy, Features and Benefits.- 6.2 AIMMS Outer Approximation (AOA) Algorithm.- 6.2.1 Problem Statement.- 6.2.2 Basic Algorithm.- 6.2.3 Open Solver Approach.- 6.2.4 Alternative Uses of the Open Approach.- 6.3 Units of Measurement.- 6.3.1 Unit Analysis.- 6.3.2 Unit-Based Scaling.- 6.3.3 Unit Conventions.- 6.4 Time-Based Modeling.- 6.4.1 Calendars.- 6.4.2 Horizons.- 6.4.3 Data Conversion of Time-Dependent Identifiers.- 6.5 The AIMMS Excel Interface.- 6.5.1 Excel as the Main Application.- 6.5.2 AIMMS as the Main Application.- 6.6 Multi-Agent Support.- 6.6.1 Basic Agent Concepts.- 6.6.2 Examples of Motivation.- 6.6.3 Agent-Related Concepts in AIMMS.- 6.6.4 Agent Construction Support.- 6.7 Future Developments.- A AIMMS Features Overview.- A.1 Language Features.- A.2 Mathematical Programming Features.- A.3 End-User Interface Features.- A.4 Connectivity and Deployment Features.- B Application Examples.- 7 Design Principles and New Developments in the AMPL Modeling Language.- 7.1 Background and Early History.- 7.2 The McDonald's Diet Problem.- 7.3 The Airline Fleet Assignment Problem.- 7.4 Iterative Schemes.- 7.4.1 Flow of Control.- 7.4.2 Named Subproblems.- 7.4.3 Debugging.- 7.5 Other Types of Models.- 7.5.1 Piecewise-Linear Terms.- 7.5.2 Complementarity Problems.- 7.5.3 Combinatorial Optimization.- 7.5.4 Stochastic Programming.- 7.6 Communicating with Other Systems.- 7.6.1 Relational Database Access.- 7.6.2 Internet Optimization Services.- 7.6.3 Communication with Solvers via Suffixes.- 7.7 Updated AMPL Book.- 7.8 Concluding Remarks.- 8 General Algebraic Modeling System (GAMS).- 8.1 Background and Motivation.- 8.2 Design Goals and Changing Focus.- 8.3 A User's View of Modeling Languages.- 8.3.1 Academic Research Models.- 8.3.2 Domain Expert Models.- 8.3.3 Black Box Models.- 8.4 Summary and Conclusion.- A Selected Language Features.- B GAMS External Functio