6 Initializing Abstract Models with Data Command Files Model Data The set Command Simple Sets... 68

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1 Contents 1 Introduction Mathematical Modeling Modeling Languages for Optimization Modeling Graph Coloring Motivating Pyomo Open Source Customizable Capability Solver Integration Modern Programming Language Getting Started Book Summary Discussion Pyomo Modeling Strategies Modeling Components Concrete Models: Specifying Components Via Expressions Concrete Models: Specifying Components Via Rules Abstract Models Optimizing Models Optimization with the pyomo Command Optimization Scripts Discussion A Examples A.1 Concrete Pyomo Model with Explicit Variables A.2 Concrete Pyomo Model with Indexed Variables A.3 Concrete Pyomo Model with External Data A.4 Concrete Pyomo Model with Constraint Rules A.5 Concrete Pyomo Model with Abstract Component Declarations A.6 Using a Function to Construct a Concrete Pyomo Model A.7 Abstract Pyomo Model A.8 A Python Script that Optimizes a Concrete Pyomo Model 26 2.A.9 A Python Script that Optimizes an Abstract Pyomo Model 27 xiii

2 xiv Contents 3 Model Components: Variables, Objectives, and Constraints Modeling with Components Variables Var Declarations Variable Initialization Working with Variables Objectives Simple Declarations Declarations with Rule Functions Constraints Declarations with Logical Expressions Declarations with Expression Tuples Constraint Lists Discussion Model Components: Sets and Parameters Set Data Set Declarations Set Initialization Set Data Validation Set Options RangeSet Discussion of Index Sets Parameter Data Param Declarations Parameter Initialization Data Validation Discussion Miscellaneous Model Components and Utility Functions Miscellaneous Components Advanced Component Indexing Functions to Support Modeling Generalized Dot Products Generating Sequences Helper Functions Discussion A Examples A.1 Error Checks in a Concrete Model A.2 Error Checks in an Abstract Model Initializing Abstract Models with Data Command Files Model Data The set Command Simple Sets

3 Contents xv Sets of Tuple Data Set Arrays The param Command One-dimensional Parameter Data Multi-Dimensional Parameter Data The import Command Simple Import Examples Import Syntax Options Interpreting Relational Tables Importing from Spreadsheets and Relational Databases The include Command Data Namespaces Discussion A Examples A.1 Namespace Data Commands A.2 The Diet Problem The Pyomo Command-line Interface Overview Building a Model Instance Specifying the Model Object Selecting Data with Namespaces Customizing Pyomo s Workflow Customizing Solver Behavior Analyze Solver Results Managing Diagnostic Output Discussion A Examples A.1 Model Object with Non-Default Name A.2 Pyomo Data Commands with Multiple Namespaces Nonlinear Programming with Pyomo Introduction Building Nonlinear Programming Formulations Nonlinear Expressions The Rosenbrock Example Solving Nonlinear Programming Formulations Nonlinear Solvers Tips for Nonlinear Programming Nonlinear Programming Examples Variable Initialization in Minimization of Multimodal Function Optimal Quotas for Sustainable Harvesting of Deer Estimation of Parameters in Infectious Disease Models Reactor Design

4 xvi Contents 8.A Examples A.1 Rosenbrock A.2 Multimodal A.3 Deer Harvesting A.4 Disease Estimation A.5 Reactor Design Stochastic Programming Extensions Introduction Stochastic Programming: Definition and Notations Modeling in PySP The Deterministic Reference Model The Scenario Tree Scenario Parameter Specification Compilation of the Scenario Tree Model Generating and Solving the Extensive Form Progressive Hedging: A Generic Decomposition Strategy The runph Script Progressive Hedging Extensions: Advanced Configuration Watson and Woodruff Extensions Solving a Constrained Extensive Form Alternative Convergence Criteria User-Defined Extensions Solving PH Scenario Sub-Problems in Parallel Discussion A Examples A.1 Farmer Model A.2 Farmer Data File A.3 Scenario Tree Model A.4 Scenario Data Command File Scripting and Algorithm Development Introduction Scripting Basics A Canonical Optimization Script Common Scripting Tasks Printing and Comparing Variable Values Looping Over Variables Initializing and Fixing Variables Adding and Dropping Constraints Sharing Solution Results Across Multiple Models Plotting Data with Matplotlib Generating Different Models with a Function Hybrid Optimization Benders Decomposition

5 Contents xvii 10.6 Discussion A Examples A.1 A Simple Optimization Script A.2 A Simple Optimization Script with Multiple Data Files A.3 A More Comprehensive Optimization Script A.4 A Comprehensive Optimization Script that Mimics the pyomo Command A.5 An Optimization Script with Multiple Models A.6 An Optimization Script that Prints the Value of Variables A.7 A Script that Performs Optimization from Two Starting Points A.8 A Script that Performs Optimization from a Grid of Starting Points A.9 A Script that Reoptimizes a Model after Fixing Variables A.10 An Iterative Optimization Process that Explicitly Activates Select Constraints A.11 Sharing Results Between Models A.12 Plotting Solver Results with Matplotlib A.13 A Sudoku Problem Solved by Iteratively Adding Cuts A.14 Hybrid Optimization for Parameter Estimation A Installing Coopr 205 A.1 Installation Overview A.2 Using an Installer A.3 Installing Coopr as a Site Package A.4 Installing a Coopr Release Using coopr install A.5 Installing a Development Branch Using coopr install A.6 Discussion B A Brief Python Tutorial 211 B.1 Overview B.2 Installing and Running Python B.3 Python Line Format B.4 Variables and Data Types B.5 Data Structures B.5.1 Strings B.5.2 Lists B.5.3 Tuples B.5.4 Sets B.5.5 Dictionaries B.6 Conditionals B.7 Iterations and Looping B.8 Generators and List Comprehensions B.9 Functions B.10 Objects and Classes

6 xviii Contents B.11 Modules B.12 Python Resources C Pyomo and Coopr: The Bigger Picture 225 C.1 Coopr Overview C.2 Optimization Solvers References 229 Index 233

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