William E. Hart Carl Laird Jean-Paul Watson David L. Woodruff. Pyomo Optimization. Modeling in Python. ^ Springer

Transcription

1 William E Hart Carl Laird Jean-Paul Watson David L Woodruff Pyomo Optimization Modeling in Python ^ Springer

2 Contents 1 Introduction 1 11 Mathematical Modeling 1 12 Modeling Languages for Optimization 3 13 Modeling Graph Coloring 4 14 Motivating Pyomo Open Source Customizable Capability Solver Integration Modern Programming Language 8 15 Getting Started 9 16 Book Summary Discussion 11 2 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 21 2A Examples 22 2A1 Concrete Pyomo Model with Explicit Variables 22 2A2 Concrete Pyomo Model with Indexed Variables 22 2A3 Concrete Pyomo Model with External Data 23 2A4 Concrete Pyomo Model with Constraint Rules 23 2A5 Concrete Pyomo Model with Abstract Component Declarations 24 2A6 Using a Function to Construct a Concrete Pyomo Model 25 2A 7 Abstract Pyomo Model 25 2A8 A Python Script that Optimizes a Concrete Pyomo Model 26 2A9 A Python Script that Optimizes an Abstract Pyomo Model 27 xiii

3 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 40 4 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 54 5 Miscellaneous Model Components and Utility Functions Miscellaneous Components Advanced Component Indexing Functions to Support Modeling Generalized Dot Products Generating Sequences Helper Functions Discussion 63 5A Examples 63 5A1 Error Checks in a Concrete Model 63 5A2 Error Checks in an Abstract Model 64 6 Initializing Abstract Models with Data Command Files Model Data The set Command Simple Sets 68

4 Contents xv 622 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 84 6A Examples 86 6A1 Namespace Data Commands 86 6 A2 The Diet Problem 87 7 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 A1 Model Object with Non-Default Name 102 7A2 Pyomo Data Commands with Multiple Namespaces Nonlinear Programming with Pyomo Introduction Building Nonlinear Programming Formulations NonHnear Expressions The Rosenbrock Example Solving Nonlinear Programming Formulations Nonlinear Solvers Tips for Nonlinear Programming Ill 84 Nonlinear Programming Examples Variable Initialization in Minimization ofmultimodal Function Optimal Quotas for Sustainable Harvesting of Deer Estimation of Parameters in Infectious Disease Models 844 Reactor Design 119

5 xvi Contents 8 A Examples 123 8A1 Rosenbrock 123 8A2 Multimodal 124 8A3 Deer Harvesting 124 8A4 Disease Estimation A5 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 A1 Farmer Model 159 9A2 Farmer Data File 162 9A3 Scenario Tree Model 163 9A4 Scenario Data Command File Scripting and Algorithm Development Introduction Scripting 1021 A Canonical Optimization Script 166 Basics Common Scripting Tasks Printing and Comparing Variable Values Looping 1033 Initializing and Fixing Over Variables 169 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 178

6 Contents xvii 106 Discussion A Examples A1 A Simple Optimization Script A2 A Simple Optimization Script with Multiple Data Files A3 A More Comprehensive Optimization Script A4 A Comprehensive Optimization Script that Mimics the pyomo Command A5 An Optimization Script with Multiple Models A6 An Optimization Script that Prints the Value of Variables 10A7 10A A Script that Performs Optimization from Two Starting Points 188 A Script that Performs Optimization from a Grid of Starting Points A9 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 A12 Plotting Solver Results with Matplotlib A13 A Sudoku Problem Solved by Iteratively Adding Cuts A 14 Hybrid Optimization for Parameter Estimation 202 A installing Coopr 205 A 1 Installation Overview 205 A2 Using an Installer 206 A3 Installing Coopr as a Site Package 207 A4 Installing a Coopr Release Using coopr_install 207 A5 Installing a Development Branch Using coopr_install 208 A 6 Discussion 209 B A Brief Python Tutorial 211 B l Overview 211 B2 Installing and Running Python 212 B3 Python Line Format 213 B4 Variables and Data Types 214 B5 Data Structures 216 B51 Strings 216 B52 Lists 216 B53 Tuples 217 B54 Sets 217 B55 Dictionaries 218 B6 Conditionals 218 B7 Iterations and Looping 219 B8 Generators and List Comprehensions 220 B9 Functions 221 B10 Objects and Classes 222

7 xviii Contents Bll Modules 222 B 12 Python Resources 223 C Pyomo and Coopr: The Bigger Picture 225 C 1 Coopr Overview 225 C-2 Optimization Solvers 226 References 229 Index 233