Pyomo-optimization modeling in python / Michael L. Bynum [and seven others].

Format:

Book

Author/Creator:

Bynum, Michael L., author.

Series:

Springer optimization and its applications ; Volume 67.

Springer Optimization and Its Applications ; Volume 67

Language:

English

Subjects (All):

Computer simulation.

Mathematical optimization--Computer simulation.

Mathematical optimization.

Python (Computer program language).

Physical Description:

1 online resource (231 pages).

Edition:

3rd ed.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. In the third edition, much of the material has been reorganized, new examples have been added, and a new chapter has been added describing how modelers can improve the performance of their models. The authors have also modified their recommended method for importing Pyomo. A big change in this edition is the emphasis of concrete models, which provide fewer restrictions on the specification and use of Pyomo models. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.

Contents:

Intro

Preface

Goals of the Book

Who Should Read This Book

Revisions for the Third Edition

Acknowledgments

Disclaimers

Comments and Questions

Contents

Chapter 1 Introduction

1.1 Modeling Languages for Optimization

1.2 Modeling with Pyomo

1.2.1 Simple Examples

1.2.2 Graph Coloring Example

1.2.3 Key Pyomo Features

Python

Customizable Capability

Command-Line Tools and Scripting

Concrete and Abstract Model Definitions

Object-Oriented Design

Expressive Modeling Capability

Solver Integration

Open Source

1.3 Getting Started

1.4 Book Summary

1.5 Discussion

Part I An Introduction to Pyomo

Chapter 2 Mathematical Modeling and Optimization

2.1 Mathematical Modeling

2.1.1 Overview

2.1.2 A Modeling Example

2.2 Optimization

2.3 Modeling with Pyomo

2.3.1 A Concrete Formulation

2.4 Linear and Nonlinear Optimization Models

2.4.1 Definition

2.4.2 Linear Version

2.5 Solving the Pyomo Model

2.5.1 Solvers

2.5.2 Python Scripts

Chapter 3 Pyomo Overview

3.1 Introduction

3.2 The Warehouse Location Problem

3.3 Pyomo Models

3.3.1 Components for Variables, Objectives, and Constraints

3.3.2 Indexed Components

3.3.3 Construction Rules

3.3.4 A Concrete Model for the Warehouse Location Problem

3.3.5 Modeling Components for Sets and Parameters

Chapter 4 Pyomo Models and Components: An Introduction

4.1 An Object-Oriented AML

4.2 Common Component Paradigms

4.2.1 Indexed Components

4.3 Variables

4.3.1 Var Declarations

4.3.2 Working with Var Objects

4.4 Objectives

4.4.1 Objective Declarations

4.4.2 Working with Objective Objects

4.5 Constraints

4.5.1 Constraint Declarations

4.5.2 Working with Constraint Objects

4.6 Set Data

4.6.1 Set Declarations

4.6.2 Working with Set Objects.

4.7 Parameter Data

4.7.1 Param Declarations

4.7.2 Working with Param Objects

4.8 Named Expressions

4.8.1 Expression Declarations

4.8.2 Working with Expression Objects

4.9 Suffix Components

4.9.1 Suffix Declarations

4.9.2 Working with Suffixes

4.10 Other Modeling Components

Chapter 5 Scripting Custom Workflows

5.1 Introduction

5.2 Interrogating the Model

5.2.1 The The value Function

5.2.2 Accessing Attributes of Indexed Components

5.2.2.1 Slicing Over Indices of Components

5.2.2.2 Iterating Over All Var Objects on a Model

5.3 Modifying Pyomo Model Structure

5.4 Examples of Common Scripting Tasks

5.4.1 Warehouse Location Loop and Plotting

5.4.2 A Sudoku Solver

Chapter 6 Interacting with Solvers

6.1 Introduction

6.2 Using Solvers

6.3 Investigating the Solution

6.3.1 Solver Results

Part II Advanced Topics

Chapter 7 Nonlinear Programming with Pyomo

7.1 Introduction

7.2 Nonlinear Progamming Problems in Pyomo

7.2.1 Nonlinear Expressions

7.2.2 The Rosenbrock Problem

7.3 Solving Nonlinear Programming Formulations

7.3.1 Nonlinear Solvers

7.3.2 Additional Tips for Nonlinear Programming

Variable Initialization

Undefined Evaluations

Model Singularities and Problem Scaling

7.4 Nonlinear Programming Examples

7.4.1 Variable Initialization for a Multimodal Function

7.4.2 Optimal Quotas for Sustainable Harvesting of Deer

7.4.3 Estimation of Infectious Disease Models

7.4.4 Reactor Design

Chapter 8 Structured Modeling with Blocks

8.1 Introduction

8.2 Block structures

8.3 Blocks as Indexed Components

8.4 Construction Rules within Blocks

8.5 Extracting values from hierarchical models

8.6 Blocks Example: Optimal Multi-Period Lot-Sizing

8.6.1 A Formulation Without Blocks

8.6.2 A Formulation With Blocks.

Chapter 9 Performance: Model Construction and Solver Interfaces

9.1 Profiling to Identify Performance Bottlenecks

9.1.1 Report Timing

9.1.2 TicTocTimer

9.1.3 Profilers

9.2 Improving Model Construction Performance with LinearExpression

9.3 Repeated Solves with Persistent Solvers

9.3.1 When to Use a Persistent Solver

9.3.2 Basic Usage

9.3.3 Working with Indexed Variables and Constraints

9.3.4 Additional Performance

9.3.5 Example

9.4 Sparse Index Sets

Chapter 10 Abstract Models and Their Solution

10.1 Overview

10.1.1 Abstract and Concrete Models

10.1.2 An Abstract Formulation of Model (H)

10.1.3 An Abstract Model for the Warehouse Location Problem

10.2 The pyomo Command

10.2.1 The help Subcommand

10.2.2 The solve Subcommand

10.2.2.1 Specifying the Model Object

10.2.2.2 Selecting Data with Namespaces

10.2.2.3 Customizing Pyomo's Workflow

10.2.2.4 Customizing Solver Behavior

10.2.2.5 Analyze Solver Results

10.2.2.6 Managing Diagnostic Output

10.2.3 The convert Subcommand

10.3 Data Commands for Abstract Model

10.3.1 The set Command

10.3.1.1 Simple Sets

10.3.1.2 Sets of Tuple Data

10.3.1.3 Set Arrays

10.3.2 The param Command

10.3.2.1 One-dimensional Parameter Data

10.3.2.2 Multi-Dimensional Parameter Data

10.3.3 The include Command

10.3.4 Data Namespaces

10.4 Build Components

Part III Modeling Extensions

Chapter 11 Generalized Disjunctive Programming

11.1 Introduction

11.2 Modeling GDP in Pyomo

11.3 Expressing logical constraints

11.4 Solving GDP models

11.4.1 Big-M transformation

11.4.2 Hull transformation

11.5 A mixing problem with semi-continuous variables

Chapter 12 Differential Algebraic Equations

12.1 Introduction

12.2 Pyomo DAE Modeling Components

12.3 Solving Pyomo Models with DAEs.

12.3.1 Finite Difference Transformation

12.3.2 Collocation Transformation

12.4 Additional Features

12.4.1 Applying Multiple Discretizations

12.4.2 Restricting Control Input Profiles

12.4.3 Plotting

Chapter 13 Mathematical Programs with Equilibrium Constraints

13.1 Introduction

13.2 Modeling Equilibrium Conditions

13.2.1 Complementarity Conditions

13.2.2 Complementarity Expressions

13.2.3 Modeling Mixed-Complementarity Conditions

13.3 MPEC Transformations

13.3.1 Standard Form

13.3.2 Simple Nonlinear

13.3.3 Simple Disjunction

13.3.4 AMPL Solver Interface

13.4 Solver Interfaces and Meta-Solvers

13.4.1 Nonlinear Reformulations

13.4.2 Disjunctive Reformulations

13.4.3 PATH and the ASL Solver Interface

13.5 Discussion

Appendix A A Brief Python Tutorial

A.1 Overview

A.2 Installing and Running Python

A.3 Python Line Format

A.4 Variables and Data Types

A.5 Data Structures

A.5.1 Strings

A.5.2 Lists

A.5.3 Tuples

A.5.4 Sets

A.5.5 Dictionaries

A.6 Conditionals

A.7 Iterations and Looping

A.8 Generators and List Comprehensions

A.9 Functions

A.10 Objects and Classes

A.11 Assignment, copy and deepcopy

A.11.1 References

A.11.2 Copying

A.12 Modules

A.13 Python Resources

Bibliography

Index.

Notes:

Description based on print version record.

ISBN:

3-030-68928-X

OCLC:

1244620167