Mathematical Optimization with GAMS and Pyomo (Python)

Name: Mathematical Optimization with GAMS and Pyomo (Python)
Rating: 4.3 (241 reviews)

Learn how to mathematically formulate 16 business problems and find their optimal solutions with GAMS and Pyomo (Python)

Created byHossein Shahandeh, Sanjula Kammammettu

Last updated 3/2024

English

What you'll learn

Mathematical optimization
Linear programming
Integer programming
Nonlinear programming
Hands-on coding experience in GAMS
Hands-on coding experience in Pyomo (Python)

Course content

8 sections • 52 lectures • 8h 20m total length

Welcome message0:33
Course introduction7:50
Course curriculum overview4:42
Explore the course curriculum for mathematical optimization with GAMS and Pyomo in Python. Set up coding environment—from GAMS to Google Colab—and solve three examples per section with GAMS and Python.
Why GAMS and Pyomo?8:35

Example 1: introduction7:11
Learn to model and solve linear programming problems using GAMS and Pyomo with Python by formulating a two-ad campaign for Dorian Auto, minimizing cost under audience constraints.
Example 1: solution (GAMS)8:02
Example 1: solution (Pyomo)15:15
Example 2: introduction4:45
Minimize hires of full-time staff by modeling x_i as employees beginning on day i, enforcing five consecutive workdays and two days off, and meeting requirements with GAMS in Google Colab.
Example 2: solution (GAMS)7:20
Example 2: solution (Pyomo)9:51
Demonstrate solving the post office workers scheduling problem in Pyomo, defining x1 through x7, minimizing total workers, and applying daily constraints with GLPK, then enforce non-negativity.
Example 3: introduction3:40
Define sets i, c, and a to compress a mathematical optimization model; organize items, customers, and ads with theta_a, alpha_c, mu_a_c, and set a cost objective with viewership constraints.
Example 3: solution (GAMS)8:43
Example 3: solution (Pyomo)10:17
How to manage Pyomo code on Google Colab1:38
Learn to manage Pyomo code on Google Colab by saving notebooks to Drive or GitHub, uploading or renaming, and downloading as ipynb or py files for single or multiple models.
Section summary0:45
LP Assignment

Example 1: introduction6:21
Example 1: solution (GAMS)8:27
Example 1: solution (Pyomo)15:22
Example 1: importance of initial guess2:30
illustrate how initial guesses influence nlp solutions, contrasting linear and nonlinear models with coefficients a1, a2, b1, b2, b3, and note Gams sensitivity versus Pyomo robustness.
Example 2: introduction5:34
Example 2: solution (GAMS)6:54
Example 2: solution (Pyomo)10:00
Example 2: importance of solver2:40
Explore the importance of solvers for NLP problems, showing how IPOPT, SNOPT, and KNITRO can yield multiple locally optimal solutions and how results differ between GAMS and Pyomo.
Example 3: introduction5:43
Example 3: solution (GAMS)11:39
Example 3: solution (Pyomo)13:54
Section summary0:51
NLP Assignment

Example 1: introduction9:04
Learn to model and solve mixed-integer linear programs in GAMS and Pyomo, using big-M and either-or constraints across three examples: automobile manufacturing, power scheduling, and flowshop scheduling.
Example 1: solution (GAMS)15:03
Solve the Dorian auto manufacturing milp in GAMS by defining sets, x_a, y_a, phi, mu_a, alpha, sigma, gamma, and M, then maximize z using cplex.
Example 1 solution (Pyomo)19:11
Learn how to build and solve a mixed-integer linear problem in Pyomo on Google Colab, defining a ConcreteModel, sets, variables, big-M bounds, and GLPK-powered optimization, with result export.
Example 2: introduction6:40
Example 2: solution (GAMS)16:29
Example 2: solution (Pyomo)16:05
solve the second milp power scheduling problem with pyomo in google colab, building a concrete model, defining sets and variables, and solving with glpk.
Example 3: introduction6:04
Example 3: solution (GAMS)14:57
Example 3: solution (Pyomo)17:21
Example 3: visualization of an optimal schedule6:38
Section summary1:05
MILP Assignment

Example 1: introduction12:06
Formulate and solve mixed integer nonlinear programming problems in GAMS and Pyomo, illustrated by a power scheduling example with binary and continuous variables and a nonlinear fuel consumption curve.
Example 1: solution (GAMS)10:15
Example 1: solution (Pyomo)14:13
Example 2: introduction10:35
Example 2: solution (GAMS)13:54
Example 2: solution (Pyomo)13:46
Example 3: introduction17:58
Example 3: solution (GAMS)28:08
Example 3: solution (Pyomo)26:56
Section summary1:03
MINLP Assignment

Requirements

This course is designed for complete beginners to mathematical optimization. There are no coding prerequisites either, as we go through the functions and syntaxes in GAMS and Pyomo in detail. We instruct you on the download and demo license installation for GAMS. Pyomo is an open source package which we use Google Colaboratory to run. Therefore, all you need is a functional Google account, and you are ready to get started on this introductory journey to optimization!

Description

This introductory course to optimization in GAMS and Pyomo (Python) contains 4 modules, namely,

Linear programming
Nonlinear programming
Mixed Integer Linear Programming, and
Mixed-Integer Nonlinear Programming

In each module, we aim to teach you the basics of each type of optimization through 3 different illustrative examples and 1 assingment from different areas of science, engineering, and management. Using these examples, we aim to gently introduce you to coding in two environments commonly used for optimization, GAMS and Pyomo. GAMS is a licensed software, for which we use a demo license in this course. Pyomo is an open-source package in Python, which we use Google Colaboratory to run. As we proceed through the different examples in each module, we also introduce different functionalities in GAMS and Python, including data import and export.

At the end of this course, you will be able to,

Read a problem statement and build an optimization model
1. Be able to identify the objective function, decision variables, constraints, and parameters
Code an optimization model in GAMS
1. Define sets, variables, parameters, scalars, equations
2. Use different solvers in GAMS
3. Leverage the NEOS server for optimization
4. Import data from text, gdx, and spreadsheet files
5. Export data to text, gdx, and spreadsheet files
6. Impose different variable ranges, and bounds
Code an optimization model in Pyomo
1. Define models, sets, variables, parameters, constraints, and objective function
2. Use different solvers in Pyomo
3. Leverage the NEOS server for optimization
4. Import data from text, gdx, and spreadsheet files
5. Export data to text, gdx, and spreadsheet files
6. Impose different variable ranges, and bounds

Who this course is for:

We have designed this course to be accessible to students and professionals in various disciplines including, but not limited to, operations research, engineering, science, and management. Hence, we have chosen illustrative examples for each module within the course from different disciplines such as production scheduling, chemical and electrical engineering, geometry, etc. For each example, we will go through the problem statement in detail before proceeding to coding in GAMS and Python, so rest assured that you can follow through regardless of your field of learning and work.

Mathematical Optimization with GAMS and Pyomo (Python)

What you'll learn

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Course content

Course introduction4 lectures • 22min

Installation and setting up2 lectures • 8min

Introduction to mathematical optimization1 lecture • 14min

Introduction to linear programming (LP) using GAMS and Pyomo11 lectures • 1hr 17min

Introduction to nonlinear programming (NLP) using GAMS and Pyomo12 lectures • 1hr 30min

Introduction to mixed-integer linear programming (MILP) using GAMS and Pyomo11 lectures • 2hr 9min

Introduction to mixed-integer nonlinear programming (MINLP) using GAMS and Pyomo10 lectures • 2hr 29min

Wrap up1 lecture • 11min

Requirements

Description

Who this course is for: