Basic Modeling for Discrete Optimization

Go to Course: https://www.coursera.org/learn/basic-modeling

Introduction

### Course Review: Basic Modeling for Discrete Optimization on Coursera In an increasingly complex world where decision-making plays a critical role in the success of businesses and everyday life, the course on **Basic Modeling for Discrete Optimization** offered on Coursera comes as a timely resource for those looking to enhance their problem-solving and modeling skills. Whether you’re a student, a professional seeking career advancement, or simply interested in optimization techniques, this course is designed to equip you with the foundational knowledge and practical skills necessary to tackle a variety of discrete optimization problems. #### Course Overview The overarching theme of the course revolves around the power of optimization in decision-making. From simple tasks like solving Sudoku puzzles to complex industrial applications, the principles of optimization govern many processes in our society. Understanding this field can lead to more effective management of resources, optimizing nobody will able to provide crucial decisions that could potentially save millions of dollars in corporate settings. **Basic Modeling for Discrete Optimization** focuses on using MiniZinc, a high-level modeling language, to formulate and solve various optimization problems. This course is particularly valuable because it touches on a diverse range of applications, including scheduling, production planning, and transportation logistics. ### Syllabus Breakdown 1. **MiniZinc Introduction** The course kicks off with an introduction to MiniZinc, laying the groundwork for learners. The material is well-structured and presents a clear path toward mastering this powerful tool for discrete optimization. Participants will grasp how to solve diverse problems, from knapsack challenges to graph coloring, and even delve into Cryptarithm puzzles. The focus on open-source solving technologies also empowers students to implement their learning in real-world scenarios without heavy reliance on commercial software. 2. **Modeling with Sets** The second module dives into set selection problems, crucial for many practical applications. Key concepts such as cardinality (fixed, bounded, and unbounded) are explored, along with the necessary steps to validate model decisions. This module is particularly beneficial as it emphasizes not just theoretical understanding but also practical implementation, ensuring that learners can articulate valid decision-making processes. 3. **Modeling with Functions** As learners progress to the third module, they are introduced to modeling pure assignment and partition problems; this exploration allows them to understand the practical applications of these concepts in rostering and constrained clustering. The discussion around common subexpression elimination and the global cardinality constraint introduces learners to advanced modeling techniques, making this content ideal for those serious about deepening their programming and optimization skill set. 4. **Multiple Modeling** The final module of the course opens the door to advanced thinking in discrete optimization. By demonstrating how problems can be approached from multiple viewpoints, the course cultivates a more holistic understanding among its participants. This segment is crucial for learners to appreciate the versatility required in optimization modeling, as well as how combining different models can create synergistic advantages. ### Recommendations The **Basic Modeling for Discrete Optimization** course is highly recommended for individuals looking to build or enhance their skills in optimization. Here are a few reasons to enroll: - **Practical Applications:** The course covers a wide range of real-world applications, making it useful for professionals in many fields, including logistics, production, and project management. - **Hands-On Learning:** The use of MiniZinc allows students to translate theory into practice effectively. The course's hands-on approach to problem-solving solidifies understanding and builds confidence. - **Flexible Access:** Being on Coursera, the course allows learners to study at their own pace, making it suitable for busy professionals or students balancing various commitments. ### Conclusion In conclusion, the **Basic Modeling for Discrete Optimization** course on Coursera is a valuable addition to the curriculum of anyone interested in decision-making and optimization. With engaging content, practical applications, and a robust framework for understanding discrete optimization through MiniZinc, this course promises to enhance both your skills and your career opportunities. Whether you're starting your journey in optimization or looking to reinforce your existing knowledge, this course provides a comprehensive foundation that is hard to beat. Enroll today and unlock the power of effective decision-making!

Syllabus

MiniZinc introduction

In this first module, you will learn the basics of MiniZinc, a high-level modeling language for discrete optimization problems. Combining the simplicity of MiniZinc with the power of open-source industrial solving technologies, you will learn how to solve applications such as knapsack problems, graph coloring, production planning and tricky Cryptarithm puzzles, with great ease.

In this module, you will learn how to model problems involving set selection. In particular, you will see different ways of representing set variables when the variable has no constraints on its cardinality, has fixed cardinality and bounded cardinality. You also have to ensure all model decisions are valid decisions, and each valid decision corresponds to exactly one model decision.

In this module, you will learn how to model pure assignment problems and partition problems, which are functions in disguise. These problems find applications in rostering and constrained clustering. In terms of modeling techniques, you will see the power of common subexpression elimination and intermediate variables, and encounter the global cardinality constraint for the first time. MiniZinc also provides constraints for removing value symmetries.

In the final module of this course you will see how discrete optimization problems can often be seen from multiple viewpoints, and modeled completely differently from each viewpoint. Each viewpoint may have strengths and weaknesses, and indeed the different models can be combined to help each other.