Operations Research (2): Optimization Algorithms

Go to Course: https://www.coursera.org/learn/operations-research-algorithms

Introduction

**Course Review: Operations Research (2): Optimization Algorithms on Coursera** **Course Overview:** Operations Research (OR) is essential for anyone looking to efficiently solve complex optimization problems in various fields, such as business, engineering, and computer science. The course "Operations Research (2): Optimization Algorithms" on Coursera offers a deep dive into deterministic optimization techniques, providing students with key algorithms necessary for solving linear programs, integer programs, and nonlinear problems. This course serves as the second part of a comprehensive series on Operations Research, and it builds on fundamental concepts that are vital for understanding advanced optimization techniques. The curriculum is structured to not only impart theoretical knowledge but also practical applications of the concepts learned. **Syllabus Breakdown:** 1. **Course Introduction and Linear Algebra Review:** The first lecture sets the stage by reviewing essential concepts in linear algebra, preparing students for the mathematical rigor required in the course. Understanding Gaussian elimination is critical, as it serves as the foundation for many optimization techniques. 2. **The Simplex Method:** This section introduces one of the most important methods in linear programming, the Simplex Method, developed by Dr. George Dantzig. The course does an excellent job breaking down complex concepts into manageable lessons, including discussions on the standard form of linear programs and the implications of unbounded and infeasible solutions. 3. **The Branch-and-Bound Algorithm:** Transitioning to integer programming, students learn about the Branch-and-Bound algorithm, including the concept of linear relaxation. This segment highlights the nuances of integer variables and offers insights into real-world applications of these methods. 4. **Gradient Descent and Newton’s Method:** This section shifts focus to nonlinear programming, where students explore optimization methods that are applicable to more complex problems. The course provides a clear comparison between gradient descent and Newton’s method, equipping learners with the tools to choose the appropriate algorithm for their specific needs. 5. **Design and Evaluation of Heuristic Algorithms:** In a hands-on approach, students dive into a case study involving NEC Taiwan, tackling a practical facility location problem. This real-world application emphasizes the importance of heuristic algorithms and showcases how optimization can lead to significant cost savings. 6. **Course Summary and Future Learning Directions:** The course concludes with a comprehensive review of the key topics covered and introduces students to advanced courses for continuing their education in Operations Research. This forward-thinking approach ensures that learners can strategize their next steps for personal and professional development. **Why You Should Take This Course:** "Operations Research (2): Optimization Algorithms" is an invaluable resource for professionals and students aiming to enhance their problem-solving skills in practical situations. The blend of theory and case studies fosters a deep understanding of optimization methods, making it applicable across various industries. The clear structure of the syllabus allows learners to progress logically, building on previous knowledge without feeling overwhelmed. Furthermore, the course is suitable for both beginners and those with prior experience in OR, as it progresses from fundamental concepts to advanced techniques. The industry's reliance on data-driven decision-making means that skills learned in this course will remain relevant and in demand. The knowledge gained will empower you to approach optimization challenges with confidence and creativity. In conclusion, whether you’re pursuing a career in business, engineering, or data science, taking the Operations Research (2): Optimization Algorithms course on Coursera is a step towards mastering essential optimization techniques that can significantly enhance your professional capabilities. Sign up and take your first step towards becoming an operations research expert today!

Syllabus

Course Overview

In the first lecture, we briefly introduce the course and give a quick review about some basic knowledge of linear algebra, including Gaussian elimination, Gauss-Jordan elimination, and definition of linear independence.

Complicated linear programs were difficult to solve until Dr. George Dantzig developed the simplex method. In this week, we first introduce the standard form and the basic solutions of a linear program. With the above ideas, we focus on the simplex method and study how it efficiently solves a linear program. Finally, we discuss some properties of unbounded and infeasible problems, which can help us identify whether a problem has optimal solution.

Integer programming is a special case of linear programming, with some of the variables must only take integer values. In this week, we introduce the concept of linear relaxation and the Branch-and-Bound algorithm for solving integer programs.

In the past two weeks, we discuss the algorithms of solving linear and integer programs, while now we focus on nonlinear programs. In this week, we first review some necessary knowledge such as gradients and Hessians. Second, we introduce gradient descent and Newton’s method to solve nonlinear programs. We also compare these two methods in the end of the lesson.

As the last lesson of this course, we introduce a case of NEC Taiwan, which provides IT and network solutions including cloud computing, AI, IoT etc. Since maintaining all its service hubs is too costly, they plan to rearrange the locations of the hubs and reallocate the number of employees in each hub. An algorithm is included to solve the facility location problem faced by NEC Taiwan.

In the final week, we review the topics that we have learned and give students a summary. Besides, we briefly preview the advanced course to provide future direction of studying.