Operations Research (2): Optimization Algorithms from Coursera

What's inside

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.

The Simplex Method

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.

The Branch-and-Bound Algorithm

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.

Gradient Descent and Newton’s Method

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.

Design and Evaluation of Heuristic Algorithms

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.

Course Summary and Future Learning Directions

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Teaches tools and techniques that are indispensable in business, management, economics, and technology

Provides a comprehensive overview of deterministic optimization techniques within operations research

Involves computer implementation of algorithms, providing practical experience

Involves real-world case studies, connecting theories to practical applications

Introduces essential optimization algorithms like the Simplex Method, Branch-and-Bound, and Gradient Descent

Covers nonlinear programming, extending the scope of optimization techniques

Reviews summary

Easy-to-understand, practical optimization algorithms course

Learners say this course provides clear and comprehensive coverage of optimization algorithms, with engaging assignments and helpful real-world examples. The lectures are easy to understand, even for beginners. Some learners have found the exams a bit vague and abstract, and the homework assignments could be improved with more detailed instructions. Overall, students appreciate the course's practical approach and find it helpful for preparing for exams and their careers.

Suitable for learners new to optimization algorithms.

"good for beginners!!"

"I like it a lot."

"very practical and omits details that are not required to understand the topic."

Straightforward explanations make concepts easy to grasp.

"Very clear explanations"

"The videos are very easy to understand"

"I like it a lot."

Emphasis on practical applications with real-world examples.

"It's a course that teaches you to solve the model you've built."

"Very clear explanations and great coverage from main points of view -- mathematical, technical and even business"

"I am learning a lot."

Homework assignments could use more detailed instructions.

"The course is good, but homework assignments could be made clear."

"For heuristics algorithms hints, it is better to hint the type of algorithm (greedy, brute-force, dynamic, etc) and let the students find their solutions"

Some exam questions could be more specific.

"Some questions in tests were a little vague, abstract."

"Last quiz was disproportionately difficult to the content of the course."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Operations Research (2): Optimization Algorithms with these activities:

OR Industry Meetup

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Networking with professionals in the field can provide insights into career opportunities and industry trends.

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Research and identify an industry meetup related to OR.
Prepare an elevator pitch and some questions to ask other attendees.
Attend the meetup and actively engage in conversations.

Linear Algebra Practice

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Reviewing key concepts from linear algebra helps you to build a strong foundation for operations research.

Browse courses on Linear Algebra

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Solve systems of linear equations using Gaussian elimination or Gauss-Jordan elimination.
Calculate nullspaces and column spaces of matrices
Determine if a set of vectors is linearly independent or dependent.

Introduction to Operations Research

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This book can offer a comprehensive overview of Operations Research, covering fundamental concepts and techniques that are essential for the course.

View ISE Introduction to Operations Research on Amazon

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Read the chapters on linear programming, integer programming, and nonlinear programming.
Solve the practice problems at the end of each chapter.

Three other activities

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Gradient Descent Tutorial

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This tutorial can provide a clear and structured approach to understanding the concepts behind gradient descent.

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Review the basics of derivatives and partial derivatives.
Learn how to calculate the gradient of a function.
Apply gradient descent to optimize a simple function.

Operations Research Workshop

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Attending a workshop can provide valuable hands-on experience and allow you to learn from experts in the field.

Browse courses on Operations Research

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Research and identify a relevant workshop.
Register for the workshop and prepare any necessary materials.
Attend the workshop and actively participate in discussions and exercises.

Develop a Simulation Model

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Building a simulation model allows you to test and evaluate different scenarios and gain insights into complex systems.

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Define the system or process to be simulated.
Collect and analyze relevant data.
Develop a simulation model using an appropriate software tool.
Run the simulation and analyze the results.

Career center

Learners who complete Operations Research (2): Optimization Algorithms will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts (QAs) create and apply mathematical and statistical models to solve problems for financial institutions and other companies. They use their knowledge of mathematics, statistics, and computer programming to analyze data, identify trends, and make predictions. The Operations Research (2): Optimization Algorithms course can help QAs build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for QAs who need to develop and implement optimization models that solve real-world problems facing companies.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts apply mathematical and analytical techniques to improve the efficiency and effectiveness of operations within organizations. They use their knowledge of mathematics, statistics, and computer programming to analyze data, identify problems, and develop solutions. The Operations Research (2): Optimization Algorithms course can help Operations Research Analysts build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Operations Research Analysts who need to develop and implement optimization models that solve real-world problems facing organizations.

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Management Consultant

Management Consultants help organizations improve their performance by providing advice on strategy, operations, and technology. They use their knowledge of business, mathematics, and computer programming to analyze data, identify problems, and develop solutions. The Operations Research (2): Optimization Algorithms course can help Management Consultants build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Management Consultants who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Management Consultant

Financial Analyst

Financial Analysts use their knowledge of mathematics, statistics, and computer programming to analyze financial data and make investment recommendations. They work in a variety of industries, including banking, investment management, and insurance. The Operations Research (2): Optimization Algorithms course can help Financial Analysts build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Financial Analysts who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Financial Analyst

Actuary

Actuaries use their knowledge of mathematics, statistics, and computer programming to assess and manage risk. They work in a variety of industries, including insurance, pension funds, and healthcare. The Operations Research (2): Optimization Algorithms course can help Actuaries build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Actuaries who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Actuary

Data Scientist

Data Scientists use their knowledge of mathematics, statistics, and computer programming to analyze data, identify trends, and make predictions. They work in a variety of industries, including finance, healthcare, and retail. The Operations Research (2): Optimization Algorithms course can help Data Scientists build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Data Scientists who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Data Scientist

Industrial Engineer

Industrial Engineers use their knowledge of mathematics, statistics, and computer programming to improve the efficiency and effectiveness of industrial processes. They work in a variety of industries, including manufacturing, transportation, and healthcare. The Operations Research (2): Optimization Algorithms course can help Industrial Engineers build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Industrial Engineers who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Industrial Engineer

Systems Analyst

Systems Analysts use their knowledge of mathematics, statistics, and computer programming to analyze and design computer systems. They work in a variety of industries, including technology, finance, and healthcare. The Operations Research (2): Optimization Algorithms course can help Systems Analysts build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Systems Analysts who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Systems Analyst

Business Analyst

Business Analysts use their knowledge of mathematics, statistics, and computer programming to analyze business processes and identify opportunities for improvement. They work in a variety of industries, including technology, finance, and healthcare. The Operations Research (2): Optimization Algorithms course can help Business Analysts build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Business Analysts who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Business Analyst

Software Engineer

Software Engineers use their knowledge of mathematics, statistics, and computer programming to design, develop, and implement software applications. They work in a variety of industries, including technology, finance, and healthcare. The Operations Research (2): Optimization Algorithms course can help Software Engineers build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Software Engineers who need to develop and implement optimization models that solve real-world problems facing organizations.

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Operations Manager

Operations Managers use their knowledge of mathematics, statistics, and computer programming to manage the operations of organizations. They work in a variety of industries, including manufacturing, transportation, and healthcare. The Operations Research (2): Optimization Algorithms course can help Operations Managers build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Operations Managers who need to develop and implement optimization models that solve real-world problems facing organizations.

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Statistician

Statisticians use their knowledge of mathematics, statistics, and computer programming to collect, analyze, and interpret data. They work in a variety of industries, including technology, finance, and healthcare. The Operations Research (2): Optimization Algorithms course can help Statisticians build a foundation in the mathematical and algorithmic techniques used to solve optimization problems. This course covers topics such as linear programming, integer programming, and nonlinear programming, which are all essential for Statisticians who need to develop and implement optimization models that solve real-world problems facing organizations.

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Economist

Economists use their knowledge of mathematics, statistics, and computer programming to analyze economic data and make predictions about the economy. They work in a variety of industries, including government, academia, and business. The Operations Research (2): Optimization Algorithms course may be helpful for Economists who need to develop and implement optimization models that solve real-world problems facing organizations.

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Financial Planner

Financial Planners use their knowledge of mathematics, statistics, and computer programming to help individuals and families plan for their financial future. They work in a variety of industries, including banking, investment management, and insurance. The Operations Research (2): Optimization Algorithms course may be helpful for Financial Planners who need to develop and implement optimization models that solve real-world problems facing organizations.

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Market Researcher

Market Researchers use their knowledge of mathematics, statistics, and computer programming to collect and analyze data about consumer behavior. They work in a variety of industries, including technology, finance, and healthcare. The Operations Research (2): Optimization Algorithms course may be helpful for Market Researchers who need to develop and implement optimization models that solve real-world problems facing organizations.

See salaries and explore the career path for Market Researcher