Postgraduate Course: Optimization under Uncertainty (MATH11247)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Optimization under uncertainty aims to find optimal decisions in problems which involve uncertain data. There are various frameworks for optimization under uncertainty such as stochastic programming, robust optimization, distributionally robust optimization, chance-constrained programming, and Markov decision processes, along with their data-driven variants. These fields develop rapidly with contributions from many disciplines including operations research, mathematics, probability, statistics and computer science, and have applications in a wide variety of domains such as energy, logistics, transportation, scheduling, healthcare, and finance. This course will make a broad overview of these main themes and delve into selected methodologies. Since the incorporation of uncertainty yields computationally challenging models, there will be a particular emphasis in the course on practical implementation and tools for solving such models efficiently. |
| Course description |
Optimization under uncertainty frameworks deal with classes of models and algorithms in which data is affected by uncertainty, i.e., some of the input data are not perfectly known at the time the decisions are made, a crucial aspect of real-world applications. The course will provide a general overview of a range of such frameworks and delve into the fundamental concepts and advanced methodologies of selected ones, including but not limited to stochastic programming and Markov decision processes. Key topics will include ways to model uncertainty (e.g., in the form of a probability distribution or uncertainty set) and incorporate it into decision-making (such as building two-stage stochastic programs for strategic problems and Markov decision process models for operational problems), and efficient solution methods for the presented model classes (such as decomposition algorithms and value function approximations). The course will also highlight more recent advances, e.g., data-driven model variants and algorithmic enhancements via the integration of machine learning. Applications 4 from various domains will be used as examples throughout the course. The course will provide a solid foundation in both the theoretical and practical aspects of optimization under uncertainty. Complementing the lectures, interactive workshops will deepen understanding by applying concepts to practical scenarios, reinforcing the link between theory and real-world applications. This will also help prepare students to competently apply optimization under uncertainty strategies in their future careers. The course's flexible design ensures it remains relevant amidst the evolving landscape of optimization and uncertainty,
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2024/25, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
64 )
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| Assessment (Further Info) |
Written Exam
50 %,
Coursework
50 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework : 50%
Examination : 50% |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Develop a deep understanding of the fundamentals of a couple of major frameworks for optimization under uncertainty, such as stochastic programming and Markov decision processes, and various solution methodologies.
- Become familiar with many practical applications of optimization under uncertainty.
- Develop insight and intuition on modelling important (structural) problems arising from practical applications using appropriate optimization under uncertainty tools.
- Know how to compare commonly used deterministic mathematical models with the ones incorporating uncertainty and be able to point out some deficiencies of the traditional models (i.e., justify the use of stochastic models).
- Develop and implement the algorithms to efficiently solve the presented stochastic models (e.g., decomposition algorithms).
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Reading List
Introduction to Stochastic Programming, Springer-Verlag, Birge and Louveaux, 2011.
Lectures on Stochastic Programming ¿ Modeling and Theory, SIAM, Shapiro, Dentcheva, and Ruszczynski, 2021.
Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, Puterman, Martin L., 2014.
Reinforcement Learning and Stochastic Optimization: A unified framework for sequential decisions, John Wiley & Sons, Powell, Warren B., 2022.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | OUU,Optimization |
Contacts
| Course organiser | Dr Merve Bodur
Tel:
Email: merve.bodur@ed.ac.uk |
Course secretary | Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk |
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