IE586-Syllabus-Spring23

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University of Houston *

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Industrial Engineering

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Oct 30, 2023

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IE 586: Computational Optimization – Spring 2023 • Instructor: Taghi Khaniyev, Office: EA-323, e-mail: taghi.khaniyev@bilkent.edu.tr • Teaching Assistant: Deniz Akkaya, e-mail: deniz.akkaya@bilkent.edu.tr • Class hours: Mondays 8:30-10:20 (EE-3) and Wednesdays 13:30-15:20 (EE-3) • Office hours: By appointment. • Course Description: The goal of this course is to develop efficient computational methods for large-scale discrete optimization problems. Large-scale optimization problems find applications in areas as diverse as telecommunication, production, facility location, healthcare, etc. With the advent of Big Data, our ability to realistically model real-life problems with mathematical programs have tremendously increased. But modeling a problem is one thing and actually solving is another. Most of the realistic large-scale optimization models originating from complex systems are hard to solve both theoretically and computationally. Although having increased their computational efficiency thousands-fold over the past few decades, commercial optimization software (such as Gurobi, CPLEX, XPRESS, SAS) are far from satisfying the demand from industry to solve problems with ever-increasing sizes. Research in various application settings has shown that the key to tackle problems with very large sizes is to effectively integrate relaxation, decomposition, and computational algorithms that can detect and exploit structural properties in the models and data. Such methods are superior to traditional heuristic solutions because they often yield provably near-optimal solutions or good approximation bounds. Throughout the course, you will be introduced to these methods in the context of well-known optimization problems motivated by interesting application domains. Besides covering the analytical intuition and steps to implement these techniques, we will have a strong emphasis on practically implementing the techniques on toy examples as well as realistic examples using programming languages and optimization software. • Course Objectives: The students are expected to achieve the following outcome from the course: – Understand the difficulties of solving large scale optimization models – Apply decomposition methods to solve large scale optimization models – Derive strong formulations for optimization problems – Study the recent computational techniques in the optimization field and contemplate potential applications to own research – Have hands-on experience of the software that can be used to implement different optimization approaches. • Prerequisites: There are no formal prerequisites for this course. However, students will be expected to have a ba- sic knowledge of mathematical programming and be comfortable with using the required software (Gurobi/CPLEX/SAS, Python/R). • Recommended Textbooks: We will not have a formal textbook in this course. The material will be extracted from a number of books and articles, that will be pointed out as the material is covered. Some references are: – Conforti M., Cornuejols G., and Zambelli G. Integer Programming, Springer, 2014. – Winston W.L. and Venkataramanan M. Introduction to mathematical programming, Duxbury Press, 2003. – Nemhauser G.L. and Wolsey L.A., Integer and Combinatorial Optimization, Wiley, 1999. – Martin R.K, Large Scale Linear & Integer Optimization: a Unified Approach, Kluwer Academic Publishers, 1999. – Wolsey L.A., Integer Programming, Wiley, 1998. • Assignments: There will be two assignments each including both analytical and coding parts. Assignments will be done individually. • Mini-lecture Presentation: Students will be asked to form groups of 2. Each group will be given a paper on a recent advance in the optimization field. Students will be expected to read the paper thoroughly, understand the methodology described in the paper, find other relevant papers on the topic, contemplate about its possible uses in their own research and prepare a 15-minute mini lecture to share with the class.

• Group Project: Students will be asked to form groups of 3 to work on a computational project. The goal of the project is to have a hands-on experience in designing and implementing the techniques studied in class using programming and optimization software. You will be given a specific problem and a preliminary data to work with. The project deliverables are (i) a code implementation, (ii) report, and (iii) demo+oral presentation. Details of the projects will be announced at the beginning of March. • Software: Students are encouraged to use Python and Gurobi/CPLEX throughout the course. However, for the full branch-and-price implementation that will be required for the project, students may use the SAS/DECOMP module available to academics. • Exams: There will be one in-class midterm and an in-class comprehensive final exam. The exact dates and places will be announced during the semester. • Make-up Policy: A make-up examination will only be given under highly unusual circumstances (such as serious health or family problems). The student should contact the instructor as early as possible and provide the instructor with proper documentation (such as a medical note certified by Bilkent University’s Health Center). • Grading Policy: Your overall score will be computed as follows: – Assignments: 20% – Paper Presentation: 10% – Group Project: 20% – Midterm Exam: 20% – Final Exam: 30% • FZ Policy: There is no FZ grade, everyone is entitled for the final exam. • Classes: In a typical week, all four reserved slots will be used, i.e., Monday 8:30-9:20 is a regular class hour (not a spare). In weeks where a class hour will be skipped, instructor will inform students in advance. • Tentative Course Content: – Introduction & Large-scale optimization examples – Revised simplex – Column generation – Dantzig-Wolfe decomposition – Lagrangian relaxation – Lagrangian decomposition – Bender’s decomposition – Two-stage stochastic programming – Robust optimization – Other topics: Valid inequalities, cutting planes, extended formulations – Other topics: heuristics – Recent advances in optimization (Mini lectures) • Communication: All of our communications will be conducted through the STARS system. Please check your e-mail regularly for announcements. • Cheating and plagiarism , which commonly takes the form of presenting somebody else’s work as your own, is not tolerated. You can consult with other students about your assignments or project, but you must submit your own work. Violations will be reported and disciplinary action will be taken. 2

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