Μάθημα : Optimization Techniques

Dear all,

The final exam material includes Lecture slides 1-9 from the E-Class for the Full Course, and the sets 1-6 for the Half Course.

Note that in 9 you should mainly focus on the simple Benders Decomposition approach (not Logic Based Benders) and the Constraint programming c(see up to slide 81 in Lecture 9). 

Note also that you will need be examined in the RL part (Lecture slides 10) - as this will be done through the assigned project.  

For more details and examples for the material within the Lecture slides you can study the following:

a) Simplex algorithm, Chapters 4-5 of Hillier & Lieberman, “Introduction to Operations Research”,

b) LP Duality Theory, Chapter 6 of Hillier & Lieberman, “Introduction to Operations Research”,

c) Convex sets and functions, Chapters 2-3 of Boyd & Vandenberghe “Convex Optimization”,

d) Descent methods, Chapter 9 of Boyd & Vandenberghe “Convex Optimization”

e) Lagrange duality, Chapter 5 Boyd & Vandenberghe “Convex Optimization”.

f) Interior point methods: Sections 11.1-11.3, Boyd & Vandenberghe, and  Lecture notes from the course on Machine Learning by Ryan Tibshirani: https://www.stat.cmu.edu/~ryantibs/convexopt/lectures/barr-method.pdf

g) Integer programming Chapter 11, Hillier & Lieberman, “Introduction to Operations Research”, 

h) Branch and Bound, Section 11.6, Hillier & Lieberman, “Introduction to Operations Research”.

i) Benders’ decomposition, in Hooker, J.N. (2019). Logic-Based Benders Decomposition for Large-Scale Optimization. In: Velásquez-Bermúdez, J., Khakifirooz, M., Fathi, M. (eds) Large Scale Optimization in Supply Chains and Smart Manufacturing. Springer Optimization and Its Applications, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-030-22788-3_1 (access with VPN from AUEB)

j) Contstraint programming,  Rossi, F., Van Beek, P. and Walsh, T. eds., 2006. “Handbook of constraint programming, Elsevier”

On Monday 16/06, after presenting an application of RL to job shop scheduling, we are going to discuss the solutions of your homework assignment and will answer any questions you may have about the exam material.

Concerning the examination process:

- Please be there at 18:10 so we can start as soon as possible. 

- You may bring with you one A4 sheet on which you can write anything you want, on both sides. The sheet can be handwritten. There are no restrictions on what you can write on it. For example, you can write down an algorithm that you find hard to remember. However, don't overdo it—don't spend too much time preparing the A4 sheet.

Concerning your project submission you can submit it until Friday, July 10.

Best Regards,

G.