Duration
30h Th
Number of credits
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Module 1 - stochastic programming :
Basic introduction on uncertainty in the data, structure of a stochastic program (first-stage, second-stage, recourse), deterministic equivalent, risk-aversion, conditional value at risk, chance constraints, scenario generation and if time permits a few words about solution techniques.
Module 2- robust optimization :
Basic introduction of uncertainty sets, classic robust (worst-case) approach with either uncertainty set or Gamma-robustness, adjustable robust optimization (with recourse), distributionally robust.
Module 3 - multiobjective optimization :
Definition of the Pareto front, tradeoffs of the modeler, utopia points, Nadir points, using them for normalization, scalarization techniques.
Module 4 - bilevel programming :
The leader-follower principle, types of bilevel programming and their complexity (both theoretical and practical), KKT reformulation, cases in which the bilevel simplifies.
Learning outcomes of the learning unit
- Model optimization problems considering uncertainty or with two actors.
- Have a high insight on the efficiency of modeling techniques in terms of computational requirements.
- Analyze and interpret the results of an optimization model.
- Identify the modeling techniques that can be used for a specific problem.
Prerequisite knowledge and skills
A first course in linear and integer programming as well as basic notions of probabilities.
Planned learning activities and teaching methods
The course is composed of four modules: stochastic optimization, robust optimization, bilevel optimization, multiobjective optimization. Each module consists of 3 hours of theoretical courses and 6 hours of practical use cases where the student has to implement the model, use an off-the-shelve solver and discuss the different choices of modeling. The student will present their results at the end of each module.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Further information:
Face-to-face for courses and use cases.
Course materials and recommended or required readings
Platform(s) used for course materials:
- LOL@
Further information:
The slides of the theoretical course as well as data sets for the project are available on Lol@.
Exam(s) in session
Any session
- In-person
oral exam
Written work / report
Further information:
Two formative projects are organized during the semester, with mandatory participation on the defense dates which will be announced at the beginning of the year. These projects are mandatory to take part in the examination.
The evaluation is oral and consists of general questions on the course and on a personal project the students will work on throughout the semester. The project consists of integrating several modeling techniques in a same model, justifying the methodology used for the modeling techniques, and performing numerical experiments to present results of the model used with its strengths and weaknesses. Students will receive individual feedback during the semester.
Work placement(s)
Organisational remarks and main changes to the course
The course is given in English, with one block of three hours of course per week.
Contacts
Jérôme De Boeck : jerome.deboeck@uliege.be
Quentin Louveaux : q.louveaux@uliege.be