Duration
30h Th, 20h Pr, 25h Proj.
Number of credits
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Consider a salesman who must visit 20 potential customers in 20 different cities. A natural question he may ask is to know what is the optimal order in which he has to visit all cities so as to minimze the total distance. This famous problem is better known as the traveling salesman problem. It is the typical example of a discrete optimization problem. Indeed, there is a finite number of solutions (the 20! possible permutations of cities) and we may think of testing them all in order to find the optimal one. This approach is however impossible to perform in practice. Even if we were able to test a billion of these solutions per second, it would take us 77 years to test them all.
The traveling salesman problem is one of many discrete optimization problems. Indeed in particular the problems where binary decisions (such as yes or no) have to be taken often arise in practical applications.
Concerning the contents of the course, as a first part, we concentrate on modeling discrete problems as linear integer programs. We discuss some good principles in order to come up with a formulation. We also see what is needed in order to have a good formulation.
Then the last part of the course deals with the solving techniques of integer programs: mainly branch-and-bound, branch-and-cut, lagrangian relaxation, dynamic programming and approximation algorithms. We also consider some classes of important discrete problems that are well solved, namely flow and matching problems.
Learning outcomes of the learning unit
At the end of the course, the student
- will be able to formulate a real problem as an integer programming model
- will be able to compare two formulations of a problem
- will know the main methods to solve integer progamming problems
- will be able to recognize a tractable discrete optimization problem
This course contributes to the learning outcomes I.1, I.2, I.3, II.1, III.1, III.2, III.4, IV.1, IV.4, VI.1, VI.2, VI.3, VII.3, VII.4, VII.5 of the MSc in data science and engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, III.4, IV.1, VI.1, VI.2, VI.3, VII.3, VII.4, VII.5 of the MSc in electrical engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, III.1, III.2, III.4, IV.1, IV.3, VI.1, VI.2, VI.3, VII.3, VII.4, VII.5 of the MSc in computer science and engineering.
Prerequisite knowledge and skills
A basic course in linear programming.
Planned learning activities and teaching methods
Traditional tutorials are organized. An implementation project must be achieved.
Three modeling homeworks are asked during the semester.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Recommended or required readings
The main reference is
L. Wolsey, Integer Programming. Wiley, 1998.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Written work / report
Additional information:
The final exam is written and composed of theory and exercises.
The final grade is made of 2/3 of the exam grade and 1/3 of the three homeworks.
Work placement(s)
Organisational remarks and main changes to the course
The course is given in the second semester.
All documents related to the course are available on ecampus.