2018-2019 / MQGE0002-3

Computational Optimization


30h Th

Number of credits

 Master in data science (120 ECTS)5 crédits 
 Master in data science and engineering (120 ECTS)5 crédits 
 Master in business engineering (120 ECTS)5 crédits 
 Master in mathematics (120 ECTS)5 crédits 


Yves Crama

Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The aim of this course is to present various aspects of mathematical modeling and of problem-solving strategies as they are used in operations research for the solution of realistic, large-scale, complex problems.
The course contains several independent parts:
- General-purpose heuristic strategies for the solution of combinatorial optimization problems, such as simulated annealing, tabu search or genetic algorithms; the practical implementation of such methods is illustrated on a variety of optimization problems.
- Integer programming and network problems. Branch-and-bound method. Modeling and solution of large-scale models.

Learning outcomes of the learning unit

By the end of this course, the students will be able to model complex decision-making problems and to implement appropriate methods for their solution. They will better understand the opportunities offered by optimization methods, as well as their intrinsic limitations.
As a side-benefit, they will also develop advanced computer programming skills that are transferable to different business contexts.
Intended Learning Outcomes addressed by the course:

  • Establish a strategy in order to optimize the value chain of an organization, taking into account its scientific and technological context, and demonstrating a critical mind and scientific precision.
  • Take charge of the everyday management of a company, an organization or a project, taking into account its scientific, technological and entrepreneurial dimensions, ensuring a good interface between its technological and managerial aspects, and capitalizing on the characteristics of a digitalized world.
  • Plan and implement the performance and quality control in a company, an organization or a project, using the appropriate analytical tools.
  • Communicate efficiently in English, internally and externally, about a company, organization or project. 
  • Adapt his/her managerial practice to the needs of a fast-evolving world, showing curiosity, scientific precision, creativity, and autonomy.

Prerequisite knowledge and skills

- Mathematics: calculus and matrix algebra.
- Operations research: an introductory course covering linear programming models and methods.
- General proficiency with personal computers.
Command of a computer programming language (MathLab, SciLab, Pascal, C, Visual Basic,...) is an asset, but is not a strict prerequisite. An introduction to the language "Julia" will be provided, and the students are encouraged to use it for the development of their projects.

Planned learning activities and teaching methods

Group and individual projects: computer implementations, written reports and oral presentations.

Mode of delivery (face-to-face ; distance-learning)

Lectures and computer labs. Group and individual projects: computer implementations, reports and presentations. Attendance is mandatory.

Recommended or required readings

Lecture notes: Y. Crama, Computational Optimization, ULg, 2016.

Assessment methods and criteria

The final note will be based on:

  • the evaluation of group projects (written reports and oral presentations): 75% of the final note
  • individual assessment (homework and oral exam in May-June): 25%

Work placement(s)

Organizational remarks

This course is taught in English.
See the Lola Web site
for additional information.


Instructor: Prof. Y. Crama HEC Liège (Building N1)
Teaching assistant: Marie Baratto HEC Liège (Building N1) Room 334