NDAK14003U Discrete Optimization (DO)
MSc Programme in Computer Science
Discrete Optimization is concerned with solving optimization
problems with discrete variables. Such variables may represent
indivisible commodities or yes/no decisions to buy, invest, hire,
build, etc. Discrete optimization problems arise in countless
scenarios, e.g., when developing time tables for airplanes, trains
or buses, in scheduling problems, in facility location problems and
in network design problems.
Many discrete optimization problems can be formulated as integer
linear programming (ILP) problems with integer variables, a linear
objective function and linear constraints. The advances of ILP have
been remarkable over the last 25 years. Many difficult practical
ILP problems can today be solved to near-optimality not because of
faster computers but because of new theoretical results.
The purpose of this course is to familarized participants with the
state-of-the-art ILP techniques. The course will cover such topics
as lower bound techniques (e.g., linear and Lagrangian relaxations)
and their importance in branch-and-bound algorithms. Cutting
planes, column generation and branch-and cut algorithms will also
be covered. Since linear programming (with continuous variables)
plays a key role in solving ILP problems, this topic will be
covered and the SIMPLEX algorithm will be explained in detail.
Not all ILP problems can be solved within reasonable time limits.
The course will therefore also cover approximation algorithms and
heuristic methods where the optimality requirement is abandoned but
where it is possible to either bound the deviation from the optimum
or where reasonable solutions can be produced very fast but without
any error guarantees.
Knowledge:
- Comprehensive knowledge of discrete optimization problems (linear and integer programming in particular).
- Familarity with algorithms and heuristics that can solve discrete optimization problems.
Skills:
- Formulation of (simple) real-life problems as (integer) linear programming problems.
- Selection of appropriate algorithms suitable to solve a particular discrete optimization problem.
- Application of software packages or self-implemented software to solve such problems.
Competences:
- Recognition of real-life problems solvable by methods introduced in this course.
- Identification of suitable algorithms to solve such problems.
- Design of new algorithms and heuristics for existing and new problems.
See Absalon
- Category
- Hours
- Exam
- 75
- Exercises
- 14
- Lectures
- 28
- Preparation
- 89
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment1. Students will have to write lecture notes on a selected topic covered in the course.
2. Students will have to implement and document two related assignments.
3. Students will have to take an oral examination, 30 min. without preparation. The examination will consist of two parts: questions related to the assignments mentioned in (2) and questions covering the syllabus of the course. (1) and (2) have to be handed in in order to participate in the oral examination.
The grade will be based on the overall evaluation of (1), (2) and (3). - Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
- Re-exam
Same as ordinary exam.
Resubmission of written parts (1) and (2) and an oral exam (30 min. without preparation).
The grade will be based on the overall evaluation of (1), (2) and (3).
Criteria for exam assesment
See Learning Outcome.
Course information
- Language
- English
- Course code
- NDAK14003U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- B
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Computer Science
Course Coordinators
- Pawel Winter (5-78697f6d74486c7136737d366c73)