TAOP33 · 4 credits · Basic level (G2F) · Matematik, Tillämpad matematik
Combinatorial Optimization, Introductory Course
Active · next start HT 2026
69%
passed the latest ordinary exam
TEN2 · 24 Oct 2025 · 93 students
79%
passed the ordinary exams, all sittings over the last 5 years
TEN2 · 463 students
57%
Harder than 57% of courses at basic level
Compared with 874 courses at the same level, ordinary exams over the last three academic years. 187 students.
Part of 2 programmes
Exam
TEN2 Written examination
- 5
- 4
- 3
- U
Ordinary exams
79% passed · 463 students
- 69%93
- 82%94
- 89%101
- 74%77
- 78%98
Re-exams
56% passed · 81 students
- 20%5
- 44%25
- 50%8
- 30%10
- 75%8
- 82%11
- 60%5
- 89%9
- Pass the re-exam: 56% (81 students), compared with 79% (463 students) on the ordinary exam
- Get 4 or 5: 43% (544 students)
Show small sittings (4)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
- 100%1
- 0%1
- 50%4
- 67%3
Other modules
Partial exams, hand-ins and labs. They are not part of the figures at the top.
Hand-in or lab
LAB2 Laboratory work
- G
Main rounds
100% passed · 389 students
- 100%78
- 100%84
- 100%86
- 100%73
- 100%68
Later rounds
100% passed · 7 students
- 100%7
- Pass a later round: 100% (7 students), compared with 100% (389 students) on the ordinary exam
Show small sittings (24)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
- 100%2
- 100%2
- 100%1
- 100%1
- 100%2
- 100%2
- 100%1
- 100%2
- 100%4
- 100%1
- 100%2
- 100%1
- 100%2
- 100%3
- 100%2
- 100%3
- 100%1
- 100%1
- 100%2
- 100%4
- 100%4
- 100%2
- 100%3
- 100%2
About the course
Aim
The course deals with mathematical tools for solving and analyzing combinatorial optimization problems. Focus lies on modeling the problem, choosing and using the most efficient algorithm for each specific problem structure and using software to solve different types of problems. The learning outcomes of the course are categorized into the following two main headings and the learning outcomes M1-M6 within this structure specify what the student should be able to do aftercompleting the course.
1. In mathematical modeling and the use of software to solve optimization problems, be able to:
- (M1) identify optimization issues, describe and formulate important types of combinatorial optimization problems as mathematical models and determine the difficulty of the problems with the help of complexitytheory;
- (M2) combine knowledge in modeling optimization problems, use of optimization software and programming to solve a given optimization problem, and carry out plausibility assessment and analysis of the result;
- (M3) apply optimization to sustainable development problems.
2. Within solution methods and theory, be able to
- (M4) use basic concepts and theorems, and choose and apply appropriate methods to solve and analyze linear programming problems modeled with continuous decision variables;
- (M5) use basic concepts and theorems, and choose and apply appropriate methods to solve and analyze linear programming problems modeled with discrete decision variables or in the form of a network;
- (M6) develop a simple heuristic for a structured combinatorial optimization problem within the scope of what is described by the course content.
- As part of (M4), (M5) and (M6) be able to clearly report calculations and reasoning,and make simpler plausibility assessments of the results.
Content
Introduction to optimization, problem formulation, graphical solution,computational complexity. The simplex method, linear duality andsensitivity analysis. Basic graph theory, models and methodsfor finding minimal spanning tree, traveling salesman tour, postman tour, shortest path, minimum cost flow and maximal flow. Methods for integer programming, such as branch-and-bound. Problem complexity, heuristics.
- Examiner
- Roghayeh Hajizadeh
- Scheduled hours
- 44 h
- Main field of study
- Matematik, Tillämpad matematik