Discrete Modelling 7.5 credits

About the course

The course consists of two parts.

Module 1 (4.5 ECTS): Theory of discrete modelling.
This part of the course treats theory for discrete modelling, from problem formulation and choice of model, via specific model formulation and implementation, to evaluation of appropriateness and effectiveness of the model.

This part of the course starts with general theory for formulating an integer program from a given problem description, and general theory for SAT formulations of optimization and decision problems. In connection to this, complexity theory and the general theory of polynomial reduction from one problem to another.
Integer formulations and SAT formulations are then connected to different classes of graph models, in particular matchings, the travelling salesman problem. In addition to this, Hamilton cycles, Euler cycles, assignment problems and stable matchings are studied.
Both exact and heuristic models are studied with regard to effectiveness. Artificial intelligence is treated by means of an introduction to genetic algorithms, especially for the travelling salesman problem.
Following this, concrete large scale examples of applied discrete modelling are studied, and an introduction to literature search in the area of discrete modelling is given. The theory is concluded with an introduction to simulation using randomized scenarios.

Module 2 (3 ECTS): Lab assignment.
This part of the course treats implementation of discrete models, and comparisons between different formulations as regards computational efficiency. To handle problems where solution to optimality is not feasible, simulation methods for discrete models are implemented. Finally, methods from the broadly construed area of artificial intelligence are treated, such as genetic algorithms and simulated annealing.

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Autumn 2025
- Discrete Modelling
  
  Autumn 2025 / Umeå / English / On site
  
  Submit a late application
  
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  Starts
  3 November 2025
  
  Ends
  18 January 2026
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-58022
  
  Eligibility The course requires 90 ECTS including 15 ECTS in Computer Programming, a course in Linear Programming, a course in Integer Programming on advanced level and a basic course in Mathematical Statistics or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies
  
  Selection
  Guaranteed place
  
  Application
  Application deadline was 15 April 2025. Submit a late application at Universityadmissions.se.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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