FMAF35F

Temporary

Linear and Combinatorial Optimization

6

Course given jointly for second and third cycle

FMAF35, FMA240

7151 (Centre of Mathematical Sciences / Mathematics)

FMAF35, FMA240

2021-03-01

Professor Thomas Johansson

English

Every spring semester

In science, technology and economics, linear and combinatorial optimization problems appear more and more often. The most well known example is linear programming, where the so called simplex method has been of utmost importance in industry since it was invented in the middle of the 20th century. Other important problems, e.g. for effective data processing, contain discrete variables, for example integers. In connection with these, the importance of combinatorial methods has grown. The aim of the course is to make the students aware of problems in linear and combinatorial optimization which are important in the applications, and to give them knowledge about mathematical methods for their solution. The aim is also to make the students develop their ability to solve problems, with and without the use of a computer.

Linear programming. Integer programming. Transport problems. Assignment problems. Maximal flow. Local search. Simulated annealing. Genetic optimization. Neural networks. Dynamic programming. Algorithm complexity.

understand and be able to clearly explain the theory behind the simplex method.
be able to describe and informally explain the mathematical theory behind central algorithms in combinatorial optimization (including local search, branch and bound methods, simulated annealing, genetic optimization, neural networks).

be able to show a good capability to (i) identify problems in the area, (ii) formulate these in mathematical terms, (iii) choose an appropriate method to solve them, and finally (iv) carry out the solution, possibly with the help of a computer.
be able to write computer programs to solve linear and combinatorial optimization problems.
with proper terminology, in a well structured way and with clear logic be able to explain the solution to a problem within linear and combinatorial optimization.

Lectures

Laboratory exercises

Exercises

Written exam

Oral exam

Miscellaneous

Computer sessions. Written and/or oral test, to be decided by the examiner. Some minor projects should be completed before the exam.

Failed, pass

FMAB20 Linear Algebra.

Holmberg, K.: Optimering: metoder, modeller och teori för linjära, olinjära och kombinatoriska problem. 2010. ISBN 9789147099351.
Kolman & Beck: Elementary Linear Programming with Applications.. Academic Press, 1995.

FMAF35F

2021-03-01

Professor Thomas Johansson