(Created 2010-07-25.)

LINEAR AND COMBINATORIAL OPTIMIZATION | FMA240 |

**Aim**

Linear and combinatorial optimisations problems appear more and more often, in science technology and economics. 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 this, combinatorial methods have grown in importance. The aim of the course is to make the students aware of problems in linear and combinatorial optimisation 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.

*Knowledge and understanding*

For a passing grade the student must

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

with and without the use of a computer, using appropriate computer packages, be able to show good ability to solve transport problems, assignment problems, minimal cut and maximal flow problems.

*Skills and abilities*

For a passing grade the student must

be able to write computer programs to solve linear and combinatorial optimisation 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 optimisation.

**Contents**

Linear programming. Transport problems. Maximal flow. Local search. Simulated annealing. Genetic optimization. Neural networks.

**Literature**

Kolman, B. - Beck, R.E.: Elementary Linear Programming with Applications.

Acdemic Press 1995. ISBN 0-12-417910.

Some supplementary material.

There might be a change of course book.