Combinatorical optimization

Combinatorial Optimization deals with the identification of optimal choices in a large set of alternatives. This topic is of great importance in many fields of applications, such as planning, crew scheduling portfolio management and many more. In this report we give an introduction to combinatorial optimization with the help of a famous example, the traveling salesman problem. Then we describe the integer programming approach to combinatorial optimization and describe two of our results in this area. One concerns the generation of cutting planes and one concerns the complexity of integer programming in fixed dimension.