### Mathematical Heuristics in Discrete Optimisation

**German Title:**Mathematische Heuristiken in der Diskreten Optimierung

**Cycle:**Every spring term

**Regular Courses:**Mathematics M.Sc., Computer Science M.Sc., Mathematics B.Sc.

**Workload:**9 CP (4 SWS)

**Contact:**maheu@combi.rwth-aachen.de

**Recommended Prerequisites:**Knowledge in discrete optimization (e.g. Optimization B), especially complexity of algorithms and knowledge in graph theory (e.g. Graph Theory I or Optimization B).

**Content:**Single Solution Based Heuristics (e.g., Local Search, Greedy Randomized Adaptive Search Procedure, Variable Neighborhood Search, Tabu Search, Simulated Annealing); analysis of heuristics (Run- time analysis, approximation ratio); tuning of heuristics; Population Based Heuristics (e.g., Genetic Algorithms, Genetic Programming, Parallel Implementation, Ant Colony Optimization); Hybrid Approaches; Matheuristics.

**Learning Outcomes:**Participants know basic principles of heuristics and metaheuristics, and approximation ratios. They can differentiate between problems that allow for an exact solutions and cases where using heuristic methods is appropiate. Participants can evaluate their ability to apply their theoretical knowledge. They are able to use heuristic methods to solve a real world problems.

**Exam Type:**Oral examination and practical project.

**Exam Requirements:**Solving and presentation of several excercises throughout the term.