Abstract: Convex optimization is well-understood and still at the core of tremendous amounts of research, pushing the speed and accuracy of optimization algorithms. Many non-convex optimization problems have a much more difficult structure and algorithms are typically tailored to specific problems, such as, for example, TSP. However, there are also general purpose algorithms for solving such tasks, such as genetic algorithms or swarm optimization algorithms.

In this talk we discuss a genetic algorithm employing so-called crossover operators in order to optimize a non-convex test function, using tools from the analysis of randomized algorithms. Crossover requires diversity to work at all, and we show how, on the one hand, diversity emerges naturally, and on the other hand, how we can increase diversity artificially. Finally, we give some indication of how such work on test functions can lead to better algorithms for combinatorial optimization problems.