Theory of swarm intelligence

The theory of swarm intelligence has made rapid progress in the last 5 years. Following a very successful line of research in evolutionary computation, various results on the computational complexity of swarm intelligence algorithms have appeared. These results shed light on the working principles of swarm intelligence algorithms, help to identify the impact of parameters and other design choices on performance, and contribute to a solid theoretical foundation of swarm intelligence.

This tutorial will give a comprehensive overview of theoretical results on swarm intelligence algorithms, with an emphasis on their computational complexity. In particular, it will be shown how techniques for the analysis of evolutionary algorithms can be used to analyze swarm intelligence algorithms and how the performance of swarm intelligence algorithms compares to that of evolutionary algorithms. The tutorial will be divided into a first, larger part on ant colony optimization (ACO) and a second, smaller part on particle swarm optimization (PSO).

For ACO we will consider simple variants of the MAX-MIN ant system. Investigations of example functions in pseudo-Boolean optimization demonstrate that the choice of the pheromone update strategy and the evaporation rate has a drastic impact on the running time, even for very simple functions like ONEMAX. We will also elaborate on the effect of using local search within the ACO framework. In terms of combinatorial optimization problems, we will look at the performance of ACO for minimum spanning trees, shortest path problems, and the TSP.

For particle swarm optimization, the tutorial will cover results on PSO for pseudo-Boolean optimization as well as a discussion of theoretical results in continuous spaces.