Fixed-parameter evolutionary algorithms and the vertex cover problem

In this paper, we consider multi-objective evolutionary algorithms for the Vertex Cover problem in the context of parameterized complexity. We relate the runtime of our algorithms to the input size and the cost of a minimum solution and point out that the search process of evolutionary algorithms creates partial solutions that are similar to the effect of a kernelization (i. e. a special type of preprocessing from parameterized complexity). Based on this, we show that evolutionary algorithms solve the vertex cover problem efficiently if the size of a minimum vertex cover is not too large, i.e. the expected runtime is bounded by O(f(OPT) · nc ), where c is a constant and f a function that only depends on OPT. This shows that evolutionary algorithms are randomized fixed-parameter tractable algorithms for the vertex cover problem. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity General Terms: Theory, Algorithms, Performanc...

• Type: Conference
• Year: 2009
• Where: GECCO
• Authors: Stefan Kratsch, Frank Neumann
• Keywords: Artificial Intelligence, Evolutionary Algorithms, GECCO 2009, Multi-objective Evolutionary Algorithms, Vertex Cover Problem