Parameterized analysis of multiobjective evolutionary algorithms and the weighted vertex cover problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann (2013) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann (2013), we provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a (1+ɛ)-approximation in expected time O(n·2min{n,2(1-ɛ)OPT}+n3).Mojgan Pourhassan, Feng Shi and Frank Neuman

Parameterized analysis of bio-inspired computing

The parameterized analysis of bio-inspired computing provides a new way of gaining additional insights into the working behavior of popular approaches such as evolutionary algorithms and ant colony optimization. We give an overview of two important approaches in this area. The area of parameterized runtime analysis studies the runtime of bio-inspired computing with respect to different parameters of the given problem instance and builds on the success of rigorous runtime analysis of bio-inspired computing in the last 20 years. The feature-based analysis of algorithms for a given optimization problem uses statistical methods to figure out which features of a given problem instance lead to a good or bad performance of the algorithm under consideration. It often uses an evolutionary algorithm for evolving problem instances that exhibit performance differences between a given set of solvers and can be used for effective algorithm selection.Frank Neuman