Chapter 1 PARTICLE SWARM OPTIMIZATION AND SEQUENTIAL SAMPLING IN NOISY ENVIRONMENTS Thomas Bartz-Beielstein Chair of Algorithm Engineering and Systems Analysis, Department of Computer Science, Dortmund University, Germany thomas.bartz-beielstein@udo.edu Daniel Blum Chair of Algorithm Engineering and Systems Analysis, Department of Computer Science, Dortmund University, Germany daniel.blum@udo.edu J¨ urgen Branke Institute AIFB, University of Karlsruhe 76128 Karlsruhe, Germany branke@aifb.uni-karlsruhe.de Abstract For many practical optimization problems, the evaluation of a solution is subject to noise, and optimization heuristics capable of handling such noise are needed. In this paper, we examine the influence of noise on particle swarm optimization and demonstrate that the resulting stagna- tion can not be removed by parameter optimization alone, but requires a reduction of noise through averaging over multiple samples. In order to reduce the number of required samples, we propose a combination of particle swarm optimization and a statistical sequential selection pro- cedure, called optimal computing budget allocation, which attempts to distribute a given number of samples in the most effective way. Exper- imental results show that this new algorithm indeed outperforms the other alternatives. Keywords: Particle Swarm Optimization, Noise, Sequential Sampling