Problem difficulty analysis for particle swarm optimization

This paper studies the problem difficulty for a popular optimization method - particle swarm optimization (PSO), particularly for the PSO variant PSO-cf (PSO with constriction factor), and analyzes its predictive measures. Some previous measures and related issues about other optimizers, mainly including deception and modality, are checked for PSO. It is observed that deception is mainly the combination of three factors - the measure ratios of attraction basins, the relative distance of attractors and the relative difference of attractors' altitudes. Multimodality and multi-funnel are proved not to be the essential factors contributing to the problem difficulty for PSO. The counterexamples and comparative experiments in this paper can be taken as a reference for further researches on novel comprehensive predictive measures of problem difficulty for PSO.