Quantifying the Impact of Modules and Their Interactions in the PSO-X Framework

Abstract: The PSO-X framework incorporates dozens of modules that have been proposed for solving single-objective continuous optimization problems using particle swarm optimization. While modular frameworks enable users to automatically generate and configure algorithms tailored to specific optimization problems, the complexity of this process increases with the number of modules in the framework and the degrees of freedom defined for their interaction. Understanding how modules affect the performance of algorithms for different problems is critical to making the process of finding effective implementations more efficient and identifying promising areas for further investigation. Despite their practical applications and scientific relevance, there is a lack of empirical studies investigating which modules matter most in modular optimization frameworks and how they interact. In this paper, we analyze the performance of 1424 particle swarm optimization algorithms instantiated from the PSO-X framework on the 25 functions in the CEC'05 benchmark suite with 10 and 30 dimensions. We use functional ANOVA to quantify the impact of modules and their combinations on performance in different problem classes. In practice, this allows us to identify which modules have greater influence on PSO-X performance depending on problem features such as multimodality, mathematical transformations and varying dimensionality. We then perform a cluster analysis to identify groups of problem classes that share similar module effect patterns. Our results show low variability in the importance of modules in all problem classes, suggesting that particle swarm optimization performance is driven by a few influential modules.