Towards Explainable Metaheuristics: Feature Mining of Search Trajectories through Principal Component Projection

While population-based metaheuristics have proven useful for refining and improving explainable AI systems, they are seldom the focus of explanatory approaches themselves. This stems from their inherently stochastic, population-driven searches, which complicate the use of standard explainability techniques. In this article, we present a method to identify which decision variables have the greatest impact during an algorithm’s trajectory from random initialsation to convergence. We apply Principal Component Analysis to project each population onto a lower-dimensional space, then introduce two metrics—Mean Variable Contribution and Proportion of Aligned Variables—to identify the variables most responsible for guiding the search. Using four different population-based methods (Particle Swarm Optimisation, Genetic Algorithm, Differential Evolution, and Covariance Matrix Adaptation Evolution Strategy) on 24 BBOB benchmark functions in 10 dimensions, we find that these metrics highlight meaningful variable relationships and provide a window into each method’s search dynamics. By comparing the features extracted across algorithms and problems, we illustrate how certain variable subsets consistently drive major improvements in solution quality. In doing so, new evolutionary algorithm variants can be designed to take advantage of these influential variables, while also identifying underutilised variables that may benefit alternative search strategies.