A technique for the visualization of population-based algorithms

A technique for the visualization of stochastic population-based algorithms in multidimensional problems with known global minimizers is proposed. The technique employs projections of the populations in the 2-dimensional vector space spanned by the two extremal eigenvectors of the Hessian matrix of the objective function at a global minimizer. This space condenses information regarding the shape of the objective function around the given minimizer. The proposed approach can provide intuition regarding the behavior of the algorithm in unknown high-dimensional problems. It also provides an alternative visualization framework for problems of any dimension, which alleviates drawbacks of the most popular projection methods. The proposed technique is illustrated for three well-known population-based algorithms, namely, differential evolution, covariance matrix adaptation evolution strategies and particle swarm optimization, on three test problems of different dimensionality.