Ant Colony Optimization for Density Functionals in Strongly Correlated Systems

The Ant Colony Optimization (ACO) algorithm is a nature-inspired metaheuristic method used for optimization problems. Although not a machine learning method per se, ACO is often employed alongside machine learning models to enhance performance through optimization. An ACO algorithm was adopted to optimize the so-called FVC density functional for the ground-state energy of strongly correlated systems. The parameter configurations that maximize optimization efficiency were found, while reducing the mean relative error (MRE) of the ACO functional. Then, it was analyzed the performance of the algorithm across different dimensionalities (1D-5D), which are related to the number of parameters to be optimized within the FVC functional. Our results indicate that 15 ants with a pheromone evaporation rate superior to 0.2 are sufficient to minimize the MRE for a vast regime of parameters of the strongly-correlated system - interaction, particle density, and spin magnetization. While the 1D, 2D, and 4D optimizations yield 1.5% < MRE < 2.7%, the 3D and 5D optimizations lower the MRE to ca. 0.8%, reflecting a 67% error reduction compared to the original FVC functional (MRE = 2.4%). As the simulation time grows almost linearly with dimension, our results highlight the potential of ant colony algorithms for density-functional problems, combining effectiveness with low computational cost.