  The Ornstein-Zernike equation is solved for the hard-sphere and square-well
fluids using a diverse selection of closure relations; the attraction range of
the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids
we mainly focus on the solution based on a three-parameter version of the
Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free
parameters of the latter, an unconstrained optimization problem is defined as a
condition of thermodynamic consistency based on the compressibility and solved
using Evolutionary Algorithms. For the hard-sphere fluid, the results show good
agreement when compared with mean-field equations of state and accurate
computer simulation results; at high densities, i.e., close to the freezing
transition, expected (small) deviations are seen. In the case of the
square-well fluid, a good agreement is observed at low and high densities when
compared with event-driven molecular dynamics computer simulations. For
intermediate densities, the explored closure relations vary in terms of
accuracy. Our findings suggest that a modification of the optimization problem
to include, for example, additional thermodynamic consistency criteria could
improve the results for the type of fluids here explored.
