  By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then
considering the distance to the nearest integer function of the result, we turn
the sum of three cubes problem into an optimisation one. We then apply three
stochastic optimisation algorithms to this function in the case with $k=2$,
where there are many known solutions. The goal is to test the effectiveness of
the method in searching for integer solutions. The algorithms are a
modification of particle swarm optimisation and two implementations of
simulated annealing. We want to compare their effectiveness as measured by the
running times of the algorithms. To this end, we model the time data by
assuming two underlying probability distributions -- exponential and
log-normal, and calculate some numerical characteristics for them. Finally, we
evaluate the statistical distinguishability of our models with respect to the
geodesic distance in the manifold with the corresponding Fisher information
metric.
