I am currently using different optimization algorithms for finding constrained portfolio that best replicate choosen index. So i have a optimization task to minimize tracking error. I wonder why every paper use evolutionary algorithms, particle swarm optimizers or to lesser extent simmulated annealing or bayesian optimization, when using standard OLS with constrains should suffice as it is already minimizing similar measure analyticaly, ergo more preicisely. My comparison have also shown that PSO or bayesian optimization wont converge and gives worse recommended parameters than OLS. Why are they more popular ?
It would have been helpful had you provided links to those papers.
But in general, you need to distinguish between the optimisation model, and the numerical technique used to solve the model.
Suppose you wanted to estimate a linear regression,
with the mean squared residual as the criterion of fit,
and without further constraints. This is a model. Now
you can solve this model via a
QR decomposition, say;
or you can use a heuristic such as Differential
Evolution or Particle Swarm Optimisation
(PSO). If done properly, all techniques will give you
exactly the same fit (up to numerical precision). That
is because they all solve the same model, and it is a
model that is easy to solve. (Btw, you cannot use
Least-Squares techniques when you have inequality
The advantage of using heuristics such as PSO is that you can now solve other, more complex models: you may, for instance, include cardinality constraints or UCITS (5/10/40) constraints. See for instance "The Threshold Accepting Heuristic for Index Tracking" or "Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints".