# Why is it better to use evolutionary algorithms than OLS for solving index tracking problem?

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 ?

• Some people have problems to solve and they look for mathematical techniques to solve them. Some people know fancy mathematical techniques and look for problems to solve, so they can publish articles in journals showing how innovative they are in applying new techniques. – Alex C Aug 10 at 23:02

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 constraints.)
• @Enrico Schumann: Thanks for your examples but what does $X$ represent in those two cases. Maybe they are return exposures to some underlying factor model ? So X represents the loadings that the target fund has with respect to that factor model ? Then, the resulting $\beta_{i}$ are the weights that should be used for each of the factors ? Thanks. – mark leeds Aug 12 at 14:12