When Heuristics Help with Index Tracking Constraints
Summary
The document distinguishes an optimization model from the numerical method used to solve it. For an unconstrained linear regression objective such as minimizing mean squared residuals, standard least-squares methods and properly implemented heuristics should reach the same fit, subject to numerical precision. The optimization objective determines the problem; the solver does not make an unsuitable model more appropriate.
Heuristic methods such as particle swarm optimization or differential evolution can be useful when the index-tracking model includes more complex requirements, such as limits on the number of holdings or regulatory concentration constraints. The answer cautions that ordinary least-squares techniques do not handle inequality constraints as stated, so solver choice must match the actual formulation. It offers no empirical comparison or evidence that heuristics outperform conventional constrained optimization on a particular portfolio; the questioner’s report of weak heuristic convergence is not analyzed in detail.
Key ideas
- Separate the portfolio objective and constraints from the algorithm used to solve them.
- Different solvers should produce comparable fits when solving the same simple, well-specified regression problem.
- Heuristics can support more complex index-tracking models with constraints such as limits on holdings.
- Solver suitability depends on the mathematical formulation, and the document gives no comparative performance study.
Tags
Full text
# Why is it better to use evolutionary algorithms than OLS for solving index tracking problem? # 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 ? ## Answer by Enrico Schumann (score 3, accepted) https://quant.stackexchange.com/a/47067 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 constraints.) 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".
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.