Heuristic Search Algorithms for the Minimum Volume Ellipsoid

A method of robust estimation of multivariate location and shape that has attracted a lot of attention recently is Rousseeuw’s minimum volume ellipsoid estimator (MVE). This estimator has a high breakdown point but is difficult to compute successfully. In this article, we apply methods of heuristic search to this problem, including simulated annealing, genetic algorithms, and tabu search, and compare the results to the undirected random search algorithm that is often cited. Heuristic search provides several effective algorithms that are far more computationally efficient than random search. Furthermore, random search, as currently implemented, is shown to be ineffective for larger problems.