On The Use of Genetic Algorithm with Elitism in Robust and Nonparametric Multivariate Analysis

In this paper, we provide a general formulation for the problems that arise in the computation of many robust and nonparametric estimates in terms of a combinatorial optimization problem. There is virtually no hope for solving such optimization problems exactly for high dimensional data, and people usually resort to various approximate algorithms many of which are based on heuristic search strategies. However, for such algorithms it is not guaranteed that they will converge to the global optimum as the number of iterations increases, and there are always possibilities for such algorithms getting trapped in some local optimum. Here we propose genetic algorithm with elitism as a way to solve that general problem by probabilistic search method. We establish convergence of our algorithm to the global optimal solution and demonstrate the performance of this algorithm using some numerical examples.