On The Use of Genetic Algorithm with Elitism in Robust and
Nonparametric Multivariate Analysis
Biman Chakraborty and Probal Chaudhuri
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.
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