A differential evolution algorithm for multidimensional arrays

Abstract

In this paper, we propose a differential evolution (DE) algorithm which aims to optimize a system whose parameters form a multidimensional array. Determination of the optimal demixing matrix in a blind signal separation problem can be considered as an example of this type of system. Since the DE algorithm performs only on column vectors, it can be used after the multidimensional array is transformed into a column vector. Once the optimization is completed, the solution vector must be transformed back into its original multidimensional form. These transformations increase computational complexity of regular DE algorithm that may be costly especially when the number of parameters is large. The proposed algorithm directly performs on multidimensional arrays without transformations between the array and the vector forms. Another advantage of using the array form is to have better intuition through optimization task. We derive this algorithm from regular DE algorithm by viewing the multidimensional array as a vector in the Cartesian product of real valued vectors. The dimensions of the real valued vectors are not required to be the same. We verify the robustness and effectiveness of this algorithm with two examples.