A parallel strategy for an evolutionary stochastic algorithm: application to the CP decomposition of nonnegative N-th order tensors

In this article, we address the problem of the Canonical Polyadic decomposition (a.k.a. CP, Candecomp or Parafac decomposition) of N-th order tensors that can be very large. In our case, this decomposition is performed under nonnegativity constraints. While this problem is often tackled thanks to deterministic approaches, we focus here, on a stochastic approach based on a memetic algorithm. It relies on the evolution of a population and a local search stage. The main drawback of such algorithms can be their relative slowness. It is the reason why we suggest and implement a parallel strategy to increase the acceptance rate of the original algorithm and thus to accelerate its convergence speed. Numerical simulations are performed in order to illustrate the effectiveness of our approach on simulated 3D fluorescence spectroscopy tensors.