Tensor decomposition-based alternate sub-population evolution for large-scale many-objective optimization

Abstract

• Introduce tensor decomposition to divide higher-dimensional heterogeneous decision variables. • The alternate sub-population evolution asymptotically optimizes the whole population. • A cross-population matching scheme is designed to reconstruct the whole population accurately. • Tensor decomposition-based model can be applied to other MOEAs with large-scale variables. A novel alternate evolution of sub-populations based on tensor decomposition called, TASE is proposed, for solving multi- and many-objective optimization problems with large-scale decision variables in this work. Tensor canonical polyadic (CP) decomposition is introduced for the first time to divide the heterogeneous variables of higher-dimensional decision space into several lower-dimensional sub-components. Furthermore, these sub-populations are optimized alternatively to search for improved solutions in their respective lower-dimensional decision subspace . Finally, a cross-population matching scheme is designed to reconstruct the whole population accurately. The experiments use some largescale multi- and many-objective problems with 2–6 objectives and 1000–5000 variables. The proposed algorithm is compared with other state-of-the-art algorithms, and the experimental results indicate that it can solve some problems that other well-known large-scale optimization algorithms cannot, as well as outperforming other algorithms in terms of solution quality and convergence rate.