A Multifactorial Optimization Framework Based on Adaptive Intertask Coordinate System

The searching ability of the population-based search algorithms strongly relies on the coordinate system on which they are implemented. However, the widely used coordinate systems in the existing multifactorial optimization (MFO) algorithms are still fixed and might not be suitable for various function landscapes with differential modalities, rotations, and dimensions; thus, the intertask knowledge transfer might not be efficient. Therefore, this article proposes a novel intertask knowledge transfer strategy for MFOs implemented upon an active coordinate system that is established on a common subspace of two search spaces. The proper coordinate system might identify some common modality in a proper subspace to some extent. In this article, to seek the intermediate subspace, we innovatively introduce the geodesic flow that starts from a subspace, reaching another subspace in unit time. A low-dimension intermediate subspace is drawn from a uniform distribution defined on the geodesic flow, and the corresponding coordinate system is given. The intertask trial generation method is applied to the individuals by first projecting them on the low-dimension subspace, which reveals the important invariant features of the multiple function landscapes. Since intermediate subspace is generated from the major eigenvectors of tasks' spaces, this model turns out to be intrinsically regularized by neglecting the minor and small eigenvalues. Therefore, the transfer strategy can alleviate the influence of noise led by redundant dimensions. The proposed method exhibits promising performance in the experiments.