An Anisotropic Expected Improvement Criterion for Kriging-Assisted Evolutionary Computation

The expected improvement (EI) criterion has been widely used in Kriging-assisted evolutionary algorithms to select individuals for expensive evaluations. It measures the amount of improvement the candidates are expected to gain compared with the current best solution, based on which the best individuals will be picked for expensive evaluations. Since all the candidate individuals are measured by the current best solution when calculating the EI values, the population moves gradually towards the current best solution, which will decrease the diversity of the population. In this work, we propose a new anisotropic expected improvement (AEI) criterion to resolve this issue. Instead of comparing all the individuals with the current best solution, the proposed AEI compares the individuals with their corresponding parent solutions. By measuring the candidate individuals with different solutions, the AEI is able to bring more directions for the population to evolve, thus increase the diversity of the population. Numerical experiments show that the proposed AEI criterion performs significantly better than four state-of-the-art Kriging-based infill criteria. This work provides a new promising criterion for Kriging-assisted evolutionary computation.