Multilevel Evolution Strategies for Multigrid Problems
Ofer M. Shir · 2016
We introduce a multilevel mechanism into Evolution Strategies (ESs) to address multigrid problems, which represent real-world applications of extremely high dimensions possessing a multiscale nature (i.e., low-resolution variants provide coarser approximations to the original problem). ESs may obtain fine solutions to the high-scale formulations only within an impractically large number of objective function calls, and we therefore devise a novel multilevel ES framework to efficiently treat such problems. We propose an automated leveling-up scheme to facilitate guided-search over increasingly finer levels of the optimization problem, which terminates after a solution to the ultimate high-scale problem is attained. We instantiate the proposed multilevel self-adaptive ES framework by two specific strategies: the elitist single-child (1+1)-ES and the non-elitist multi-child derandomized (\mu_W,\lambda)-sep-CMA-ES. We show that the proposed approach is suited for targeting a global optimization problem which was heretofore viewed as too complex to address.