Topology optimization of metagratings using the advanced slime mold algorithm combined with a gradient-based method: the chimera of uniqueness of the optimal solution

In this paper, we discuss the use of a metaheuristic (MH) gradient-free optimization method, specifically, the slime mold algorithm (SMA), combined with a gradient-based method to topologically optimize metagratings. In the proposed method, the gradient-based optimization method is applied to a set of initial geometries with only a few iterations. Then, the resulting pre-refined set of designs is used to initialize an enhanced version of the SMA. At the end of each iteration, the gradient of the figure of merit is used again to generate two new individuals from the best current solution. The numerical results show that our approach outperforms the original SMA, the gradient-based method, and other state-of-the-art optimization methods.