Meta-Initialized Hierarchical Surrogate Optimization for Computationally Efficient Topology Optimization

Abstract

Topology optimization enables lightweight, high-stiffness designs, but practical deployment is limited by repeated finite element method (FEM) cost and sensitivity to numerical regularization, such as density-filter-radius tuning. We propose meta-initialized hierarchical surrogate optimization (MH-SO), a compute-budgeted acceleration framework for task families across benchmark types, mesh resolutions, and volume fractions. MH-SO integrates first-order model-agnostic meta-learning (FO-MAML), hierarchical reinforcement learning (HRL) using proximal policy optimization (PPO) and asynchronous advantage actor-critic (A3C), an interface-aware update map, and a graph neural network (GNN) surrogate for rapid response evaluation. Periodic full-FEM guarding bounds surrogate drift, and all objectives are recomputed by full-FEM evaluation. On canonical two-dimensional (2D) linear-elastic compliance benchmarks, MH-SO improves normalized compliance over a soft-kill bidirectional evolutionary structural optimization (Soft-BESO) baseline by up to 3.04% and reduces wall-clock time by 3.4–3.5 times under compute parity with matched stopping criteria for all compared methods. Transferring the same pipeline to linearized eigenvalue buckling load factor (BLF) maximization achieves a 12.91% BLF increase and up to 7.2 times wall-clock speedup relative to a solid isotropic material with penalization (SIMP) baseline. Held-out mean absolute percentage error (MAPE) is 1.9–2.6% for compliance surrogates and 4.38–4.71% for the buckling surrogate. MH-SO is a complementary acceleration layer for early-stage screening, not a replacement for full-FEM-based analysis workflows.