To address the limitations of traditional optimization algorithms in the design of complex energy-absorbing structures—specifically their poor convergence and limited population diversity—this study proposes a Contrastive Learning-based Non-dominated Sorting Genetic Algorithm (NSGA-II-CL). The proposed method is applied to the multi-objective optimization of a three-dimensional double-layer pyramidal lattice structure. Compared with conventional single-layer pyramidal lattices, the proposed design introduces double-layer pyramid units reinforced with vertical struts and stiffening ribs, thereby enhancing structural stability and energy absorption capacity. The samples were fabricated using Selective Laser Melting and hot-press molding techniques. Both quasi-static compression tests and finite element simulations were conducted to validate the structural performance. The specific energy absorption (SEA) and peak crushing force (PCF) were defined as optimization objectives, and a Response Surface surrogate model was constructed. The leg size, leg inclination angle, and carbon fiber ply orientation were selected as design variables. The proposed NSGA-II-CL introduces a contrastive learning mechanism, where positive and negative sample pairs are constructed based on the non-dominated hierarchy. Through multi-dimensional feature fusion and an adaptive parameter adjustment strategy, the algorithm achieves a dynamic balance between exploration and convergence during the evolutionary process. Results demonstrate that, compared with the conventional NSGA-II, the proposed NSGA-II-CL achieves improvements of 11.7% in Spacing, 1.0% in Convergence, and 1.2% in HV performance, resulting in a more uniform Pareto front distribution. Both simulation and experimental validation confirm the reliability of the optimized results, with SEA and PCF prediction errors of 2.51% and 2.26%, respectively. These findings verify the effectiveness of the proposed algorithm and structural design methodology, providing a novel approach and technical pathway for intelligent optimization of energy-absorbing structures.
Xiao et al. (Sat,) studied this question.