Twenty-six nested structures with a circumferentially corrugated circular outer wall and inner ribs are investigated under quasi-static axial compression using the finite element method. The finite element model is validated by literature. Also, theoretical predictions for the nested structures are derived and compared with finite element analyses. Among the structures whose crashworthiness performances are examined, CO1D and CSIN2D are selected as the best ones. The comparisons have shown that the ribs attached to the closest points of the corrugated outer wall provide stable collapse modes and better crash performance. Also, the crashworthiness performance of the nested structures with octagon inner structures is higher than other alternative structures because the number of corner members and the cross-section lengths are more efficient. Finally, the objective functions developed by the surrogate modeling method are optimized by non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), paired offspring generation for constrained large-scale multiobjective optimization (POCEA) and an evolutionary algorithm for large-scale many-objective optimization (LMEA). Optimum CO1D and CSIN2D designs obtained by the NSGAII method have 37.00% and 26.68% higher SEA values, respectively than 'Cribs' structure at the same PCF value.