Summary: Evolutionary structural design has been the topic of much recent research; however, such designs are usually hampered by the time-consuming stage of prototype evaluations using standard finite element analysis (FEA). Replacing the time-consuming FEA by neural network approximations may be a computationally efficient alternative, but the error in such approximation may misguide the optimization procedure. In this paper, a multi-objective meta-level (MOML) soft computing-based evolutionary scheme is proposed that aims to strike a balance between accuracy vs. computational efficiency and exploration vs. exploitation. The neural network (NN) is used here as a pre-filter when fitness is estimated to be of lesser significance while the standard FEA is used for solutions that may be optimal in their current population. Furthermore, a fuzzy controller updates parameters of the genetic algorithm (GA) in order to balance exploitation vs. exploration in the search process, and the multi-objective GA optimizes parameters of the membership functions in the fuzzy controller. The algorithm is first optimized on two benchmark problems, i.e. a 2-D Truss frame and an airplane wing. General applicability of the resulting optimization algorithm is then tested on two other benchmark problems, i.e. a 3-layer composite beam and a piezoelectric bimorph beam. Performance of the proposed algorithm is compared with several other competing algorithms, i.e. a fuzzy-GA-NN, a GA-NN, as well as a simple GA that only uses only FEA, in terms of both computational efficiency and accuracy. Statistical analysis indicates the superiority as well as robustness of the above approach as compared with the other optimization algorithms. Specifically, the proposed approach finds better structural designs more consistently while being computationally more efficient.