An Improved Multi-Objective GA for Low-Frequency Metamaterial Unit Robust Optimization Under Uncertainty

Metamaterial (MM) is very promising in engineering applications since it exhibits extraordinary physical properties that do not exist in nature. Nevertheless, the development of an MM still faces some bottleneck problems, such as maximizing the negative permeability and ensuring the robustness of the high permeability at the working frequency in engineering applications. To address the inefficiencies of the existing multi-objective robust optimization methodologies in applications to MM designs, an improved multi-objective genetic algorithm and an adaptive surrogate model are proposed. To accelerate the solution speed of the original multi-objective algorithm in finding both high-quality solutions and distributing them uniformly, two polynomial approximation-based move operations are proposed. Moreover, some dominant techniques including the construction of the relationship between different objective functions and the relationship between the objectives and the design variables are investigated. Also, an adaptive surrogate model is introduced to efficiently quantify the robust performance of a solution. The numerical results of optimizations of two mathematical benchmark problems and a prototype MM unit have demonstrated the feasibility and merits of the proposed methodology.