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In this article, the design sensitivity is examined using the material derivative concept of the shape sensitivity analysis to use a gradient-based algorithm for the multi-objective benchmark testing electromagnetic analysis methods (TEAMs) problem. To calculate the shape sensitivity, the original objective functions are replaced with the definite integral form of the functionals, and the p-norm expression is used to handle the minimax problem. The computed sensitivities are validated using the finite-difference numerical sensitivities. The validity of the modified objectives is demonstrated using the results of the single-objective optimization. The results show that the analytical sensitivities agree well with the numerical ones, and the modified objective functions are valid for the benchmark optimization problem. [ABSTRACT FROM AUTHOR]

A novel multi-objective topology optimization method is developed by simultaneously considering the diversity and uniformity of the optimum solutions in the objective and design variable spaces. To guarantee the diversity of the solutions, a configuration-based clustering scheme is developed and applied to avoid similar designs. By clustering Pareto optimal designs during the optimization process, the searching region in the objective space is gradually reduced, and the time cost required for optimization can be decreased. Additionally, the uniformity of the solutions in the objective space is considered using an adaptive weight determination scheme. The results of the benchmark problems confirm that using the proposed method could reduce the time cost. Furthermore, the overall Pareto front and configuration of different designs are also explored. • Weights are systematically determined to obtain evenly distributed optimum solutions. • Reference point-based compromise programming is employed in the non-convex region of the Pareto front. • Clustering scheme is proposed to distinguish the Pareto optimal designs. • Adaptive weighted-sum and configuration-based clustering are incorporated in the optimization process. • The Pareto front can be explored while reducing the optimization process time cost. [ABSTRACT FROM AUTHOR]