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This paper proposes a multi-objective optimization method using an adaptive weight determination scheme and tunneling method. To find the optimum designs that are evenly distributed on the Pareto front, the weights of different objective functions are adaptively determined by using the concept of a hyperplane so that new solutions can be gradually found in the objective space. In addition, to avoid locally optimized solutions that are dominated by other Pareto optimum designs, a tunneling method is employed in the optimization process. To confirm the effectiveness of the proposed method, topology optimization of the magnetic actuator is performed. The magnetic force and volume of the actuator are considered as two conflicting objective functions in the optimization problem, and Pareto optimum solutions that are evenly distributed in the objective space could be obtained. [ABSTRACT FROM AUTHOR]

Summary: Finding an optimum design that satisfies all performances in a design problem is very challenging. To overcome this problem, multiobjective optimization methods have been researched to obtain Pareto optimum solutions. Among the different methods, the weighted sum method is widely used for its convenience. However, since the different weights do not always guarantee evenly distributed solutions on the Pareto front, the weights need to be determined systematically. Therefore, this paper presents a multiobjective optimization using a new adaptive weight determination scheme. Solutions on the Pareto front are gradually found with different weights, and the values of these weights are adaptively determined by using information from the previously obtained solutions' positions. For an n‐objective problem, a hyperplane is constructed in n ‐dimensional space, and new weights are calculated to find the next solutions. To confirm the effectiveness of the proposed method, benchmarking problems that have different types of Pareto front are tested, and a topology optimization problem is performed as an engineering problem. A hypervolume indicator is used to quantitatively evaluate the proposed method, and it is confirmed that optimized solutions that are evenly distributed on the Pareto front can be obtained by using the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective topology optimization method for a magnetic actuator design considering both magnetic force and actuator volume. We use a gradient-based optimization algorithm and the multi-objective optimization problem is formulated using a weighted sum of the objective functions. An adaptive weight determination scheme is iteratively employed to update the weighting coefficients of the objective functions to obtain non-dominated solutions. To ensure that the optimal solutions are evenly distributed in the objective domain, $\varepsilon $ -equality constraints are applied in the empty regions of the non-dominated solutions. The values of the constraints are determined by considering the distance ratios of the objective functions. The optimization problem is formulated to maximize the magnetic force and minimize the volume of the actuator. A level set function is used as a topological design variable to obtain optimal designs that have clear structural boundaries. [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]