Bi-objective topology optimization for direct current concentration and heat flux cloaking using adaptive weighting method

This study presents a topology optimization method for direct current concentration and heat flux cloaking. For bi- functionality regarding different physical flow manipulations, two objective functions are constructed to define each physical performance, and utility functions are established using a weighted norm approach for simultaneous performance improvement. An initial and utopia points-based adaptive weighting method is proposed to appropriately reflect preferences between conflicting objective functions. Using different preferences, a Pareto-optimal solution set evenly distributed in the objective space is explored. The optimization process is based on the phase field approach which introduces the reaction-diffusion equation combined with the double well potentials as an update scheme. The effectiveness of the proposed method is verified through two numerical examples.

Automated summary

This study proposes a topology optimization method for cloaking direct current concentration and heat flux. Two objective functions are constructed to define each physical performance, and utility functions are established using a weighted norm approach. An adaptive weighting method is proposed to appropriately reflect preferences between conflicting objective functions. The effectiveness of the method is verified through numerical examples.