Abstract
In many fields of engineering and science, it is necessary to solve nonlinear equation systems (NESs). When using multiobjective optimization to solve NESs, there are two problems: 1) how to transform an NES into a multiobjective optimization problem and 2) how to design an algorithm to solve the transformed problems. In this work, we propose a multilayer bi-objective transformation technique, which can transform an NES into a bi-objective optimization problem, and it overcomes the curse of dimensionality and the problem of missing roots caused by the decrease of solutions discernibility in previous transformation techniques. Then, combining the multilayer bi-objective transformation technique, we design a multiobjective brainstorm optimization with a diversity preservation mechanism, which can effectively locate multiple roots of NESs in a single run. Compared with several state-of-art methods on 30 NESs with different features, our approach provides very competitive performance with the highest root ratio and success ratio.
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