Evolutionary multitasking for solving nonlinear equation systems

Over the past few years, many evolutionary algorithms have been developed to find multiple roots of the nonlinear equation system (NES). However, they can only solve one NES in a single run, ignoring the potentially useful information and solving experience derived from different NESs. To this end, an evolutionary multitasking NES optimization framework called MTNES, is proposed for the first time in this paper for solving multiple NESs simultaneously. Specifically, we first initialize multiple NES tasks in a 0-1 unified search space to establish an implicit relationship between NESs to facilitate knowledge transfer. Then, combining differential evolution and neighborhood technique, a neighborhood knowledge transfer is presented to reduce negative knowledge transfer and thus help find more roots. In addition, a novel resource reallocation mechanism is developed to release the found roots, thereby improving population diversity as well as aiding the search for more promising areas. Numerous empirical results reveal that the proposed approach can achieve a higher root rate and success rate when compared with several well -established algorithms on eighteen complex NESs. Moreover, experimental results on two real -world applications further show the potential practicability of the proposed multitasking NES -solving framework.