Aiming at the problems such as incomplete solutions, low accuracy and slow convergence speed of current algorithms in solving nonlinear equations, this paper proposed a multimodal multi-objective differential evolution algorithm. Firstly, it transformed the nonlinear equations into multimodal multi-objective optimization problems, and initialized a random population and evaluated all individuals in the population. Through the non-dominated sorting and decision space crowding distance selection mechanism, it selected half of the individuals in the population to mutate. Then it used a new mutation strategy and boundary processing method to increase the diversity of solutions. Finally, it evolved the high-quality individuals through crossover and selection mechanism until it found all the optimal solutions. The experimental results on selected test function sets and engineering examples show that the algorithm can effectively search for optimal solutions and it is superior to the other four algorithms in the number of solutions and success rate.

[2019-05-05] Printed Article /doc/2017.11.0734/v2