A Special Multiobjective Evolutionary Algorithm for Solving Complicated Nonlinear Equations Systems

Abstract

It is well known that nonlinear equations systems (NESS) is a subclass of nonlinear optimization problem, it exists in many application fields, such as information industry, network design, mechanics and robotics, etc.. How to design feasible and effective optimization methods to obtain the optimal solution or satisfied precision requirement’s optimal solution for complicated NESS is very important in computation fields. In this paper, each nonlinear sub-equation of NESS is approximately regarded as a sub-objective function of multi-objective optimization problem, then the original nonlinear equations systems is transformed into a multi-objective optimization problem, and the equivalence relation of the solution between the original NESS and the transformed multi-objective optimization problem is given. In order to effectively solve the nonlinear equations systems, a self-adaptive levy mutation operation is proposed, and a multi-objective optimization evolutionary algorithm to solve the nonlinear equations systems was designed. Computer simulations demonstrate the proposed algorithm can not only increase the diversity of evolutionary population but also make the evolution population quickly to approach the optimal solution or satisfied precision requirement’s optimal solution.