Decomposition-based multiobjective optimization for nonlinear equation systems with many and infinitely many roots

Abstract

Although the development of Pareto-dominance-based multiobjective optimization algorithms has enabled the solution of nonlinear equation systems, few studies have been conducted on the use of multiobjective optimization techniques for the solution of nonlinear equation systems. Accordingly, in this study, we use decomposition-based multiobjective optimization to solve nonlinear equation system, an attempt is made at deploying the decomposition-based multiobjective optimization to solve nonlinear equation systems, including those with infinite roots. In our novel approach, a given system is transformed into a bi-objective optimization problem using reference points. An improved decomposition-based multiobjective optimization is then applied to solve a transformed bi-objective optimization problem. To ensure this optimization suits the characteristics of the problem, we develop an adaptive multiobjective differential evolution and local search approach. The roots of the original nonlinear equation system can then be identified, together with the Pareto-optimal solutions of the transformed problem. We conducted extensive experiments to compare the performance of our novel approach with that of 16 state-of-the-art algorithms in solving 30 nonlinear equation systems derived from industrial applications. The results clearly show that our novel approach achieves better performance with a shorter execution time than that of the selected single-objective-based evolutionary approaches or Pareto-dominance-based multiobjective optimization algorithms.