An improved dynamic multi-objective optimization approach for nonlinear equation systems

Solving nonlinear equation systems using evolutionary algorithms involves solving two key problems. One problem is how to efficiently optimize the nonlinear equations derived from the physical features, and the other problems is how to locate more than one optimal solution in a single trial. To address these two problems, an improved dynamic tri-objective differential evolution method is proposed in this paper. First, we transform a given system with any type and number of nonlinear equations into a dynamic tri-objective optimization problem, which targets the first problem. Second, we develop a self-adaptive ranking multi-objective differential evolution, which targets the second problem. In addition, a probability distribution-based local search is introduced, which aims to identify the optimal solutions with a high level of accuracy. Based on previous studies of numerical optimizations with multiple solutions, each component is elaborately proposed and developed, so it is more suitable for a nonlinear equation system. Experiments were conducted on 30 numerical examples collected from real-world applications. The statistical results are encouraging, showing that the performance of the proposed approach is better than that of eight state-of-the-art evolutionary algorithms, with respect to root ratio and success rate metrics.