Two-Stage Reinforcement Learning-Based Differential Evolution for Solving Nonlinear Equations

Solving nonlinear equations (NEs) requires the algorithm to locate multiple roots of NEs in one run. In this article, a generic framework based on two-stage reinforcement learning (RL) and differential evolution (DE) is proposed to effectively deal with NEs problems. The major advantage of our approach are: 1) different niching methods and mutation strategies are integrated into the DE algorithm to assist evolution; 2) the diversity is maintained by utilizing the search characteristics of different niching methods at population level; 3) additionally, each individual is regarded as an agent, and three classical mutation strategies are used as the agent's alternative actions; and 4) different state settings and reward function can be easily integrated into this framework. To verify the performance of our approach, 30 problems and 18 new NEs are selected as the test suite. The experimental results demonstrate that RL can facilitate the algorithm and improve the problem-solving ability. Moreover, the proposed method also obtains competitive performance compared with other peer algorithms.