Solving Nonlinear Equations Systems with an Enhanced Reinforcement Learning Based Differential Evolution

Abstract

Nonlinear equations systems (NESs) arise in a wide range of domains. Solving NESs requires the algorithm to locate multiple roots simultaneously. To deal with NESs efficiently, this study presents an enhanced reinforcement learning based differential evolution with the following major characteristics: (1) the design of state function uses the information on the fitness alternation action; (2) different neighborhood sizes and mutation strategies are combined as optional actions; and (3) the unbalanced assignment method is adopted to change the reward value to select the optimal actions. To evaluate the performance of our approach, 30 NESs test problems and 18 test instances with different features are selected as the test suite. The experimental results indicate that the proposed approach can improve the performance in solving NESs, and outperform several state-of-the-art methods.

Keywords

• nonlinear equations systems
• reinforcement learning
• differential evolution
• multiple roots location