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.

Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse fields. One of the main purposes of solving NEs is to locate as many roots as possible simultaneously in a single run, however, it is a difficult and challenging task in numerical computation. In recent years, Intelligent Optimization Algorithms (IOAs) have shown to be particularly effective in solving NEs. This paper provides a comprehensive survey on IOAs that have been exploited to locate multiple roots of NEs. This paper first revisits the fundamental definition of NEs and reviews the most recent development of the transformation techniques. Then, solving NEs with IOAs is reviewed, followed by the benchmark functions and the performance comparison of several state-of-the-art algorithms. Finally, this paper points out the challenges and some possible open issues for solving NEs.