A Re-initialization Clustering-Based Adaptive Differential Evolution for Nonlinear Equations Systems

Abstract

Solving nonlinear equations systems is one of the most challenges for evolutionary algorithms, especially to locate multiple roots in a single run. In this paper, a new approach which combines speciation clustering with dynamic cluster sizing, adaptive parameter control and re-initiation mechanism is proposed to deal with this optimization problem. The major advantages are as follows: (1) the speciation clustering with dynamic cluster sizing can alleviate the trivial task to set proper cluster size; (2) to improve the search ability in each species and avoid the trivial work of parameter setting, adaptive parameter control is employed; and (3) re-initialization mechanism motivates the search algorithm to find new roots by increasing population diversity. To verify the performance of our approach, 30 nonlinear equations systems are selected as the test suite. Experiment results indicate that the speciation clustering with dynamic cluster size, adaptive parameter control, and re-initialization mechanism can work effectively in a synergistic manner and locate multiple roots in a single run. Moreover, comparison of other state-of-the-art methods, the proposed method is capable of obtaining better results in terms of peak ratio and success rate.