A New Gradient Approach Based on Reproducing Kernel Applied in Metaheuristic optimization

This work introduces the kernel based gradient evolution optimization method where the concept of a reproducing kernel is incorporated for the first time as an efficient alternative to estimate the numerical gradient as part of the approximating solution rule. The presented algorithm searches for a feasible solution by means of a swarm and involves three principal stages: the updating rule, exploration (jumping) and refreshing. The steepest descent direction is determined using the kernel gradient estimation with a local Taylor series expansion. Twelve test functions were tested as a means of evaluating the performance of the introduced optimization method. Then, a comparison among some state-of-art methods was carried out. According to numerical results, the proposed method significantly outperforms five other well-known algorithms in most test functions.