Sign gradient descent method based bat searching algorithm with application to the economic load dispatch problem

Inspired by the echolocation behaviors of the bats and the swarm intelligence optimization, bat searching algorithm (BA) was developed to solve unconstrained optimization problems efficiently. However, due to the lack of the gradient term, the accuracy of the BA is not superior, and the enhancement of the algorithm is still of vital importance. The sign gradient descent method (SGD) is a first-order optimization method involving only the sign of the gradient of the function to minimize. Most importantly, the convergence and optimality issues of the SGD have been rigorously studied, which guarantees the competitive performance of SGD method. Therefore, in this paper, a combination of the BA and SGD method is proposed by integrating the SGD term into the update equation of the bats during the searching process. With the social behavior among the bats and the sign gradient descent method, the proposed algorithm shows significant improvement comparing with the original algorithm. Moreover, the convergence issue of the proposed algorithm is studied from system dynamics perspective. The numerical evaluations are provided to demonstrate the improvement of the proposed sign gradient descent method based bat searching algorithm. In the end, the economic load dispatch problem for the power system is studied as an application of the proposed BA algorithms. Based on the numerical results, the proposed BA shows superior performance.