Pseudo derivative evolutionary algorithm and convergence analysis

In this paper, a novel evolutionary algorithm (EA), called pseudo-derivative EA (called PDEA), is proposed. The basic idea of PDEA is to use pseudo-derivative, which is obtained based on the information produced during the evolution, and to help search the solution of optimization problem. The pseudo-derivative drives the search process in a more informed direction. That makes PDEA different from the random optimization methods. The convergence of PDEA is first analyzed based on systems theory. The convergence condition of PDEA is then derived though this condition is too strong to be satisfied. Next, this condition is relaxed based on the entropy theory. Finally, performances of PDEA are evaluated on the benchmark functions and an adaptive liquid level control system of a surge tank. The numeric simulation results show that PDEA is capable of finding the solutions to the optimization problems with good accuracy, reliability, and speed.