A self-competitive mutation strategy for Differential Evolution algorithms with applications to Proportional-Integral-Derivative controllers and Automatic Voltage Regulator systems

The Differential Evolution (DE) algorithm is a powerful and simple optimizer for solving various optimization problems. Based on the literature, DE has shown suitable performance in exploring search spaces and locating global optimums. However, it is typically slow in extracting the problem solution. In this paper, the exploration ability of the DE algorithm is augmented with a competitive control parameter ω based on the value of the objective function of the mutating members. A new mutation strategy is introduced, subtracting weaker members from superior weaker ones. The proposed DE algorithm, which is referred to as the self-competitive DE, has been employed for solving real-world optimization problems. Several DE algorithms are enhanced with the proposed parameter ω, and the efficiencies of the resulting enhanced algorithms are tested. Furthermore, the optimal Proportional-Integral-Derivative (PID) controller tuning for an Automatic Voltage Regulator (AVR) system is used to investigate the effectiveness of the proposed strategy in solving real-world optimization problems. Simulation results demonstrate a good performance of the proposed parameter ω over several other well-known DE algorithms.