Triple and quadruple comparison-based interactive differential evolution and differential evolution

We propose a triple comparison and a quadruple comparison based mechanism for enhancing differential evolution (DE), especially for interactive DE (IDE) where the method can be used to reduce IDE user fatigue. Besides the target vector and trial vector from normal DE, opposition vectors generated by opposition-based learning are used to determine offspring, and the best vector from among these three or four vectors becomes offspring for the next generation. We evaluate the proposed methods by comparing them with conventional IDE and conventional opposition-based IDE using a simulated IDE modeled using a four dimensional Gaussian mixture model. We also evaluate them in DE using 24 benchmark functions. The experiments show that our proposed methods can enhance IDE and DE search efficiently according to several evaluation indices. These include the converged fitness values after the same number of generations, converged fitness values after the same number of fitness calculations, fitness calculation cost, convergence success rates and acceleration rates.