A novel Differential Evolution algorithm with Gaussian mutation that balances exploration and exploitation

Differential Evolution (DE) has been demonstrated to be an effective algorithm for global optimization. Theoretical and empirical analysis of the global convergence of DE is believed to be very significant. However, not much research has so far been devoted to theoretically analyzing the convergence properties of DE, especially with a finite population. This paper proves that the canonical differential evolution (DE/rand/1/bin) with a finite population can not guarantee global convergence. A new DE variant is proposed, which incorporates three mechanisms into DE/rand/1/bin. They are Gaussian mutation, diversity-triggered reverse sampling, and fast exploitation by a small DE population. Theoretical analysis and experimental results show that not only the global convergence can be guaranteed but also desirable optimization performance can be achieved via the proposed DE algorithm.