Second-order DE algorithm

Differential evolution (DE) is a robust, efficient and simple evolutionary algorithm for various optimisation and engineering problems. It has several outstanding features such as low time complexity, ease to use and robust steadiness. So it is becoming more and more popular and is widely used in more and more applications. However, many questions are deserving to consider the critical balance between global exploration and neighbourhood exploitation. The difference vector of the mutation operator for the direction and neighbour information has not been fully exploited. Therefore, a second-order difference vectors based DE, SODE, is proposed, which can efficiently utilise different direction information from the second-order difference vector. The optimal second-order difference mechanisms are proposed for DE/rand/1 and DE/best/1 to utilise the direction and neighbour information from difference vector. Then, it will guide the individuals toward the possible more encouraging areas. Extensive experiments and comprehensive comparisons show that the second-order differenced mechanism in SODE is much better than the classical first-order difference mechanisms based mutation strategy – ‘DE/rand/1’ and ‘DE/best/1’ as far as the converging and steady performance.