Hip-DE: Historical population based mutation strategy in differential evolution with parameter adaptive mechanism

Abstract

Differential Evolution (DE) was a powerful population-based evolutionary algorithm for global optimization, and it achieved great success in both evolutionary computation competitions and engineering applications. Despite the excellent performance of the state-of-the-art DE variants, there are still two main weaknesses existing within them: one is the weakness in a given mutation strategy and the other is the weakness in the corresponding parameter control (of the mutation strategy). By reviewing the existing mutation strategies in the recent state-of-the-art DE variants, it can be seen that all of them have insufficient use of the knowledge obtained during the evolution because the historical information of the population is not taken into consideration, which inevitably leads to a bad perception of the landscapes of the objectives. Moreover, the adaptations of the control parameters including F and CR in these state-of-the-art DE variants are interlaced with one another. A bad F and a good CR may produce a good trial vector candidate, then the bad F is of misuse in the parameter control and vice versa. In this paper, a novel DE variant, called Hip-DE, meaning the latest fashion of DE, with historical population based mutation strategy was proposed to tackle the above mentioned weaknesses. Moreover, novel parameter adaptive mechanisms for control parameters F and CR as well as a platform based step-decrease scheme of population size were proposed to enhance capacity of the mutation strategy. By incorporating these three advancements, the novel Hip-DE algorithm secured an overall better performance on the tested benchmarks in comparison with the recent proposed state-of-the-art DE variants.