Two-stage differential evolution with novel parameter control

In this paper, we propose a Two-stage Differential Evolution (TDE) with novel parameter control for real parameter single objective global optimization. In the TDE algorithm, the whole evolution is divided into two stages and each stage employs a unique mutation strategy. The mutation strategy in the first stage is a novel historical-solution based mutation strategy, which can get better perception of the landscape of the objective; the mutation strategy in the second stage is an inferior-solution based mutation strategy, which can maintain better diversity of trial vector candidates while keeping better convergence speed. Furthermore, the parameter control of our TDE is novel, which means that these adaptations of control parameters are different from those in the literature: First, the adaptation schemes both for scale factor F and crossover rate CR are fitness-independent. Second, different from the fixed population size and the gradually reduced population size, the population adaptation in TDE has two different stages. Third, a stagnation indicator is proposed and a population enhancement technique can be launched if necessary when a certain individual is in the stagnation status. We examine the TDE algorithm under a relative large number of benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective global optimization, and the experiment results show the competitiveness of our TDE algorithm with several recently proposed state-of-the-art DE variants, e.g. it obtained 20 similar or better performance improvements out of the total 30 benchmarks in comparison with the winner algorithm, the LSHADE algorithm, of the CEC2014 competition and it also obtained 19 similar or better performance improvements out of the total 30 benchmarks in comparison with the winner DE variant, the jSO algorithm, of the CEC2017 competition.