Fractional Order Differential Evolution

Differential evolution (DE) is a widely recognized method to solve complex optimization problems as shown by many researchers. Yet, non-adaptive versions of DE suffer from insufficient exploration ability and uses no historical information for its performance enhancement. This work proposes Fractional Order Differential Evolution (FODE) to enhance DE performance from two aspects. Firstly, a bi-strategy co-deployment framework is proposed. The population-based and parameter-based strategies are combined to leverage their respective advantages. Secondly, the fractional order calculus is first applied to the differential vector to enhance DE's exploration ability by using the historical information of populations, and ensures the diversity of population in an evolutionary process. We use the 2017 IEEE Congress on Evolutionary Computation (CEC) test functions, and CEC2011 real-world problems to evaluate FODE's performance. Its sensitivity to parameter changes is discussed and an ablation study of multi-strategies is systematically performed. Furthermore, the variations of exploration and exploitation in FODE are visualized and analyzed. Experimental results show that FODE is superior to other state-of-the-art DE variants, the winners of CEC competitions, other fractional order calculus-based algorithms, and some powerful variants of classic algorithms.