State-of-the-Art Differential Evolution Algorithms Selection and Modifications for Difficult Functions

Differential evolution (DE) is powerful for global optimization problems and constantly improved. However, satisfactory solutions of some functions can be hardly obtained so far. According to the experimental data of many state-of-the-art DE algorithms from the literature and our pre-experiment, solutions for F12 among the 25 CEC 2005 benchmark functions have an outstanding large mean error to the optimal value, while solutions for F15, F21, and F23-F24 all fall into one or several values. It can be seen that, in the involved state-of-the-art DE algorithms, JADE obtains the best solutions for F15, while EDEV obtains the best solutions for F12. In this paper, we modify the two DE algorithms for the two functions, respectively. Experimental results show that our modifications leads to significant improvement on solutions. As a result, solutions for these two functions are improved to an unprecedented degree.