An adaptive differential evolution with exploitation and exploration by extreme individuals

In a natural population, extreme individuals are very important for survival of the population. When the main population is destroyed by catastrophes, the few extreme individuals gain significance and will insure the survival of the population. Differential Evolution (DE) has been successfully applied to various optimization problems. However, DE sometimes trapped into some local solutions, which is a kind of a catastrophe. In this study, the extreme individuals are paid attention to. The best individuals perform exploitation or local search to keep extremely good positions. The worst individuals perform exploration or global search to keep positions far from the best individuals. Other individuals perform adaptive search based on JADE which is one of the most successful algorithms on controlling algorithm parameters. In JADE, the values of two algorithm parameters are generated according to two probability density functions which are learned by the values in success cases where the child is better than the parent. The advantage of JADE with exploitation and exploration by extreme individuals is shown by solving thirteen benchmark problems.