Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving various engineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon DE by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimensional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within both macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which includes some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Thus, a limited employment of these alternative moves appears to be the best option in successfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the introduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE functioning.123 62 F. Neri, V. Tirronen Numerical results show that, among the algorithms considered in this study, the most efficient additional components in a DE framework appear to be the population size reduction and the scale factor local search. Regarding the modified DE structures, the global and local neighborhood search and self-adaptive control parameter scheme, recently proposed in literature, seem to be the most promising modifications.

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A fast adaptive memetic algorithm (FAMA) is proposed which is used to design the optimal control system for a permanent-magnet synchronous motor. The FAMA is a memetic algorithm with a dynamic parameter setting and two local searchers adaptively launched, either one by one or simultaneously, according to the necessities of the evolution. The FAMA has been tested for both offline and online optimization. The former is based on a simulation of the whole system--control system and plant--using a model obtained through identification tests. The online optimization is model free because each fitness evaluation consists of an experimental test on the real motor drive. The proposed algorithm has been compared with other optimization approaches, and a matching analysis has been carried out offline and online. Excellent results are obtained in terms of optimality, convergence, and algorithmic efficiency. Moreover, the FAMA has given very robust results in the presence of noise in the experimental system.

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