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.

This paper proposes the super-fit memetic differential evolution (SFMDE). This algorithm employs a differential evolution (DE) framework hybridized with three meta-heuristics, each having different roles and features. Particle Swarm Optimization assists the DE in the beginning of the optimization process by helping to generate a super-fit individual. The two other meta-heuristics are local searchers adaptively coordinated by means of an index measuring quality of the super-fit individual with respect to the rest of the population. The choice of the local searcher and its application is then executed by means of a probabilistic scheme which makes use of the generalized beta distribution. These two local searchers are the Nelder mead algorithm and the Rosenbrock Algorithm. The SFMDE has been tested on two engineering problems; the first application is the optimal control drive design for a direct current (DC) motor, the second is the design of a digital filter for image processing purposes. Numerical results show that the SFMDE is a flexible and promising approach which has a high performance standard in terms of both final solutions detected and convergence speed.A. Caponio

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This paper proposes the scale factor local search differential evolution (SFLSDE). The SFLSDE is a differential evolution (DE) based memetic algorithm which employs, within a self-adaptive scheme, two local search algorithms. These local search algorithms aim at detecting a value of the scale factor corresponding to an offspring with a high performance, while the generation is executed. The local search algorithms thus assist in the global search and generate offspring with high performance which are subsequently supposed to promote the generation of enhanced solutions within the evolutionary framework. Despite its simplicity, the proposed algorithm seems to have very good performance on various test problems. Numerical results are shown in order to justify the use of a double local search instead of a single search. In addition, the SFLSDE has been compared with a standard DE and three other modern DE based metaheuristic for a large and varied set of test problems. Numerical results are given for relatively low and high dimensional cases. A statistical analysis of the optimization results has been included in order to compare the results in terms of final solution detected and convergence speed. The efficiency of the proposed algorithm seems to be very high especially for large scale problems and complex fitness landscapes.

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This article proposes an Enhanced Memetic Differential Evolution (EMDE) for designing digital filters which aim at detecting defects of the paper produced during an industrial process. Defect detection is handled by means of two Gabor filters and their design is performed by the EMDE. The EMDE is a novel adaptive evolutionary algorithm which combines the powerful explorative features of Differential Evolution with the exploitative features of three local search algorithms employing different pivot rules and neighborhood generating functions. These local search algorithms are the Hooke Jeeves Algorithm, a Stochastic Local Search, and Simulated Annealing. The local search algorithms are adaptively coordinated by means of a control parameter that measures fitness distribution among individuals of the population and a novel probabilistic scheme. Numerical results confirm that Differential Evolution is an efficient evolutionary framework for the image processing problem under investigation and show that the EMDE performs well. As a matter of fact, the application of the EMDE leads to a design of an efficiently tailored filter. A comparison with various popular metaheuristics proves the effectiveness of the EMDE in terms of convergence speed, stagnation prevention, and capability in detecting solutions having high performance.

This article proposes a distributed differential evolution which employs a novel self-adaptive scheme, namely scale factor inheritance. In the proposed algorithm, the population is distributed over several sub-populations allocated according to a ring topology. Each sub-population is characterized by its own scale factor value. With a probabilistic criterion, that individual displaying the best performance is migrated to the neighbor population and replaces a pseudo-randomly selected individual of the target sub-population. The target sub-population inherits not only this individual but also the scale factor if it seems promising at the current stage of evolution. In addition, a perturbation mechanism enhances the exploration feature of the algorithm. The proposed algorithm has been run on a set of various test problems and then compared to two sequential differential evolution algorithms and three distributed differential evolution algorithms recently proposed in literature and representing state-of-the-art in the field. Numerical results show that the proposed approach seems very efficient for most of the analyzed problems, and outperforms all other algorithms considered in this study.

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