Recent advances in differential evolution: a survey and experimental analysis

Abstract

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.

Self-adaptive Ensemble Based Differential Evolution

“…For the control parameters CR and F, there is no so called distinctive rules to set their values but the setting affects the functionality of DE [8]. For example, a large value of F increases the exploration ability but decreases the exploitation ability and vice versa.…”

“…The nature of optimization problems such as noise and high dimensionality also affects parameter setting [8]. Higher dimensionality in an optimization problem requires higher values of NP.…”

An MILP model and a hybrid evolutionary algorithm for integrated operation optimisation of multi-head surface mounting machines in PCB assembly

“…An EA with two evolutionary operators are designed as follows. 2) DDE with DE/rand/1 operator for feeder assignment DE/rand/1 mutation (Das and Suganthan, 2011;Neri and Tirronen, 2010) which has been indicated to be one of the most efficient operators is adopted here.…”

Combined mutation differential evolution to solve systems of nonlinear equations

“…DE has three parameters: i) amplification factor of the differential variation, F; ii) crossover control parameter, CR; iii) population size, m. The above three operations are repeated until a termination criterion is reached. A survey with an experimental study concerned with variants of DE is found in [9]. In this section, we describe the main steps of the basic DE and a modified operation of mutation that combines three classic mutation strategies.…”