Super-fit and population size reduction in compact Differential Evolution

Although Differential Evolution is an efficient and versatile optimizer, it has a wide margin of improvement. During the latest years much effort of computer scientists studying Differential Evolution has been oriented towards the improvement of the algorithmic paradigm by adding and modifying components. In particular, two modifications lead to important improvements to the original algorithmic performance. The first is the super-fit mechanism, that is the injection at the beginning of the optimization process of a solution previously improved by another algorithm. The second is the progressive reduction of the population size during the evolution of the population. Recently, the algorithmic paradigm of compact Differential Evolution has been introduced. This class of algorithm does not process a population of solutions but its probabilistic representation. In this way, the Differential Evolution can be employed on a device characterized by a limited memory, such as microcontroller or a Graphics Processing Unit. This paper proposes the implementation of the two modifications mentioned above in the context of compact optimization. The compact versions of memetic super-fit mechanism and population size reduction have been tested in this paper and their benefits highlighted. The main finding of this paper is that although separately these modifications do not robustly lead to significant performance improvements, the combined action of the two mechanism appears to be extremely efficient in compact optimization. The resulting algorithm succeeds at handling very diverse fitness landscapes and appears to improve on a regular basis the performance of a standard compact Differential Evolution.