Differential Evolution with Event-Triggered Impulsive Control

Differential evolution (DE) is a simple but powerful evolutionary algorithm, which has been widely and successfully used in various areas. In this paper, an event-triggered impulsive control scheme (ETI) is introduced to improve the performance of DE. Impulsive control, the concept of which derives from control theory, aims at regulating the states of a network by instantly adjusting the states of a fraction of nodes at certain instants, and these instants are determined by event-triggered mechanism (ETM). By introducing impulsive control and ETM into DE, we hope to change the search performance of the population in a positive way after revising the positions of some individuals at certain moments. At the end of each generation, the impulsive control operation is triggered when the update rate of the population declines or equals to zero. In detail, inspired by the concepts of impulsive control, two types of impulses are presented within the framework of DE in this paper: stabilizing impulses and destabilizing impulses. Stabilizing impulses help the individuals with lower rankings instantly move to a desired state determined by the individuals with better fitness values. Destabilizing impulses randomly alter the positions of inferior individuals within the range of the current population. By means of intelligently modifying the positions of a part of individuals with these two kinds of impulses, both exploitation and exploration abilities of the whole population can be meliorated. In addition, the proposed ETI is flexible to be incorporated into several state-of-the-art DE variants. Experimental results over the CEC 2014 benchmark functions exhibit that the developed scheme is simple yet effective, which significantly improves the performance of the considered DE algorithms.