  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.
