  The differential evolution (DE) algorithm suffers from high computational
time due to slow nature of evaluation. In contrast, micro-DE (MDE) algorithms
employ a very small population size, which can converge faster to a reasonable
solution. However, these algorithms are vulnerable to a premature convergence
as well as to high risk of stagnation. In this paper, MDE algorithm with
vectorized random mutation factor (MDEVM) is proposed, which utilizes the small
size population benefit while empowers the exploration ability of mutation
factor through randomizing it in the decision variable level. The idea is
supported by analyzing mutation factor using Monte-Carlo based simulations. To
facilitate the usage of MDE algorithms with very-small population sizes, new
mutation schemes for population sizes less than four are also proposed.
Furthermore, comprehensive comparative simulations and analysis on performance
of the MDE algorithms over various mutation schemes, population sizes, problem
types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities,
and mutation factor ranges are conducted by considering population diversity
analysis for stagnation and trapping in local optimum situations. The studies
are conducted on 28 benchmark functions provided for the IEEE CEC-2013
competition. Experimental results demonstrate high performance and convergence
speed of the proposed MDEVM algorithm.
