Micro-differential evolution: Diversity enhancement and a comparative study

Differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. Micro-DE (MDE) algorithms utilize a very small population size, which can converge faster to a reasonable solution. Such algorithms are vulnerable to premature convergence and high risk of stagnation. This paper proposes a MDE algorithm with vectorized random mutation factor (MDEVM), 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, a new mutation scheme for population sizes less than four is 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 pre-mature convergence. The MDEVM is implemented using a population-based parallel model and studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance in convergence speed of the proposed MDEVM algorithm.