Micro-Differential Evolution: Diversity Enhancement and Comparative Study

Evolutionary algorithms (EAs), such as the differential evolution (DE) algorithm, suffer from high computational time due to large population size and nature of evaluation, to mention two major reasons. The micro-EAs employ a very small population size, which can converge to a reasonable solution quicker; while they are vulnerable to premature convergence as well as high risk of stagnation. One approach to overcome the stagnation problem is increasing the diversity of the population. In this thesis, a micro-differential evolution algorithm with vectorized random mutation factor (MDEVM) is proposed, which utilizes the small size population benefit while preventing stagnation through diversification of the population. The following contributions are conducted related to the micro-DE (MDE) algorithms in this thesis: providing Monte-Carlo-based simulations for the proposed vectorized random mutation factor (VRMF) method; proposing mutation schemes for DE algorithm with populations sizes less than four; comprehensive comparative simulations and analysis on performance of the MDE algorithms over variant mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, mutation factor ranges, and population diversity analysis in stagnation and trapping in local optimum schemes. The comparative studies are conducted on the 28 benchmark functions provided at the IEEE congress on evolutionary computation 2013 (CEC-2013) and comprehensive analyses are provided. Experimental results demonstrate high performance and convergence speed of the proposed MDEVM algorithm over variant types of functions.