Mathematical Modelling of Migration Process to Measure Population Diversity of Distributed Evolutionary Algorithms

Background/Objectives: Evolutionary Algorithms (EAs) have a major role in solving optimization problems. Distributed Evolutionary Algorithms (dEAs) improve the performance of classical EAs. In dEAs, the initial population is divided into a number of subpopulations and an independent as well as cooperative coevolution happens among the subpopulations. Methods/Statistical Analysis: The success of dEAs is mainly attributed to the migration process they follow, during the evolution. The migration process alters the diversity of the subpopulations. The contribution of the migration process over the success of dEAs can be better understood and/or improved in the light of changes it brings in the diversity of subpopulations. Three methodologies used in the modelling process are the theoretical approach, statistical approach and the empirical approach. Findings: This paper is to analyze and design a mathematical model of the migration process, for its better understanding. A statistical equation to measure the diversity changes in the subpopulation during the migration process is also derived. The derived equation is validated on different types of populations. Application/Improvement: The derived equation can be applied to study and improve the performance of distributed evolutionary algorithms.