19 Takeover Times in Graph Based Evolutionary Algorithms

This study shows that connectivity in graph based evolutionary algorithms is proportional to takeover times applied to standard genetic algorithms. Graph based evolutionary algorithms have been used to control the rate at which information spreads through population of solutions. Previous empirical studies have indicated that this rate of information transfer is proportional to the connectivity of the underlying graph. While this has given some insight into the differences between population structures, it is desirable to have a mathematical scheme that helps define this relationship. In this study, we calculate the takeover time for a superior solution present in a population for the complete and cycle graphs and compare it with results previously determined using empirical methods. Using these two graphs as extreme cases for comparison, it is shown that as the connectivity of the underlying graph decreases, the takeover time for a solution on a graph based evolutionary algorithm increases, confirming mathematical intuition for graph selection for a desired level of diversity preservation.