CS 495: Evolutionary Computation, Fall 2002 Instructor: Jeffrey Horn
(3) EVOLUTIONARY DYNAMICS: Convergence under Selection
(A) Draw a graph showing logistic convergence of a simple GA. Put time (in generations) on the x-axis, and "% of Pop." on the y-axis. Then assume that some super individual B appears in generation 5, let's say, and quickly takes over the population, approaching pop. % of 100. Plot its growth, showing the general shape of logistic growth.
(B) Now draw a similar graph as in (A), but this time assume that when the percent of Bs reaches about half of the pop. size, all of a sudden "son-of-a-B" appears. And f(son-of-a-B) > f(B). So now son-of-a-B will take over. Plot the general growth/decline rates for these two individuals.
(C) Now assume that we are using fitness sharing, such that the shared fitnesses, fsh (B) = f(B)/nB,t (that is, the shared fitness of B is the original fitness divided by the number of copies of B; ditto for "son-of-a-B"). So instead of either taking over, they should reach an equilibrium, when fsh (B) = fsh (son-of-a-B). Re-draw the plot from (B) above to show this convergence to equilibrium, qualitatively.