CS 495: Evolutionary Computation, Fall 2002 Instructor: Jeffrey Horn
(4) ENCODING: LINKAGE (order of decision variables on the chromosome)
(A) Come up with a couple of alternative orderings of the 21 pipe diameters for the NYC Tunnels Problem, assuming a binary chromosome of 84 bits, as before. (see diagram on next page for ideas)
(B) In the mid-1990s, a start-up company (Evolvica?) came up with a clever GA product. They packaged a GA as an Excel macro. If you had a complex spreadsheet model of your finances (e.g., company operations, your investment strategy, etc.), and you could identify certain cells as your decision variables, and a single cell as your objective (e.g., cost, to be minimized, or profit, to be maximized, etc.), then you could invoke a GA to "evolve" the settings of the dec. variable cells while trying to optimize the objective fitness cell. (Note, you also had to tell the GA the RANGE of values for each cell.) As far as I can tell, it had limited success. Perhaps one aspect limiting it was the fact that the GA had no idea HOW to order the decision variables on the chromosome (which is important for one and two-point crossover, where contiguous genes (dec. variable values) tend to get passed on to offspring together). Now, we can't expect the average spreadsheet user to understand us if we ask him/her to tell us an ordering of the decision variables on the string. Can you suggest any other way to get that information, or at least some idea of which dec. variables to place close to each other in the encoding? (E.,g., any information in the spreadsheet itself, or simple questions we can ask the user, or maybe a way to run the GA differently such that we don't need to know the ordering information; we can learn it or guess it).
(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.