# CS 5970 Homework 5 — Neuroevolutionary Basics

## 1. Motivation

One of the simplest forms of neuroevolution is to evolve the weights of a standard feedforward neural network (FFNN). To understand neuroevolution of weights, it makes sense to become familiar with the steps involved.

## 2. Goal

The goal of this assignment is to give you experience with carrying out and attempting to interpret (some of) the steps in evolving the weights of a FFNN. To keep this simple, our "FFNN" will consist of a single AN.

## 3. Assignment

1. Consider a single AN used for classification in a 2D space with an augmented vector as discussed in the Engelbrecht text. This AN is a summation unit (SU) and its activation function fAN is a step function with outputs γ1=1 for fAN(net) ≥ 0 and γ2=0 for fAN(net) < 0. (If this sounds familiar, that's good because this is the basic setup of Homework 1.) Draw this AN.
2. Consider in addition the following set of points and their associated labels:
• (−0.1, −0.8) γ1
• (0, 0) γ2
• (0.2, −0.2) γ2
• (1.3, 1.3) γ2
• (−1.2, −0.4) γ1
• (−0.5, 0.2) γ1
Draw (on graph or engineering paper or by using software) this set of data points.
3. Now, consider the following table of genome data for a population of AN weights. Each row of the table (other than the header row) gives the genome of an individual from the population and each column contains data as described by its header.
ID v1 v2 v3
A −1.0 −0.7   0.0
B −0.9   0.9   0.3
C   0.9 −0.3 −0.9
D −0.1   0.8 −0.4
E   1.0   0.5 −0.5
F −0.8   0.1   0.6
G −0.1   0.8   0.3
H   0.6   0.8   0.2
I −0.3 −0.2   1.0
J   0.6   0.4   0.3
Add to the graph of points the decision boundary encoded by each genome. Be sure to label each decision boundary with the individual's ID and be sure to indicate the γ1 side of the boundary.
4. Explain which decision boundaries appear to you to be closest to ideal.
5. Calculate and list the objective fitness for each individual, where objective fitness is simply the number of points correctly classified from the set of points given above.
6. Explain the maximum and minimum fitness possible using this objective function.
7. Explain whether the most fit decision boundaries (according to this fitness function) correspond to the decision boundaries that appeared to you to be closest to ideal.
8. Consider an alternative objective fitness function in which fitness is the number of points correctly classified minus the number of points incorrectly classified (again, from the set of points given above). Explain what effect, if any, using this alternative fitness function would have on a neuroevolutionary system that uses tournament selection.
9. Consider again the alternative objective fitness function just described. Explain what effect, if any, using this alternative fitness function would have on a neuroevolutionary system that uses proportional selection.
10. Select the two most fit individuals from the initial population (using the original fitness function given). Assume that they are crossed over with one another using uniform crossover to produce two new individuals. Call these new individuals "K" and "L." Assume further that K receives its first gene from its first parent and its other two genes from its other parent. Add to your graph the decision boundary encoded by each new genome. Be sure to label each decision boundary with the individual's ID and be sure to indicate the γ1 side of the boundary.
11. Calculate and list the objective fitness for each new individual, where objective fitness is simply the number of points correctly classified from the set of points given above.
12. Explain whether adding the new individuals to the population would raise or lower the average population fitness. Explain a phenomenon that appears to be at work here.

## 4. What to Turn In

You will turn in via D2L a machine readable electronic copy of your homework that completes the exercises given above.