# CS 5970 Homework 4 — Evolutionary
Computation Basics

## Due Monday, October 12, 2015

## 1. Motivation

Mutation is perhaps the most important source of variation within most
evolutionary computation systems. The generation of diversity through
mutation should be understood to comprehend complex evolutionary systems in
which both exploration and exploitation take place.

## 2. Goal

The goal of this assignment is to give you experience with a
variation-only model of evolutionary computation.

## 3. Assignment

Certainly mutation will, over time, introduce variation into a
population that initially contains none. But at what rate? Your job in
this assignment is to provide an estimate of that rate, at least for a
particular evolutionary computation setup.

Assume that you begin with a population P(0) of 100 individuals, each
with the same genotype. The genotype of each individual consists of a
single chromosome of 100 bits. The mutation rate is 1% per locus and, when
a mutation occurs at a given locus, the corresponding bit is inverted.
Answer the following questions:

- What percentage of possible alleles are present in the initial
population, that is, population P(0)?
- What percentage of possible alleles would you expect there to be in the
population after one generation, that is, in population P(1)?
- After 10 generations/P(10)?
- After 100 generations/P(100)?
- After 200 generations/P(200)?

You may use either a mathematical/logical or an empirical approach to
answering these questions. In addition to answering the questions, you
will need to **explain** your approach and **justify** it.
## 4. What to Turn In

You will turn in via D2L a machine readable electronic copy of your
homework that answers the questions above, including your explanation and
justification. If your approach is empirical, you will also need to submit
an electronic copy of your code and an electronic copy of all data
generated.