# CS 5970 Homework 4 — Evolutionary Computation Basics

## 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:

1. What percentage of possible alleles are present in the initial population, that is, population P(0)?
2. What percentage of possible alleles would you expect there to be in the population after one generation, that is, in population P(1)?
3. After 10 generations/P(10)?
4. After 100 generations/P(100)?
5. 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.