CS 5970 Homework 5 — EC Theory, Part 4, Models of Canonical EAs

Due Monday, Oct 25, 2010

NOTE: The hardcopies of the parts of this assignment are due at the beginning of the class period. This means that if you are even a minute late, you lose 20%. If you are worried about potentially being late, turn in your assignments ahead of time. Do this by submitting them to me during office hours or by sliding them under my office door. Electronic copies are due by 4:00 pm on the due date. Submit them through D2L before the time they are due. Do not send assignments to me through email or leave them in my departmental mail box.

1. Motivation

Population models of EAs can allow us to determine their expected behavior.

2. Goal

The goal of this assignment is to give you experience with population models of common EAs.

3. Assignment

As discussed in your textbook and augmented in our discussion in class, one point crossover can be modeled as the probability of creating, as the first offspring, an individual with genome i from parents with genomes j and k as the first and second parents, respectively, using the equation

onepointijk = (a−b)/(L−1) if a > b , and
onepointijk = 0 otherwise,
where a is the locus of the first allele that differs between genomes i and j (a = L if genomes i and j do not differ), b is the locus of the last allele that differs between genomes i and k (b = 1 if genomes i and k do not differ), and L is the length of the genomes.

Devise corresponding equations for the following:

  1. Two point crossover.
  2. Uniform crossover.
  3. Parameterized uniform crossover.
In addition to devising the equations, you need to define all terms (variables) and explain each equation and justify it.

4. What to Turn In

You will turn in both a typed hard copy and a machine readable electronic copy of your homework that gives the equations required, defines all terms used in them, and explains and justifies them.