CS 5970 Homework 3 — EC Theory, Part 2, Variation-Only Models

Due Wednesday, Oct 6, 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

It is known that in evolutionary systems with only variation (which De Jong refers to as “reproduction-only” models) and no mechanism for selection among the resulting varieties, populations will shift composition, potentially gaining diversity (as measured by total distinct genomes), and potentially converging to a fixed point known as the Robbins Equilibrium. This convergence is much different than the type of convergence seen in selection-only models. Convergence is an important feature of variation-only evolutionary systems that should be understood to comprehend more complex evolutionary systems in which both selection and variation can take place.

2. Goal

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

3. Assignment

Imagine a variation-only evolutionary system with fixed-size, discrete-valued, linear genomes with four genes each (L=4) and six possible values (alleles) for each gene (A, B, C, D, E, and F). Consider an initial population P(0) consisting of 128 copies of AAAA, 128 of BBBB, 128 of CCCC, and 128 of DDDD. (There are no genomes containing E or F in P(0).) Answer the following questions.

  1. How large is G, the set of all possible genotypes?
  2. What will the Robbins Equilibrium be if the only variation operator is two-parent, 1-point crossover?
  3. What will the Robbins Equilibrium be if the only variation operator is two-parent, 1-2-point crossover?
  4. What will the Robbins Equilibrium be if the only variation operator is two-parent, 2-point crossover?
  5. What will the Robbins Equilibrium be if the only variation operator is two-parent, uniform crossover?
  6. What will the Robbins Equilibrium be if the only variation operator is discrete mutation?
In addition to answering the questions, you need to explain each answer 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 answers the questions above, including your explanations and justifications. If your approach is empirical, you will also need to submit both hard and electronic copies of your code and an electronic copy of all data generated.