Assignment 1 (getting a feel for local search and landscapes)	120 points
DUE: Fri Sep 19 at 5pm PST

This assignment is a good warmup.

It is also surprisingly easy to miscode this, so read carefully, code carefully.

The Algorithm

Write a simple local search.

• The genotype (represented by a chromosome) will be the least significant 20 bits of an unsigned int.
• The genotype to phenotype mapping will:
  • First take the lowest 10 bits and linearly convert that to a double in the range 0 to 10 called x. All 10 bits zeros will be 0's and all 1's will be 10.
  • it will take the NEXT lowest 10 bits and linearly convert that to a double in the range -10 to 10 called y. All 10 bits zeros will be -10's and all 1's will be 10.
  • The phenotype (fitness) will be the value: f(x,y) = 1.0/((x-1.0)^2 + (y-3.0)^2 + 1.0) where ^ means raised to the power. [test point: f(5,1) = .047619]
• The algorithm will be a loop waiting until the number of fitness evaluations exceeds 10000. This is an important limit since these simple algorithms will run forever without it!!! This is a good thing to do in any stochastic algorithm.
• Each time through the loop it will mutate and evaluate the fitness.
• If the fitness is strictly greater than the old best fitness, the algorithm will remember the new fitness as best fitness and the new chromosome or if you like (x,y) as best seen so far. If it is not strictly greater than the old best fitness it does not replace the best fitness.
• Your algorithm will keep track of the number of fitness evaluations and the number of times an improved chromosome is found. It will also remember the number of fitness evaluations when it found the last best chromosome.
• The algorithm starts with a random 20 bit string.
• When you algorithm has looped to the limit it will print on one line in this order:
  1. The number of fitness evaluations when it found the best it found in the number of evaluations allowed.
  2. The number of improving moves made.
  3. The best x and y that gave that fitness.
  4. The best fitness found.
  That is 5 numbers: 2 integers and 3 doubles. For example:

  152 23 0.997067 3.000978 0.999990
  

The Experiments

For the experiments, you will run essentially the same program except for the different mutation operators and genotype to phenotype mappings. You will turn in your code and a report on what you find. More on the report in a moment. When you turn in your code you will need code for each of the four experiments and a single makefile (I will supply a sample makefile below).

Experiment 0

Then in the next three experiments compare them to this one. [Hint: here is a possible declartion for a mutation function:
unsigned int mutate(unsigned int chromosome, int size);]

Experiment 1

This program shall be named localBit. (note what is capitalized and what is not) For the first experiment, create a mutation operator that randomly flips exactly one bit in the chromosome that represents the current best fitness. It is important that you are always mutating the last best chromosome and not the last chromosome that failed. Why? The geneotype/phenotype mapping is as described above. Run this 20 times with different random seeds. What do you observe? Explain it. Be clear and concise. Show your data/results.

Experiment 2

This program shall be named localInc. For this experiment use a mutation operator that either increments or decrements the field of 10 bits with x in it or with y it. That is four possible mutations. This must be done very carefully since the field must wrap within each 10 bit field and not carry over into the adjacent field. Run this 20 times with different random seeds and report what you observe. Be clear and concise. Show your data/results and compare.

Experiment 3

This program shall be named localGray. For this experiment go back to the random bit flip mutation operator of experiment 1. This time alter the fitness function to use the bitDegray function from the bit utilities provided below to degray the 10 bit x and y strings before you map them to reals. This will treat your space as if it is in gray code. Run this 20 times with different random seeds and report what you observe. Compare your observations with the previous two experiments and the control.

What to turn in

The Code

make localRand 
make localBit 
make localInc
make localGray

The Report

Your report should be in a pdf file named exactly report.pdf. It should say:

• What is the point of the experiments? What do you think you learned? There is more going on here than the obvious.
• What software you wrote, as required above, to show what you think you learned.
• What you observed, being sure to supply data and statistics if any. [Hint: at least give me the mean of some of the values I have asked you to observe.]
• What your conclusions are and how they relate to the point of the experiment. [Hint: each experiment has a purpose.]
• Your report should include your data for 20 runs of each experiment as well as any summary statistics in a separate table that you would like.

Grading this Assignment

I will grade this based first be seeing that your code compilers, runs and returns a sensible answer. I will read the report to make sure it is clear and that you understand what happened when you ran the experiments. 50% of your score on each part. Your report needs to be concise and to the point. Make your points about each experiment and what you learned from that experiment.

Helpful Stuff

• A tar file of some possibly useful code for your assignments in this class. If anyone modifies the code to improve them please send me the updates and what you did. If it looks useful to the class I will post them. Please do not share code (see policy).
• A makefile tutorial
• A random number generator source
• An example makefile for this assignment. You don't have to use this. It is just there as an example of one way to do a simple makefile. Not that leading space is always tabs in a makefile!

Submission