Genetic Algorithm Exercise in Matlab

Preliminaries

Preliminaries: Open this script in the Matlab editor and change the value of the SN variable at the top  of the file to your student number, and the value of the range variable to  6 + the final digit of your  student number.

Then save and run  the  file and observe the plots that are generated. Run  the  file  again and this time set visflag=0 (also defined at the top of the script).  Using visflag=1 allows you to see  graphically how the population changes from one generation to the next in the GA, but is slow to run.

Switch between these settings as needed for the different parts of the assignment. 

Exercises 
1. Study  the  ‘Run_GA_basic’  script  and  the  various  functions  it  calls,  and  hence  determine  the specification of the chromosomes and the precise form of the GA implementation that is being  used, that is, provide details of
(i)  the problem encoding and the precision with which x and y are being computed, 
(ii) the definition of the fitness function, 
(iii) the approach to selection, and 
(iv) the crossover and mutation mechanisms used.

2. Conduct a systematic investigation of the performance of the implemented GA with gen_max=20   for mutation rates (mut_rate) of 0, 0.05, 0.1 and 0.4, and population size (pop_size) of 5, 10 and  20.   You  need  to run  the  algorithm  several  times  for each  combination  of mutation  rate and  population size and consider the average behaviour to take account of the stochastic nature of  GAs. Comment on the patterns that you observe. What combination works best?  

3. With the mutation rate set at 0.05, explore the impact on performance of varying gen_max and  pop_size,  where  the  product  of  gen_max and  pop_size  is  constrained  to  be  100.  (e.g.  test  combinations such as 10 and 10, 20 and 5, 5 and 20 and 25 and 4.  From your investigation, what  do you conclude?   

4. Modify the ‘Run_GA_basic’ script so that the GA incorporates elitist selection, where the k fittest parents  are copied  directly  into  the  next  generation  together  with  the  pop_size  ?  k  fittest  offspring. Explore the performance of elitist GA for different values of k, gen_max and pop_size when  the mutation  rate is 0.1. Hence deduce appropriate values of  these parameters  for  this  problem.  How  does  the  performance  of  the  elitist GA  compare  with  the  basic  GA  implementation? 

5. Rather than using binary genes and chromosomes, design and implement a GA that uses real? valued  genes to  solve  the  problem.  This  means  that  chromosomes,  crossover  and  mutation  operators  work  directly with  real  valued  genes,  and  the  associated  functions  will  need  to  be  changed accordingly.               

6. Compare  and  contrast  the  performance  of  binary  versus  real  valued  GAs  for  solving  the  optimisation problem.