The multi-objective genetic algorithm toolkit
NSGA-II from
Kanpur Genetic Algorithms Laboratory will be the basis of this lab. The code
has been placed in the /ai/ga/ directory on Helios. Copy the
file /ai/ga/nsga2-gnuplot-v1.1.tar to your own directory and
unpack the code using the command tar -xf nsga2-gnuplot-v1.1.tar
(the unpacked code is also visible in /ai/ga/nsga2-gnuplot-v1.1).
We will be using this toolkit to implement the genetic algorithm example in
the book from pages 227 to 229. To implement the code, you need to define
the fitness function in the file problemdef.c. Edit the file
problemdef.c and comment out the line
# define ctp8so that it will not run that default fitness function. NSGA-II by default seeks to minimize the fitness function. Since the book example wants to maximize the result of the function, we will need to negate the results (multiply by -1) to get the correct behavior. Fill in the indicated blanks in this code to implement the fitness function for the book's problem:
#define myprob
#ifdef myprob
void test_problem (double *xreal, double *xbin, int **gene, double *obj, double *constr)
{
double mod, term1, term2, res;
double st1, st2, ct1, ct2, v1, v2, e1, e2;
int i;
char gstr[17];
mod = 6.0 / (256.0 - 1.0);
/**************************************************/
/* Decode bits of gene[0] as term1 and term2 here */
/**************************************************/
/* Convert the decoded terms into the range of -3 to 3 */
term1 = (term1 * mod) - 3.0;
term2 = (term2 * mod) - 3.0;
/* Compute the squares of the terms */
st1 = pow(term1, 2);
st2 = pow(term2, 2);
/* Compute the cubes of the terms */
ct1 = pow(term1, 3);
ct2 = pow(term2, 3);
/* Compute (1-x)^2 and (y+1)^2 */
v1 = pow((1-term1), 2);
v2 = pow((term2+1), 2);
/* Compute the two exponential terms */
e1 = exp((-1 * st1) - v2);
e2 = exp((-1 * st1) - st2);
/* Calculate the result of the function */
res = (v1 * e1) - ((term1 - ct1 - ct2) * e2);
/* Put the chromosome into a printable string, highest bit to lowest bit */
for(i = 0; i < 16; i++) {
gstr[i] = (gene[0][(15-i)] ? '1' : '0');
}
gstr[i] = '\0';
printf("\nvalues: gene=%s x=%f y=%f f(x,y)=%f", gstr, term1, term2, res);
obj[0] = -1 * res;
}
#endif
Compile the code with the command make. Test your code by running
the command nsga2r <rand_seed>. You can use any value from 0 to
1 for the random seed. This will start an interactive dialog. Answer the
questions as follows:
Enter the problem relevant and algorithm relevant parameters ... Enter the population size (a multiple of 4) : 8 Enter the number of generations : 5 Enter the number of objectives : 1 Enter the number of constraints : 0 Enter the number of real variables : 0 Enter the number of binary variables : 1 Enter the number of bits for binary variable 1 : 16 Enter the lower limit of binary variable 1 : 0 Enter the upper limit of binary variable 1 : 65536 Enter the probability of crossover of binary variable (0.6-1.0): 0.7 Enter the probability of mutation of binary variables (1/nbits): 0.001 Do you want to use gnuplot to display the results realtime (0 for NO) (1 for yes) : 0Play around with the population size and number of generations to see how they affect the results. Also try changing the mutation and crossover rates to see how those affect the results