Continuous Valued Multimodality Generator for Evolutionary Algorithms

/*

Continuous multimodal test functions coded by James Kennedy 
kennedy_jim@bls.gov June 20, 1997, based on William Spears' binary functions.

*/

/*

Here is some code for the continuous-valued multimodal test functions.
These were done in Borland C / C++, and may have functions specific to
that compiler, though I don't think so.

initialization() creates j peaks on i dimensions, uniformly distributed
through the interval [0.0, 1.0].  Of course that interval can be
adjusted easily.  I have the function print the variables, too --
optional of course.

multeval(z) evaluates the performance of individual z.  In this version,
xx[z][k] is restricted to [0.0, 1.0] with a logistic transformation,
included as sigmoid().  Others may prefer to allow xx[][] to range
wider.  The multeval() function returns a value to be minimized, which
is the squared sum of the differences between sigmoid(xx[z][k]) and
landscape[k]; it also writes a global variable, target[], which
indicates which peak the individual was closest to.  I use target[] in
my trials to observe the convergence of neighboring individuals on a
single peak.

*/

void initialization()
{
     int i, j;
     printf("Landscape\n");
     for(i = 0; i < NUMBEROFPEAKS; i++) 
     {
       for(j = 0; j < DIMENSION; j++) 
       {
        landscape[i][j] = rand() / 32767.0;
        printf("%4.3f ",landscape[i][j]);
       }
        printf("\n");
     }
printf("\nPress any key to continue");
getche();
}

/* 
   This is the evaluation function.  Individuals are
   stored in a 2D array xx[][].  This code evaluates the zth
   individual xx[z][].
*/

double multeval (z)
int z;
{
       int j, k;
       double score, temp;

       temp = score = (double) DIMENSION;

       for (j = 0; j < NUMBEROFPEAKS; j++) 
       {
        score=0.0;
        for (k = 0; k < DIMENSION; k++) 
         {
                score = score + 
                     ((sigmoid(xx[z][k]) - landscape[j][k]) *
                      (sigmoid(xx[z][k]) - landscape[j][k]));
         }
         if (score < temp)
          {
           temp = score;
           target[z]=j;
          }
        }       
       return(temp / (double) DIMENSION);
}

float sigmoid(float a)
   {
    float sig;
    sig = 1 / (1 + exp(-a));
    return sig;
   }