ex27.c

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/* ----------------------------------------------------------------------------
  ex27.C
  mbwall 24mar96
  Copyright (c) 1995-1996  Massachusetts Institute of Technology

  The code for this example is adapted from an original implementation 
  by Thomas Grueninger (from Uni Stuttgart, visiting scholar at MIT)

 DESCRIPTION:
   This example shows how to use the Deterministic Crowding genetic algorithm.
You can specify one of 4 different functions (they are described in more detail
later in this file).
   (This code was originally used with a 3D OpenGL-based program to illustrate
the differences in convergence between various speciation methods.  Believe me,
it looks much better running in real-time in 3D, but, alas, there is not yet
any standard 3D cross-platform API, so you get this instead.)
---------------------------------------------------------------------------- */
#include <math.h>
#include <ga/GASStateGA.h>
#include <ga/GAList.h>
#include <ga/GA1DArrayGenome.h>

// If your compiler does not do automatic instantiation (e.g. g++ 2.6.8),
// then define the NO_AUTO_INST directive.
#ifdef NO_AUTO_INST
#include <ga/GAList.C>
#include <ga/GA1DArrayGenome.C>
#if defined(__GNUG__)
template class GAList<int>;
template class GA1DArrayGenome<float>;
#else
GAList<int>;
GA1DArrayGenome<float>;
#endif
#endif





// This is the class definition for the deterministic crowding genetic 
// algorithm.  It is based upon the steady-state genetic algorithm, but we
// modify the replacement so that it does deterministic crowding as described
// by Goldberg (not in his book) and his students.
class DCrowdingGA : public GASteadyStateGA {
public:
  GADefineIdentity("DeterministicCrowdingGA", 241);
  DCrowdingGA(const GAGenome& g) : GASteadyStateGA(g) {}
  virtual ~DCrowdingGA() {}
  virtual void step();
  DCrowdingGA & operator++() { step(); return *this; }
};

void
DCrowdingGA::step() { 
  int i,*ip;
  float d1,d2;
  GAGenome *mom, *dad;
  GAList<int> IndPool;

  while (IndPool.head()) IndPool.destroy();

  for (i=0; i<pop->size(); i++) 
    IndPool.insert(i);
    
  do {
    //select mom
    IndPool.warp(GARandomInt(0,IndPool.size()-1));
    ip=IndPool.remove();
    mom = &pop->individual(*ip);
    delete ip;
    //select dad
    IndPool.warp(GARandomInt(0,IndPool.size()-1));
    ip=IndPool.remove();
    dad = &pop->individual(*ip);
    delete ip;
    //create child
    stats.numsel += 2;		
    stats.numcro += (*(mom->sexual()))(*mom, *dad, &tmpPop->individual(0), 0);
    stats.nummut += tmpPop->individual(0).mutate(pMutation());
    stats.numeval += 1;	
    //replace closest parent
    d1 = tmpPop->individual(0).compare(*mom);
    d2 = tmpPop->individual(0).compare(*dad);
    if (d1 < d2) {
      if (minmax == MINIMIZE) {
	if (tmpPop->individual(0).score() < mom->score()) {
	  mom->copy(tmpPop->individual(0));
	  stats.numrep += 1;	
	}
      }
      else {
	if (tmpPop->individual(0).score() > mom->score()) {
	  mom->copy(tmpPop->individual(0));
	  stats.numrep += 1;	
	}
      }
    }
    else {
      if (minmax == MINIMIZE) {
	if (tmpPop->individual(0).score() < dad->score()) {
	  dad->copy(tmpPop->individual(0));
	  stats.numrep += 1;	
	}
      }
      else {
	if (tmpPop->individual(0).score() > dad->score()) {
	  dad->copy(tmpPop->individual(0));
	  stats.numrep += 1;	
	}
      }
    }
  } while (IndPool.size()>1);

  pop->evaluate(gaTrue);
  stats.update(*pop);	
}






// Set up the various 2-dimensional, real number functions that we will use.
typedef float (*Function)(float, float);

float Function1(float, float);
float Function2(float, float);
float Function3(float, float);
float Function4(float, float);
float ai[25],bi[25];

static int which = 0;
static Function obj[] = { Function1, Function2, Function3, Function4 };
static float minx[] = {-6, -60, -500, -10 };
static float maxx[] = { 6,  60,  500, 10 };
static float miny[] = {-6, -60, -500, -10 };
static float maxy[] = { 6,  60,  500, 10 };



// These are the declarations for our genome operators (we do not use the
// defaults from GAlib for this example).
float Objective(GAGenome&);
int   Mutator(GAGenome&, float);
void  Initializer(GAGenome&);
int   Crossover(const GAGenome&, const GAGenome&, GAGenome*, GAGenome*);
float Comparator(const GAGenome&, const GAGenome&);


int
main(int argc, char** argv) {
  cout << "Example 27\n\n";
  cout << "Deterministic crowding demonstration program.\n\n";
  cout << "In addition to the standard GAlib command-line arguments,\n";
  cout << "you can specify one of the four following functions:\n";
  cout << "   0 - modified Himmelblau's function\n";
  cout << "   1 - Foxholes (25)\n";
  cout << "   2 - Schwefel's nasty (1 glob. Max bei (420.96/420.96)\n";
  cout << "   3 - Mexican Hat (optimum at 0,0)\n";
  cout << endl;

  int i;

// See if we've been given a seed to use (for testing purposes).  When you
// specify a random seed, the evolution will be exactly the same each time
// you use that seed number.

  for(i=1; i<argc; i++) {
    if(strcmp(argv[i++],"seed") == 0)
      GARandomSeed((unsigned int)atoi(argv[i]));
  }

  for (i=0; i<25; i++) {
    ai[i] = 16 * ((i % 5) -2);
    bi[i] = 16 * ((i / 5) -2);
  }

  GA1DArrayGenome<float> genome(2, Objective);
  genome.initializer(::Initializer);
  genome.mutator(::Mutator);
  genome.comparator(::Comparator);
  genome.crossover(::Crossover);

  DCrowdingGA ga(genome);
  ga.maximize();
  ga.populationSize(100);
  ga.nGenerations(100);
  ga.pMutation(0.05);
  ga.pCrossover(1.0);
  ga.selectScores(GAStatistics::AllScores);
  ga.parameters(argc, argv, gaFalse);

  for (i=1; i<argc; i++){
    if(strcmp("func", argv[i]) == 0 || strcmp("f", argv[i]) == 0){
      if(++i >= argc){
        cerr << argv[0] << ": the function option needs a number.\n";
        exit(1);
      }
      else{
        which = atoi(argv[i]);
        continue;
      }
    }
    else if(strcmp("seed", argv[i]) == 0){
      if(++i < argc) continue;
      continue;
    }
    else {
      cerr << argv[0] << ":  unrecognized arguement: " << argv[i] << "\n\n";
      cerr << "valid arguments include standard GAlib arguments plus:\n";
      cerr << "  f\tfunction to use (" << which << ")\n";
      cerr << "\n";
      exit(1);
    }
  }

  ga.evolve();
  cout << "best individual is " << ga.statistics().bestIndividual() << "\n\n";
  cout << ga.statistics() << "\n";

  return 0;
}














/*****************************************************************************/
/* Type:        2D FUNCTION                                                  */
/* Name:        Objective2D_1                                                */
/* Description: 2D tooth                                                     */
/* Boundaries:  -6 < x < 6                                                   */
/*              -6 < y < 6                                                   */
/* Source:      modified Himmelblau's function from Deb, K.                  */
/*              'GA in multimodal function optimazation' Masters thesis      */
/*		TCGA Rep. 89002 / U. of Alabama                              */
/*****************************************************************************/
float
Function1(float x, float y) {
  float z = -((x*x+y-11)*(x*x+y-11)+(x+y*y-7)*(x+y*y-7))/200 + 10;
  return z;
}


/*****************************************************************************/
/* Type:        2D FUNCTION                                                  */
/* Name:        Objective2D_2                                                */
/* Description: Foxholes (25)                                                */
/* Boundaries:  -60 < x < 60                                                 */
/*              -60 < y < 60                                                 */
/* Source:      Shekel's Foxholes problem from De Jong's Diss.(1975)         */
/*              'GA in multimodal function optimazation' Masters thesis      */
/*		TCGA Rep. 89002 / U. of Alabama                              */
/*****************************************************************************/
float
Function2(float x, float y) {
  int i;
  float sum = 0;
  for (i=0; i<25; i++) {
    sum += (1 / (1 + i + pow((x-ai[i]),6) + pow((y-bi[i]),6)));
  }
  float z = 100.0 - (1 / (0.02 + sum));
  return z;
}


/*****************************************************************************/
/* Type:        2D FUNCTION                                                  */
/* Name:        Objective2D_3                                                */
/* Description: Schwefel's nasty (1 glob. Max bei (420.96/420.96)            */
/* Boundaries:  -500 < x < 500                                               */
/*              -500 < y < 500                                               */
/* Source:      Schwefel's function in Schoeneburg                           */
/*****************************************************************************/
float
Function3(float x, float y) {
  float z = fabs(x) * sin(sqrt(fabs(x))) + fabs(y) * sin(sqrt(fabs(y)));
  //float z = 100  *  ( sin(sqrt(fabs(x))) * sin(sqrt(fabs(y))) );
  return (z);
}


/*****************************************************************************/
/* Type:        2D FUNCTION                                                  */
/* Name:        Objective2D_4                                                */
/* Description: Mexican Hat                                                  */
/* Boundaries:  -10 < x < 10                                                 */
/*              -10 < y < 10                                                 */
/* Source:                                                                   */
/*****************************************************************************/
float
Function4(float x, float y) {
  float z = sin(sqrt(x*x + y*y))*sin(sqrt(x*x + y*y)) - 0.5;
  z /= ((1.0 + 0.001*(x*x + y*y))*(1.0 + 0.001*(x*x + y*y)));
  z = (0.5 - z);
  return (z);
}













// These are the operators that we'll use for the real number genome.
float
Objective(GAGenome& g) {
  GA1DArrayGenome<float>& genome = (GA1DArrayGenome<float>&)g;
  return (obj[which])(genome.gene(0), genome.gene(1));
}

void
Initializer(GAGenome& g) {
  GA1DArrayGenome<float>& genome = (GA1DArrayGenome<float>&)g;
  genome.gene(0, GARandomFloat(minx[which], maxx[which]));
  genome.gene(1, GARandomFloat(miny[which], maxy[which]));
}

int
Mutator(GAGenome& g, float pmut) {
  GA1DArrayGenome<float>& genome = (GA1DArrayGenome<float>&)g;
  int nmut = 0;

  if(GAFlipCoin(pmut)){
    genome.gene(0, genome.gene(0) + 
		10*GARandomFloat() * (GARandomFloat() - GARandomFloat()));
    genome.gene(1, genome.gene(1) + 
		10*GARandomFloat() * (GARandomFloat() - GARandomFloat()));
    nmut++;
  }

  if(genome.gene(0) < minx[which]) genome.gene(0, minx[which]);
  if(genome.gene(0) > maxx[which]) genome.gene(0, maxx[which]);
  if(genome.gene(1) < minx[which]) genome.gene(1, minx[which]);
  if(genome.gene(1) > maxx[which]) genome.gene(1, maxx[which]);

  return nmut;
}

int
Crossover(const GAGenome& g1,const GAGenome& g2,GAGenome* c1,GAGenome* c2){
  GA1DArrayGenome<float>& mom = (GA1DArrayGenome<float>&)g1;
  GA1DArrayGenome<float>& dad = (GA1DArrayGenome<float>&)g2;

  int n = 0;
  float distance = 0.0, midpoint = 0.0;

  if(c1) {
    GA1DArrayGenome<float>& sis = (GA1DArrayGenome<float>&)*c1;
    distance = midpoint = 0.0;

    midpoint = (mom.gene(0) + dad.gene(0)) / 2;
    distance = fabs(mom.gene(0) - dad.gene(0));
    sis.gene(0, midpoint + distance * (GARandomFloat() - GARandomFloat()));

    midpoint = (mom.gene(1) + dad.gene(1)) / 2;
    distance = fabs(mom.gene(1) - dad.gene(1));
    sis.gene(1, midpoint + distance * (GARandomFloat() - GARandomFloat()));

    if(sis.gene(0) < minx[which]) sis.gene(0, minx[which]);
    if(sis.gene(0) > maxx[which]) sis.gene(0, maxx[which]);
    if(sis.gene(1) < minx[which]) sis.gene(1, minx[which]);
    if(sis.gene(1) > maxx[which]) sis.gene(1, maxx[which]);

    n += 1;
  }
  if(c2) {
    GA1DArrayGenome<float>& bro = (GA1DArrayGenome<float>&)*c2;
    distance = midpoint = 0.0;

    midpoint = (mom.gene(0) + dad.gene(0)) / 2;
    distance = fabs(mom.gene(0) - dad.gene(0));
    bro.gene(0, midpoint + distance * (GARandomFloat() - GARandomFloat()));

    midpoint = (mom.gene(1) + dad.gene(1)) / 2;
    distance = fabs(mom.gene(1) - dad.gene(1));
    bro.gene(1, midpoint + distance * (GARandomFloat() - GARandomFloat()));

    if(bro.gene(0) < minx[which]) bro.gene(0, minx[which]);
    if(bro.gene(0) > maxx[which]) bro.gene(0, maxx[which]);
    if(bro.gene(1) < minx[which]) bro.gene(1, minx[which]);
    if(bro.gene(1) > maxx[which]) bro.gene(1, maxx[which]);

    n += 1;
  }

  return n;
}

float
Comparator(const GAGenome& g1, const GAGenome& g2) {
  GA1DArrayGenome<float>& a = (GA1DArrayGenome<float>&)g1;
  GA1DArrayGenome<float>& b = (GA1DArrayGenome<float>&)g2;

  float valx=(a.gene(0)-b.gene(0)) * (a.gene(0)-b.gene(0));
  float valy=(a.gene(1)-b.gene(1)) * (a.gene(1)-b.gene(1));
  return sqrt(valx+valy);
}