problems with minimizing an objective function

[Douglas McNab]

Hi List Users,

I am having problems minimizing my objective function using GALIB.

I am using an array of 8 real numbers as my genome with limits set by
other variables in my code.

Here is an extract of my code for running the GA:

GARealAlleleSetArray alleles;
alleles.add(m_xLower, m_xUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_yLower, m_yUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_zLower, m_zUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_tiltLower, m_tiltUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_skewLower, m_skewUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_orientationLower, m_orientationUpper, 0.5,
GAAllele::INCLUSIVE, GAAllele::INCLUSIVE);
alleles.add(m_widthLower, m_widthUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
alleles.add(m_lengthLower, m_lengthUpper, 0.5,
GAAllele::INCLUSIVE,GAAllele::INCLUSIVE);
		
GARealGenome genome(alleles, ObjectiveFunction);

// set the operators on the genome, depending on what kind
// of genome we have and what operators are desired.  note that
// we could just use the defaults that are in GAlib, but by
// doing it here we know exactly what operators we will be 
// using.  (defaults are listed in the GAlib documentation)
// Note that the default operators for the real genome are uniform 
// initializer,gaussian mutator, and uniform crossover.


// Now that we have the genomes, create a parameter list that will be
used // by the genetic algorithms and the genome.
GAParameterList params;
GASteadyStateGA::registerDefaultParameters(params);
params.set(gaNnGenerations, 500);// THE NUMBER OF GENERATIONS TO EVOLVE
params.set(gaNpopulationSize, 110);	// HOW MANY IN THE POPULATION
params.set(gaNscoreFrequency, 10);	// KEEP THE SCORES OF
GENERATIONS
params.set(gaNpMutation,0.01);	// LIKELYHOOD OF MUTATING NEW OFFSPRING
params.set(gaNpCrossover, 0.9); // LIKELYHOOD OF CROSSING OVER NEW
PARENTS
params.set(gaNflushFrequency, 50);	// SPECIFY HOW OFTEN TO WRITE
THE SCORE 
params.set(gaNselectScores, (int)GAStatistics::Mean|
(int)GAStatistics::Maximum | (int)GAStatistics::Minimum);
	
GASteadyStateGA ga(genome);	// NOW CREATE THE GA FOR RUNNING THE
GENOME
ga.minimize();		// SET THE OBJECTIVE FUNCTION TO MINIMIZATION
ga.parameters(params);		// SET THE PARAMETERS FOR THE GA OBJECT


ga.set(gaNscoreFilename, "..\\Output\\worstCaseScores.dat"); 
		
ga.initialize();
ofstream outfile;

// dump the initial population to file
cout << "printing initial population to file..." << endl;
outfile.open("..\\Output\\initialPopulation.dat", (ios::out |
ios::trunc));
for(int ii=0; ii<ga.population().size(); ii++){
	genome = ga.population().individual(ii);
	outfile << genome.gene(0) << "\t" << genome.gene(1) << "\t" <<
genome.gene(2) << "\t" << genome.gene(3) << "\t" << genome.gene(4) 
	<< "\t" << genome.gene(5) << "\t" << genome.gene(6) << "\t" <<
genome.gene(7) << "\t" << genome.score() << "\n";
}
outfile.close();

while(!ga.done()) ga.step(); // RUN THE GA!!!!

// dump the final population to file

cout << "printing final population to file..." << endl;
outfile.open("..\\Output\\finalPopulation.dat", (ios::out |
ios::trunc));
	for(int i=0; i<ga.population().size(); i++){
		genome = ga.population().individual(i);
		outfile << genome.gene(0) << "\t" << genome.gene(1) <<
"\t" << 		genome.gene(2) << "\t" << genome.gene(3) << "\t"
<< 				genome.gene(4) << "\t" << genome.gene(5)
<< "\t" << 				genome.gene(6) << "\t" <<
genome.gene(7) << "\t" << 				genome.score()
<< "\n";
	}
outfile.close();

cout << "the ga generated:\n" << ga.statistics().bestIndividual() <<
endl; 
cout << "objective: " << genome.score() << endl; // BEST GENE OBJECTIVE 

Using this setup the GA does not seem to minimize the objective
function.  My objective function is very problem specific so it wouldn't
really mean much if I presented it here but all it is doing is carrying
out a calculation which has a result in the range [0-1].  I want to
minimize and find the lowest possible values, here is an extract of my
initial populations and final population; the last column contains the
score:

Initial:

67.5	50	80	-44.5	0	0	10	100	1
46.5	50	80	-45.5	0	0	10	100	1
67.5	50	80	-47.5	0	0	10	100	1
48.5	50	80	-46.5	0	0	10	100	1
24	50	80	-45.5	0	0	10	100	1
86	50	80	-36.5	0	0	10	100	0.923725
47.5	50	80	-40	0	0	10	100	0.918861
88.5	50	80	-41	0	0	10	100	0.914851
19.5	50	80	-48.5	0	0	10	100	0.905531
62	50	80	-48	0	0	10	100	0.905434
79	50	80	-50.5	0	0	10	100	0.902146
27.5	50	80	-51	0	0	10	100	0.901866
52.5	50	80	-48	0	0	10	100	0.901818
24	50	80	-49.5	0	0	10	100	0.899786
65	50	80	-49.5	0	0	10	100	0.899786
24.5	50	80	-53	0	0	10	100	0.898862
67.5	50	80	-52.5	0	0	10	100	0.898036
83.5	50	80	-55	0	0	10	100	0.897259
20.5	50	80	-54.5	0	0	10	100	0.894487
61	50	80	-54.5	0	0	10	100	0.893837
41	50	80	-56	0	0	10	100	0.893459

final:


46.5	50	80	-42.5	0	0	10	100	1
72.5	50	80	-46.5	0	0	10	100	1
46.5	50	80	-42.5	0	0	10	100	1
59	50	80	-42.5	0	0	10	100	1
48.5	50	80	-46.5	0	0	10	100	1
46.5	50	80	-45.5	0	0	10	100	1
48.5	50	80	-45.5	0	0	10	100	1
48.5	50	80	-42.5	0	0	10	100	1
71.5	50	80	-46.5	0	0	10	100	1
46.5	50	80	-46.5	0	0	10	100	1
48.5	50	80	-45.5	0	0	10	100	1
46.5	50	80	-46.5	0	0	10	100	1
71.5	50	80	-42.5	0	0	10	100	1
71.5	50	80	-46.5	0	0	10	100	1
40	50	80	-46.5	0	0	10	100	1
46.5	50	80	-46.5	0	0	10	100	1

So you can see that it has maximized the objective function and has
closed in on the maximum value of 1 even though I have set the GA to
minimize with the command: ga.minimize();  I want to find the minimum
value say around 0 (probably).

Have I set up the GA correctly?  And if so do you have any ideas what
could be causing it to maximize?

Cheers,

Douglas

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Douglas McNab - Research Assistant
CUE - Centre for Ultrasonic Engineering
University of Strathclyde, 204 George Street
Glasgow, G1 1XW
 
Tel: +44 (0)141 548 3477 Fax: +44 (0)141 548 2950
 
http://www.cue.ac.uk
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~