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GA (genetic algorithm) moves away from better values

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Hans
Hans on 14 Jun 2012
I am running a ga-optimization and I often get results like this one:
Best Mean Stall
Generation f-count f(x) f(x) Generations
1 932 -9.372e+005 1.231e+010 0
2 1398 -1.514e+005 7.911e+009 1
3 1864 7.705e+004 -3.975e+017 2
4 2330 -2.988e+004 -1.812e+015 0
5 2796 -2.988e+004 -1.135e+007 1
6 3262 -2.988e+004 -9.866e+007 2
7 3728 -563.1 -3.495e+007 3
8 4194 -563.1 -8.067e+006 4
9 4660 -563.1 -2.998e+007 5
10 5126 -563.1 -7.216e+006 6
11 5592 -563.1 -7.953e+006 7
12 6058 -288.2 -3.525e+006 8
13 6524 51.32 -3.823e+005 9
14 6990 -40.55 -1.176e+005 0
15 7456 19.38 2.5e+004 1
16 7922 14.31 9165 0
17 8388 14.31 8330 1
18 8854 6.788 6995 0
19 9320 6.788 8568 1
20 9786 5.907 8970 0
21 10252 1.453 1.218e+004 0
i wonder how (with an elite count set to 40 out of a population of 466) the algorithm moves to worse values first. How can this be improved? Thanks a lot for your answers!

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Hans
Hans on 14 Jun 2012
You can see the function below. I just do not get why it doesnt at least keep the good individuals. I just thought I kind of use a "shotgun" and throw a larger number of individuals at it so i dont get lost in minor "valleys". Can you recommend any change in the settings or so?
function ll=bbva(param)
given=[0.9018585500777736 0.0054652585568056855 0.006730395774728828 -0.08559786078631593];
L=0.45;
theta=given(1);
mu=given(2);
sigma=given(3);
p=param(1);
q=param(2);
v=param(3);
s=param(4);
l=param(5);
m=param(6);
sigmacc=param(7);
a1=param(8);
b1=param(9);
lambdar=given(4);
lambdac=param(10);
lambdab=param(11);
Data = xlsread('bbva-spain');
r=Data(:,3);
k=Data(:,1);
f=Data(:,2);
%col=Data(:,4);
%cou=Data(:,5);
Brc=zeros(length(k),1);
Arc=zeros(length(k),1);
Brb=zeros(length(f),1);
Arb=zeros(length(f),1);
Bc=zeros(length(k),1);
Ac=zeros(length(k),1);
Bb=zeros(length(f),1);
Ab=zeros(length(f),1);
hcdach=zeros(length(k),1);
hbdach=zeros(length(f),1);
singleliker=zeros(length(k),1);
singleliker(1)=0;
singlelikec=zeros(length(k),1);
singlelikec(1)=0;
singlelikeb=zeros(length(k),1);
singlelikeb(1)=0;
singlelike=zeros(length(k),1);
singlelike(1)=0;
for i=1:length(k);
Brc(i)=(1/theta)*(1-exp(-theta*k(i)));
Arc(i)=exp((mu-sigma^2/2*theta^2)*(Brc(i)-k(i))-sigma^2*Brc(i)^2/4*theta);
Brb(i)=(1/theta)*(1-exp(-theta*f(i)));
Arb(i)=exp((mu-sigma^2/2*theta^2)*(Brb(i)-f(i))-sigma^2*Brb(i)^2/4*theta);
Bc(i)=(1/p)*(1-exp(-p*k(i)));
Ac(i)=exp((q-v^2/(2*p^2))*(Bc(i)-k(i))-(v^2*Bc(i)^2)/(4*p));
Bb(i)=(1/s)*(1-exp(-s*f(i)));
Ab(i)=exp((l-m^2/(2*s^2))*(Bb(i)-f(i))-(m^2*Bb(i)^2)/(4*s));
hcdach(i)=1/(L*Bc(i))*(log(Ac(i))-log(Data(i,4))+log(Arc(i))+(1+L*a1)*Brc(i)*r(i));
hbdach(i)=1/(L*Bb(i))*(log(Ab(i))-log(Data(i,5))+log(Arb(i))+(1+L*b1)*Brb(i)*r(i));
end
Vr=(sigma^2)/(2*theta)*(1-exp(-2*theta));
Vc=(v^2)/(2*p)*(1-exp(-2*p));
Vb=(m^2)/(2*s)*(1-exp(-2*s));
Varcou=Vb-(v*m*sigmacc)^2/Vc;
for i=2:length(k);
singleliker(i)=-1/(2*log(Vr))-(1/(2*Vr))*(r(i)-mu-(lambdar*sigma)/theta-(r(i-1)-mu-(lambdar*sigma)/theta)*exp(-theta))^2;
singlelikec(i)=-1/(2*log(Vc))-(1/(2*Vr))*(hcdach(i)-q-(lambdac*v)/p-((hcdach(i-1)-q-(lambdac*v)/p))*exp(-p))^2;
singlelikeb(i)=-1/(2*log(Varcou))-(1/(2*Varcou))*(hbdach(i)-l-(lambdab*m/s)-(hbdach(i-1)-l-(lambdab*m)/s)*exp(-s)-(sigmacc*v*m)/Vb*(hcdach(i)-q-(lambdac*v/p)-(hcdach(i-1)-q-(lambdac*v)/p)*exp(-p)))^2;
singlelike(i)=singleliker(i)+singlelikec(i)+singlelikeb(i);
end
ll=-(sum(singlelike)+(3/2)*(length(k)-1)*(2*pi));
end
Hans
Hans on 14 Jun 2012
Could it be due to complex results (there are some logarithms in the function to be minimized)? Let's say MATLAB displays some result a, then there's actually a result a+ib with a lower absolute value or lower [minus absolue value] than one of the older results. Could that be it?
Hans
Hans on 15 Jun 2012
I am trying again now with constraints preventing complex results. However, the algorithm is still moving away(only two generations so far becasue it needs 26500 function evaluations per generation) but still..

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Answers (1)

Richard Crozier
Richard Crozier on 14 Jun 2012
But only the mean gets worse, the best improves with every generation, and this is all that matters surely?
Random combinations with nonlinear responses can easily throw up huge values which distort the mean, while not affecting the overall progress of the search.
For example, imagine the following with a population of 7:
Gen 1 scores: 100, 100, 150, 140, 111, 100, 119
best score: 100
mean score: 117.14
Gen2 scores: 87, 66, 167, 1000000000000, 55, 98, 206
best score: 55
mean score: 1.4286 x 10^11
The really bad individual would have a very low chance of passing its genes to the next generation so it's ok.

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Hans
Hans on 15 Jun 2012
I did as I said, now the algorithm is running (has been running for 8 hours) and I'm getting the following result:
Best max Stall
Generation f-count f(x) constraint Generations
1 26500 -0.00245613 0 0
2 52500 -0.00055561 0 0
So: Still the algorithm moves away from the better (the first generation) value..
Richard Crozier
Richard Crozier on 15 Jun 2012
It still looks like it's moving towards zero? Another way to test your theory would be to modiy your function to return a poor score for complex results (e.g. 10000 * real(ll) if ll is complex or something like this) instead of the actual value of the function.
What GA are you using, is it the Matlab GA toolbox (which I haven't used) or some other one? You could try the problem out in the GA Toolbox from the University of Sheffield available here: http://www.shef.ac.uk/acse/research/ecrg/gat to see if you get the same behaviour.
Richard Crozier
Richard Crozier on 15 Jun 2012
or actually abs(10000 * real(ll) ) would be better.

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