I'm trying to solve an optimization problem on GAMS, but only for a subset. Right now, i have a code that optimizes for all the elements of set t:
t time in hours / 1 * 8760 /
How do I run the optimization only for t from 1 to 3500, AND from 6500 to 8760 (for example)? FYI, all of my parameters data (from .csv) that i imported to GAMS have 8760 values. Here's a simple objective function to use:
eObjFunc.. vZ =e= sum(t, v1(t));
The simplest way I could think of is to edit all my .csv data so they only have the t values that I care for. In this case, define set t = 1 to 3500, 6500 to 8760. Then, just run the optimization.
However, I'm sure there's a smarter way to do this without having to modify my .csv data...
Really appreciate your help!
You can define subsets like this (assuming t is defined already as 1*8760):
Set tt(t) /1*3500, 6500*8760/;
And then use tt instead of t in your equation:
eObjFunc.. vZ =e= sum(tt, v1(tt));
Related
I need your help to solve this "Little" problem I'm having programming with GAMS.
In my objective function I have this member that is z = [...]-TWC(j)*HS(j).
Where HS(j)is a variable.
Now, TWC(j) should be a parameter that works like this:
TWC(j) = 0 when HS(j) < 1000
and
TWC(j) = 3.21 when HS(j) >=1000.
Any idea how to implement this in GAMS? my attempts all failed.
EDIT: this is what I tried I defined an equation called TWCup(j) that was:
TWCup(j)$(HS.l(j) >= 1000).. TWC(j) =e= 3.21;
Thanks ;)
Probably not relevant for the OP anymore (since the question is more than 3 years old), but maybe useful for someone else that looks at this question.
If TWC(j) is a function of your variable HS(j), it is not a parameter. It is another variable. So you should define TWC(j) as a variable and not as a parameter. This is probably the reason you were getting errors.
There are some ways to fix your problem: One is to actually turn TWC(j) into a variable. But this would turn your problem into non-linear which could be (or not) an issue. Also, this could need the use of binary variables, which could also become a problem (again, or not).
But I think this issue could be resolved with a different specification of the LP. The cost function f(HS(j)) = TWC(j)*HS(j) is linear by parts and convex, which you can represent in a standard LP using auxiliary variables (assuming you are minimizing).
* declare auxiliary variable
Variable
w(j);
* declare equations for linear by part cost function
Equation
costfun1(j)
costfun2(j);
;
* define costfun1 and costfun2
costfun1(j).. w(j) =g= 0;
costfun2(j).. w(j) =g= -3210 + 3.21*HS(j);
*redefine objective function (note that I changed to plus because I assumed this is a cost function that you are minimizing)
z = [...]+w(j)
This solution is very problem dependent. I assumed you were minimizing and I changed the sign in the objective function to '+'. If this was not the case, this would not work (would not be convex). Then we would need to check other approaches.
But the takeaway here is to stress that something that is a function of a variable is also a variable. But you may have options to reformulate your problem to address the problem.
I defined a set in GAMS to represent users number. I need to use the set multiple times to define transmission power for each user, the channel quality...etc. However, I think in GAMS you can not use the name of the set for different variables, My question is do I need to define a different set for each variable?
Code example:
set I number of users /i1,i2/ ;
Parameters
CP(I) circuit power per user /
i1 10
i2 10 /
h(I) channel quality /
i1 48.9318
i2 106.2280/ ;
Thank you in advance for any help or for any hints.
No, you don't need to define different sets if you always want to refer to the same elements (users in your case). It is actually the idea of sets to do exactly this. So, your example code is just right.
You can also look at a simple example like this one here: http://www.gams.com/modlib/libhtml/trnsport.htm
There you will see, that the sets i and j are used all over for different parameters, variables and equations.
I hope that helps,
Lutz
I am trying to compute numerically the solutions for a system of many equations and variables (100+). I tried so far three things:
I now that the vector of p(i) (which contains most of the endogenous variables) is decreasing. Thus I gave simply some starting points, and then was increasing(decreasing) my guess when I saw that the specific p was too low(high). Of course this was always conditional on the other being fixed which is not the case. This should eventually work, but it is neither efficient, nor obvious that I reach a solution in finite time. It worked when reducing the system to 4-6 variables though.
I could create 100+ loops around each other and use bisection for each loop. This would eventually lead me to the solution, but take ages both to program (as I have no idea how to create n loops around each other without actually having to write the loops - which is also bad as I would like to increase/decrease the amount of variables easily) and to execute.
I was trying fminsearch, but as expected for that wast amount of variables - no way!
I would appreciate any ideas... Here is the code (this one the fminsearch I tried):
This is the run file:
clear all
clc
% parameter
z=1.2;
w=20;
lam=0.7;
tau=1;
N=1000;
t_min=1;
t_max=4;
M=6;
a_min=0.6;
a_max=0.8;
t=zeros(1,N);
alp=zeros(1,M);
p=zeros(1,M);
p_min=2;
p_max=1;
for i=1:N
t(i)= t_min + (i-1)*(t_max - t_min)/(N-1);
end
for i=1:M
alp(i)= a_min + (i-1)*(a_max - a_min)/(M-1);
p(i)= p_min + (i-1)*(p_max - p_min)/(M-1);
end
fun=#(p) david(p ,z,w,lam,tau,N,M,t,alp);
p0=p;
fminsearch(fun,p0)
And this is the program-file:
function crit=david(p, z,w,lam,tau,N,M,t,alp)
X = zeros(M,N);
pi = zeros(M,N);
C = zeros(1,N);
Xa=zeros(1,N);
Z=zeros(1,M);
rl=0.01;
rh=1.99;
EXD=140;
while (abs(EXD)>100)
r1=rl + 0.5*(rh-rl);
for i=1:M
for j=1:N
X(i,j)=min(w*(1+lam), (alp(i) * p(i) / r1)^(1/(1-alp(i))) * t(j)^((z-alp(i))/(1-alp(i))));
pi(i,j)=p(i) * t(j)^(z-alp(i)) * X(i,j)^(alp(i)) - r1*X(i,j);
end
end
[C,I] = max(pi);
Xa(1)=X(I(1),1);
for j=2:N
Xa(j)=X(I(j),j);
end
EXD=sum(Xa)- N*w;
if (abs(EXD)>100 && EXD>0)
rl=r1;
elseif (abs(EXD)>100 && EXD<0)
rh=r1;
end
end
Ya=zeros(M,N);
for j=1:N
Ya(I(j),j)=t(j)^(z-alp(I(j))) * X(I(j),j)^(alp(I(j)));
end
Yi=sum(Ya,2);
if (Yi(1)==0)
Z(1)=-50;
end
for j=2:M
if (Yi(j)==0)
Z(j)=-50;
else
Z(j)=(p(1)/p(j))^tau - Yi(j)/Yi(1);
end
end
zz=sum(abs(Z))
crit=(sum(abs(Z)));
First of all my recommendation: use your brain.
What do you know about the function, can you use a gradient approach, linearize the problem, or perhaps fix most of the variables? If not, think twice before you decide that you are really interested in all 100 variables and perhaps simplify the problem.
Now, if that is not possible read this:
If you found a way to quickly get a local optimum, you could simply wrap a loop around it to try different starting points and hope you will find a good optimum.
If you really need to make lots of loops (and a variable amount) I suppose it can be done with recursion, but it is not easily explained.
If you just quickly want to make a fixed number of loops inside each other this can easily be done in excel (hint: loop variables can be called t1,t2 ... )
If you really need to evaluate a function at a lot of points, probably creating all the points first using ndgrid and then evaluating them all at once is preferable. (Needless to say this will not be a nice solution for 100 nontrivial variables)
I am using SPSS and have about 300 variables (categorical, scalar and ordinal) to model. I need an Easy / Quick way to create interaction variable composites for Logistic Regression where interactions exist. R does this automatically and creates about 158 composites (variables that have interactions) – there does not appear to be any automated way to create and input interaction variables in SPSS; having to manually input and or test these 158 composites every time I run a new model is going to be A LOT OF WORK!! Any suggestions on a quick way to do this?
If you are going to be repeatedly running this model and need a way to create these synthetic variables, you should most likely create a syntax file that will do it for you. When you use the GUI in SPSS to run a command, SPSS generates the syntax in the output window. You can copy this syntax and use it to create your own script. So, for instance you might write something like this:
DO IF (!MISSING Var1).
COMPUTE Var2 = Var1 * dummy1.
END IF.
EXECUTE.
And sadly, yes you would have to write this block of code 300 times the first go around, but in the future you can simply run it and have all the new variable computed.
Another approach is to name your variables sequentially and use a loop to process them. So assuming that your variables were sequentially named VarA, VarB, & VarC, then you could do a loop like so:
VECTOR VectorVar = VarA TO VarC.
LOOP #cnt = 1 to 3 by 1.
COMPUTE VectorVar(#cnt) = VectorVar * dummy1.
ENDLOOP.
EXECUTE.
Are you really looking to put in all 158 interaction terms? I'd be skeptical of that approach. But if you want to build variables representing all these interaction terms rather than specify them in the model, you can do it with the CREATE DUMMIES extension command available from the SPSS Community website (www.ibm.com/developerworks/spssdevcentral).
You could also use Python programmability to build the explicit interaction terms in the logistic procedure.
HTH,
Jon Peck
Does anyone know how can I calculate pi (π) in VB?
System.Math.Pi
Assuming you actually want to compute pi instead of just using the built in constants, there are a bunch of ways that you can do it. Here are a few links that could be useful:
http://www.codeproject.com/KB/recipes/CRHpi.aspx
http://en.wikipedia.org/wiki/Pi#Computation_in_the_computer_age
http://en.wikipedia.org/wiki/Machin-like_formula
If you mean VB6, it doesn't have a pi constant. You can use:
Dim pi as Double
pi = 4 * Atn(1)
If the OP is asking about algorithms as a learning experience, good for him/her.
If the OP wanted help finding the built-in value, s/he has it now.
But if the goal is a good value of higher precision than the built-in value with a minimum of effort, here's pi to one million digits:
http://www.eveandersson.com/pi/digits/1000000
That should be enough.
I hope the OP isn't asking how to recalculate the value of Pi each and every time it's used. That would be madness.
Meh, so efficient, accurate and most of all boring approximations... Try this instead! Pseudocode ensues:
initialize inside and total as 0
repeat an insane amount of times:
assign both x and y random values between (and including) 0 and +1.
assign distance as the square root of (x2 + y2)
if distance ≤ 1, add 1 to inside
add 1 to total
assign pi as inside / total * 4
If you don't want to use the built in values in the .net math library...
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