I am an absolute beginner in using GAMS and, although my question might seem obvious I could really use some help.
The situation is the following:
I have three sets: I,J and TR.
I is the coordinate of the origin; J is the coordinate of the destination and TR is the truck that's traveling from one place to the other.
I have a table (Trvltime_tbl(I,J)) with the Travel Time between every I and each J. I would like to create a Parameter TravelTime(I,J,TR), that contains the travel time between I and J using TR. Nevertheless the travel time is the same for each truck. How can I assign the values from the table to the parameter? I am having trouble because the table has only two dimension and the parameter has three.
Thank you so much!!
TravelTime(I,J,TR) = Trvltime_tbl(I,J);
That is, for every (I,J,TR), assign to TravelTime(I,J,TR) the value of Trvltime_tbl(I,J).
Related
CPLEX; Mixed Integer Linear Programming; Constraint Formulation:
There are 150 towns in the dataset, each town having several markets (or "mandis"). Total number of mandis in the dataset = 1800. I have a binary decision variable y[mandi][days]. I want to add a constraint which states that y[mandi][days] is equal for all mandis within any given town on any given day. y[mandi][days] could be different/same for the mandis in different towns on the same day.
Sample Data
I'm inputting the data from Excel. Please see the attached image. Can you help me out with how to formulate this constraint in OPL?
One way to achieve the above is to specify individual constraints on the set of mandis within each town. However, the number of constraints, in that case, would become 150, each referring to one town. Also, we might receive from the client an additional list of mandis for some towns, which would distort the mandi-town mapping numbering, and I would have to change the mapping in CPLEX again. Is there a better way to do this, which could take the mapping directly from excel in the attached image format?
Instead of the decision variable
dvar boolean y[mandi][days]
why not use
dvar boolean y[town][days]
?
And then when you need the y for a given mandi, you first get the town of that mandi and then get its y.
i have a dataframe with columns accounting for different characteristics of stars and rows accounting for measurements of different stars. (something like this)
\property_______A _______A_error_______B_______B_error_______C_______C_error ...
star1
star2
star3
...
in some measurements the error for a specifc property is -1.00 which means the measurement was faulty.
in such case i want to discard the measurement.
one way to do so is by eliminating the entire row (along with other properties who's error was not -1.00)
i think it's possible to fill in the faulty measurement with a value generated by the distribution based on all the other measurements, meaning - given the other properties which are fine, this property should have this value in order to reduce the error of the entire dataset.
is there a proper name to the idea i'm referring to?
how would you apply such an algorithm?
i'm a student on a solo project so would really appreciate answers that also elaborate on theory (:
edit
after further reading, i think what i was referring to is called regression imputation.
so i guess my question is - how can i implement multidimensional linear regression in a dataframe in the most efficient way???
thanks!
I´m running the DICE2013 model and want to state a condition that two variables should be equal in the first period t, before they can be optimized independently for all remaining periods.
Do I write an if statement at the beginning or how can I best achieve this?
AI(t)=BI(t) if t=1, thereafter the two should be unrelated
Thanks heaps
You could add a new equation to your model, such as:
EQUATION NewEquation;
NewEquation.. AI(1) =e= BI(1);
In this way, you are adding a constraint only for t = 1.
I hope it helps
I am working on a Traveling salesman problem and can't figure how to solve it. The problem contains ten workers, ten workplaces where they should be driven to and one car driving them one by one. There is a cost of $1.5 per km. Also, all the nodes (both workers and workplaces) are positioned in a 10*10 matrix and the distance between each block in the matrix is 1 km.
The problem should be solved using AMPL.
I have already calculated the distances between each coordinate in excel and have copy pasted the matrix to the dat.file in AMPL.
This is my mod.file so far (without the constrains):
param D > 0;
param D > 0;
set A = 1..W cross 1..D;
var x{A}; # 1 if the route goes from person p to work d,
# 0 otherwise
param cost;
param distance;
minimize Total_Cost:
sum {(w,d) in A} cost * x[w,d];
OK, so your route looks like: start-worker 1-job 1-worker 2-job 2-worker 3-job-3-...-job 10-end (give or take start & end points, depending on how you formulate the problem.
That being the case, the "worker n-job n" parts of your route are predetermined. You don't need to include "worker n-job n" costs in the route optimisation, because there's no choice about those parts of the route (though you do need to remember them for calculating total cost, of course).
So what you have here is really a basic TSP with 10 "destinations" (each representing a single worker and their assigned job) but with an asymmetric cost matrix (because cost of travel from job i to worker j isn't the same as cost of travel from job j to worker i).
If you already have an implementation for the basic TSP, it should be easy to adapt. If not, then you need to write one and make that small change for an asymmetric cost matrix. I've seen two different approaches to this in AMPL.
2-D decision matrix with subtour elimination
Decision variable x{1..10,1..10} is defined as: x[i,j] = 1 if the route goes from job i to job j, and 0 otherwise. Constraints require that every row and column of this matrix has exactly one 1.
The challenging part with this approach is preventing subtours (i.e. the "route" produced is actually two or more separate cycles instead of one large cycle). It sounds like your current attempt is at this stage.
One solution to the problem of subtours is an iterative approach:
Write an implementation that includes all requirements except for subtour prevention.
Solve with this implementation.
Check the resulting solution for subtours.
If no subtours are found, return the solution and end.
If you do find subtours, add a constraint which prevents that particular subtour. (Identify the arcs involved in the subtour, and set a constraint which implies they can't all be selected.) Then go to #2.
For a small exercise you may be able to do the subtour elimination by hand. For a larger exercise, or if your lecturer doesn't like that approach, you can create a .run that automates it. See Bob Fourer's post of 31/7/2013 in this thread for an example of implementation.
3-D decision matrix with time dimension
Under this approach, you set up a decision variable x{1..10,1..10,1..10} where x[i,j,t] = 1 if the route goes from job i to worker j at time t, and 0 otherwise. Your constraints then require that the route goes to and from each job/worker combination exactly once, that if it goes to worker i at time t then it must go from job i at time t+1 (excepting first/last issues), that it's doing exactly one thing at time t, and that the endpoint at time 10 matches the startpoint at time 1 (assuming you want a circuit).
This prevents subtours, because it forces a route that starts at some point at time 1, returns to that point at time 10, and doesn't visit any other point more than once - meaning that it has to go through all of them exactly once.
I need to perform an exponential operation of two parameters (one set: t, and the other comes from the arrays) on a set of 2D arrays (a 3D Matrix if you want).
f(t,x) = exp(t-x)
And then I need to add the result of every value in the 3rd dimension. Because it takes too much time using bsxfun to perform the entire operation I was thinking of using a look up table.
I can create the table as a matrix LUT (2 dimensional due to the two parameters), then I can retrieve the values using LUT(par1,par2). But accessing on the 3rd dimension using a loop is expensive too.
My question is: is there a way to implement such mechanism (a look up table) to have a predefined values and then just using them accessing from the matrix elements (kind of indexing) without loops. Or, how can I create a look up table that MATLAB handles automatically to speed up the exponential operation?
EDIT:
I actually used similar methods to create the LUT. Now, my problem actually is how to access it in an efficient way.
Lets said I have a 2 dimensional array M. With those values that I want to apply the function f(t,M(i,j)) for fixed value t. I can use a loop to go through all the values (i,j) of M. But I want a faster way of doing it, because I have a set of M's, and then I need to apply this procedure to all the other values.
My function is a little bit complex than the example I gave:
pr = mean(exp(-bsxfun(#rdivide,bsxfun(#minus,color_vals,double(I)).^2,m)./2),3);
That is my actual function, as you can see is more complex than the example I presented. But the idea is the same. It does an average in the third dimension of the set of M's of the exponential of the difference of two arrays.
Hope that helps.
I agree that the question is not very clear, and that showing some code would help. I'll try anyway.
In order to have a LUT make sense at all, the set of values attained by t-x has to be limited, for example to integers.
Assuming that the exponent can be any integer from -1000 to 1000, you could create a LUT like this:
LUT = exp(-1000:1000);
Then you create your indices (assuming t is a 1D array, and x is a 2D array)
indexArray = bsxfun(#minus,reshape(t,[1,1,3]), x) + 1001; %# -1000 turns into 1
Finally, you create your result
output = LUT(indexArray);
%# sum along third dimension (i.e. sum over all `t`)
output = sum(output,3);
I am not sure I understand your question, but I think this is the answer.
x = 0:3
y = 0:2
z = 0:6
[X,Y,Z] = meshgrid(x,y,z)
LUT = (X+Y).^Z