I need to consider "traffic time" in different period of time as a parameter in a VRP problem, so the equation becomes like this:
varA = sum(i$(ord(i)<varA),X(i)) + other terms
Is it possible to write such a code? Can GAMS or any other software handle such a constraint?
The equation:
I'm not familiar with GAMS syntax, but in AMPL you would do something like this:
set T; # set of time periods
param traffic_time{T}; # traffic time in each time period
Then you would refer to the traffic time parameter like traffic_time[t] for t in T. I'm sure there is something similar in GAMS. It might be called something like "parameter indexed by a set".
Related
I have a code snippet for a transport problem like:
set i /1*50/
d /1*10/
Alias(i,j,k)
parameter
edge(i,j)
distance(i,j)
possible(i,d) 'a collection of possible nodes for d'
possible_edge(i,j,d) 'a collection of possible edge for d';
binary variable x(i,j,d);
I import all the edges from an excel file. But to reduce the number of variables, I'd like to create another parameter like possible node and possible edge.
suppose we run a shortest path algorithm form a source node i and we define possible(i,d) to be all i where distance(i,j) is smaller than a predefined threshold.
In other words, when the network node become larger and larger, I want to find out if there's any possibility to not define x(i,j,d) for every (i,j) combination? Like forcing to only have x(i,j,d)$possible_edge(i,j,d)?? Is there anything like this??
Yes, you can limit the domain of variables in the model statement, like this
Model m / all, x(possible_edge) /;
So, here, the variable x would be limited by the set possible_edge wherever it occurs in model m. Note, that possible_edge must be a set here, not a parameter.
You can find more info about this concept here: https://www.gams.com/latest/docs/UG_ModelSolve.html#UG_ModelSolve_LimitedDomain
I have written an ASP program with an optimization condition in the end. When I compile it, even though I get the correct result, in the summary I get a negative value for the optimization (i.e. -3).
Do you know why this happens?
The optimization code part looks like this:
number_of_leaves(N) :- #count{X : leaf(X)} = N.
#maximize {N : number_of_leaves(N)}.
In clingo only #minimize is actually implemented. #maximize is realized by using #minimize - just with negated values. Therefore the "maximum" is negated as well - it shows -3 when the value should be 3.
My question is this:
How can I use SUBSET (a discontinuous set) to refer to an index location in another set as opposed to an actual value? I see that ord() can be used to return the position of a value in a set, but I want the reverse of this...
my reason for needing this:
I have a model in which some of the set and data statements are roughly:
set ALL_TIME := {0..20000};
param DATA {ALL_TIME}; #read from file in later data statement;
set myTIME := {0...1000};
I am looping over the myTIME set and each time solving the model and then incrementing the start and end by 1: {1..1001}, {2..1002}, {3..1003}, etc.
I have another discontinuous set being read in from a file that looks something like this (yes below is bad syntax, the "...." is just there to mean that the pattern continues until it hits 1000 so I don't have to type it all) :
set SUBSET := {6,7,8,9,10, 16,17,18,19,20, 26,27.....}
Once myTIME increments such that it no longer contains "6", I get a subscript undefined error from a constraint which I understand to be because myTIME in this case is {7..1007} and thus in the following, tSUB=6 causes ALPHA[6] and is undefined:
subject to CONSTRAINT {tSUB in SUBSET}:
ALPHA [tSUB] = ALPHA[last(tSUB)];
What I want is to be able to use SUBSET to always refer to the same index location of ALPHA, DATA, etc.
So:
SUBSET[0] (which equals 6) should always be the 6th value of for example DATA:
{tSUB in SUBSET}: DATA[tSUB]. when tSUB is 0, I want the 6th value of DATA.
(I am new to Ampl and have a hard time wrapping my head around how indexing and sets work - if anything didn't make sense, please ask and I'll try to clarify. If you think it would be more helpful to see my actual code I'll try to sanitize the company data out and post it). Also, some of the code bits above have abysmal syntax. They are not copied from my code, just approximated to try to explain my problem. :)
You can get i-th member of set S with member(i, S), where i is a 1-based index and S is an ordered set. This is described in section 5.6 Ordered sets of the AMPL book.
I am working with Wolfram Mathematica 8 and have the following problem. I have an optimization problem under certain constraints and want to have an analytical (symbolical solution). I am maximizing function piA. My input is:
piA[a_, WA1_, WA0_] =
a/(1 + a)*(X - (y*WA1 + 1)^(1/y)) - 1/(1 + a) ((y*WA0 + 1)^(1/y));
Maximize[{piA[a, WA1, WA0], WA0 >= -1/y, WA1 >= -1/y}, WA0]
What I get most of the times is:
Maximize[{-((1 + WA0 y)^((1/y))/(1 + a)) + (
a (X - (1 + WA1 y)^(1/y)))/(1 + a), WA0 >= -(1/y), WA1 >= -(1/y)},a]
Basically, the command does nothing, but outputs itself. Only once I have managed to get the proper output (too long to paste here). I have tested it with simpler functions and it works. Unfortunately, I cannot understand what causes the problem. It is not a syntax problem, since it has worked like that several times. Any help would be very much appreciated.
P.S. Just checked again and my input ALWAYS generates the wrong output. The time it generated the solution was when I accidentally set parameters X and y to certain numbers.
The most likely reason is that given the function and constraints, Mathematica doesn't know how to maximize your function with respect to WA0. Note you also have a free variables X and a in there, and it might not have enough information about the domain of X and a to be able to properly form a solution to your equation.
I've had instances where I tried feeding in some equations and constraints and Mathematica simply couldn't do anything with them because they were too general. This may be the case here as well. Is there a specific problem you're trying to solve, and is there any way you could give Mathematica more context?
I don't think this is a bug at all, but it's unfortunate that sometimes Mathematica will just spit back your input when it doesn't have any rules for solving what you gave it.
The usual reason these things happens seems to be when the expressions given are too general for Mathematica to handle, or when it it's faced with a set of expressions that are ill formed.
Just as an example, I tried passing in fractions into a function I wrote that specifically looked for rational expressions, thinking it would work. It turned out that it needed to handle both Rational[a, b] and Times[a, Power[b, -1]]. It could be the case that Mathematica is not expecting a constraint to be of the form GreaterEqual[a, b].
Mathematica returns an answer if you assign the variable a some value. Maybe you could build your strategy on that? In fact it does provide an answer if you assign a value to any of the variables.
( I would need more background of the problem to go from there... )
In algebra if I make the statement x + y = 3, the variables I used will hold the values either 2 and 1 or 1 and 2. I know that assignment in programming is not the same thing, but I got to wondering. If I wanted to represent the value of, say, a quantumly weird particle, I would want my variable to have two values at the same time and to have it resolve into one or the other later. Or maybe I'm just dreaming?
Is it possible to say something like i = 3 or 2;?
This is one of the features planned for Perl 6 (junctions), with syntax that should look like my $a = 1|2|3;
If ever implemented, it would work intuitively, like $a==1 being true at the same time as $a==2. Also, for example, $a+1 would give you a value of 2|3|4.
This feature is actually available in Perl5 as well through Perl6::Junction and Quantum::Superpositions modules, but without the syntax sugar (through 'functions' all and any).
At least for comparison (b < any(1,2,3)) it was also available in Microsoft Cω experimental language, however it was not documented anywhere (I just tried it when I was looking at Cω and it just worked).
You can't do this with native types, but there's nothing stopping you from creating a variable object (presuming you are using an OO language) which has a range of values or even a probability density function rather than an actual value.
You will also need to define all the mathematical operators between your variables and your variables and native scalars. Same goes for the equality and assignment operators.
numpy arrays do something similar for vectors and matrices.
That's also the kind of thing you can do in Prolog. You define rules that constraint your variables and then let Prolog resolve them ...
It takes some time to get used to it, but it is wonderful for certain problems once you know how to use it ...
Damien Conways Quantum::Superpositions might do what you want,
https://metacpan.org/pod/Quantum::Superpositions
You might need your crack-pipe however.
What you're asking seems to be how to implement a Fuzzy Logic system. These have been around for some time and you can undoubtedly pick up a library for the common programming languages quite easily.
You could use a struct and handle the operations manualy. Otherwise, no a variable only has 1 value at a time.
A variable is nothing more than an address into memory. That means a variable describes exactly one place in memory (length depending on the type). So as long as we have no "quantum memory" (and we dont have it, and it doesnt look like we will have it in near future), the answer is a NO.
If you want to program and to modell this behaviour, your way would be to use a an array (with length equal to the number of max. multiple values). With this comes the increased runtime, hence the computations must be done on each of the values (e.g. x+y, must compute with 2 different values x1+y1, x2+y2, x1+y2 and x2+y1).
In Perl , you can .
If you use Scalar::Util , you can have a var take 2 values . One if it's used in string context , and another if it's used in a numerical context .