MathProg (AMPL) - Variable Array Sized by Another Variable - ampl

Question

I am writing my first GNU MathProg (AMPL) program to find the minimum switch (vertex) count instances of a HyperX topology (graph) for a given radix, number of hosts, and bisection bandwidth. This is a simple first program because all of the equations have been described in the following paper: http://cal.snu.ac.kr/files/2009.sc.hyperx.pdf
I have read the specification and example programs, but I am stuck on a very simple syntax error. I need to have the following two variables: L, the number of dimensions in the network, and an array S of length L, where each element of S is the number of switches in each dimension. In my MathProg program, I express this as:
var L >= 1, integer;
var S{1 .. L} >= 2, integer;
However, when I run $ glpsol --check --math hyperx.mod, I get the following error:
hyperx.mod:28: operand following .. has invalid type
Context: ...isec ; param radix ; var L >= 1 , integer ; var S { 1 .. L }
If anybody can help explain how I should properly express this relationship, I will be grateful. Also, I am including the entire program I have written for reference and extra help. I expect there to be many syntax errors in my program, but until I fix the first one, I have no way of finding the rest.
/*
* A MathProg linear program to find an optimal HyperX topology of a
* given network size, switch radix, and bisection bandwidth. Optimal
* is simplistically defined as minimum switch count network.
*
* A HyperX topology is a multi-dimensional network (graph) where, in
* each dimension, the switches are fully connected. Every switch
* (vertex) is a point in an L-dimensional integer lattic. Each switch
* is identified by a multi-index I = (I_1, ..., I_L) where 0 <= I_k <
* S_k for each k = 1..L, where S_k is the number of switches in each
* dimension. A switch connects to all others whose multi-index is the
* same in all but one coordinate.
*/
/* Network size in number of hosts. */
param hosts;
/* Desired bisection bandwidth. */
param bisec;
/* Maximum switch radix. */
param radix;
/* The number of dimensions in the HyperX. */
var L >= 1, integer;
/* The number of switches in each dimension. */
var S{1 .. L} >= 2, integer;
/*
* Relative bandwidth of the dimension, i.e., the number of links in a
* given dimension.
*/
var K{1 .. L} >= 1, integer;
/* The number Terminals (hosts) per switch */
var T >= 1, integer;
/* Minimize the total number of switches. */
minimize cost: prod{i in 1..L} S[i];
/* The total number of links must be less than the switch radix. */
s.t. Radix: T + sum{i in 1..L} K[i] * (S[i] - 1) <= radix;
/* There must be enough hosts in the network. */
s.t. Hosts: T * prod{i in 1..L} S[i] >= hosts;
/* There must be enough bandwidth. */
s.t. Bandwidth: min{K[i]*S[i]} / (2 * T) >= bisec;
/* The order of the dimensions doesn't matter, so constrain them */
s.t. SwitchDimen: forall{i in 1..(L-1)} S[i] <= S[i+1];
/*
* Bisection bandwidth depends on the smallest S_i * K_i, so we know
* that the smallest switch count dimension needs the most links.
*/
s.t. LinkDimen: forall{i in 1..(L-1)} K[i] >= K[i+1];
# TODO: I would like to constrain the search such that the number of
# terminals, T, is bounded to T >= (hosts / O), where O is the switch
# count of the smallest switch count topology discovered so far, but I
# don't know how to do this.
/* Data section */
data;
param hosts := 32
param bisec := 0.5
param radix := 64
end;

Answer 1

Fixed number of variables in a problem is a common assumption in solvers and algebraic modelling languages including AMPL/MathProg. Therefore you can only use constant expressions, in particular parameters, not variables in indexing expressions. One possible solution is to make L a parameter, resolve your problem for different values of L and select the one that gives the best objective value. This can be done with a simple AMPL script.