Subscripted set in variable declaration

[Mateusz Nowak]

Hi, I'm trying to solve such problem using AMPL:
I have a set of Nodes and Edges that create a network. Each Edge has its own set of available wavelengths, called Lambdas (for sake of example, let's say it is 4), then each lambda can carry up to 10 Gbit/s (units are not that important here). In network are fulfilled demands between certain Nodes that have certain volume and have predefined paths able to route the traffic.

I've found a problem that I cannot solely resolve (code below):

# SETS AND PARAMETERS

# Nodes

# Consist of: a number to identify a node

param maxNode, >= 0, integer;

set Nodes=1..maxNode;

# Edges

# Consist of: nodeA and nodeB - nodes at each end of given link, and lambdas - maximum number of available wavelengths in fibre

set Edges;

param nodeA { Edges }, in Nodes;

param nodeZ { Edges }, in Nodes;

set Lambdas { Edges};

#param lambdas { Edges }, >= 0, default 1000;

# Demands

# Consist of: demand_volume - how much traffic we need to allocate, and demand_maxPath - how many paths are available to fulfill demand

set Demands;

param demand_volume { Demands }, >= 0, default 0;

param demand_maxPath { Demands }, >= 0, default 0;

# Demand_pathLinks

set Demand_pathLinks { d in Demands, dp in 1..demand_maxPath[d] } within Edges;

# VARIABLES

# x_ldp definition, cannot be higher than demand_value, cannot be lower than 0

var x_ldp {l in Lambdas[******], d in Demands, p in 1..demand_maxPath[d]} >= 0, <= demand_volume[d];

# delta_edp definition, if given link e is used in path p of demand d, then 1, else 0

var delta_edp {e in Edges, d in Demands, p in 1..demand_maxPath[d]}, binary;

# CONSTRAINTS

subject to demand_satisfaction_constraint { e in Edges, d in Demands }:

  sum {l in Lambdas[e], p in 1..demand_maxPath[d]} x_ldp[l, d, p ] = demand_volume[ d ];

  

subject to lambda_capacity_constraind {e in Edges, l in Lambdas[e] }:

  sum {d in Demands, p in 1..demand_maxPath[d]} delta_edp[e,d,p]*x_ldp[l,d,p] <= 10;

The red is part of the declaration of variable that is responsible for traffic. Basically, this variable, x_ldp, by definition in Link-path optimization method, is the amount of volume of demand d, on path p of predefined set of available paths for given demand on given wavelength (l in lambdas). But - when trying to do that, I come stand-off:
when I try to do:

l in Lambdas[e in Demand_pathLinks[d,p], d in Demands, p in 1..demand_maxPath[d], 

 

But then I got the error "e is not defined";
OR:

l in Lambdas, d in Demands, p in 1..demand_maxPath[d]

But then, I got the error, that Lambdas needs to be subscripted.

I really do will appreciate any help

[Robert Fourer]

You should write

var x_ldp {e in Edges, l in Lambdas[e], d in Demands, p in 1..demand_maxPath[d]}

>= 0, <= demand_volume[d];

Then in the constraints you should reference x_ldp[e,l,d,p].

Bob Fourer
am...@googlegroups.com

=======

[Mateusz Nowak]

Hi Bob

Thank you for your answer

I did as you suggested and it works, but I came to another problem:

When allocating traffic it gets assigned to edges that aren't in path definition. For instance, if I have Path 1 for Demand 1, connecting Node 1 to 3 via Edges 1 and 2, as in data file:

# 2 nodesparam MaxNode := 2;

 

# 3 edges

param: Edges: nodeA nodeZ :=

1 1 2

2 2 3

          3 1 3 

;

param: maxLambda := 10;

param: Demands: demand_maxPath, demand_volume:

1 1 15

;

set Demand_pathLinks[1,1] := 1 2;

Notice, that in path definition for Demand 1 there is no Edge 3. But still, it gets assigned volume, even if it shouldn't have been. I think it may be a problem with "e in Edges" declaration of x_ldp - it assignes the volume to all the Edges. Is there a way to tell the solver to use Edges, but only those, that are defined in Demand_pathLinks[d, dp]?

[Mateusz Nowak]

Hi Bob, it's me, once again :P

I've just been on the phone with my friend and he said to me, that my problem may be delta_edp, but the nature of the problem remains the same - to differientate Edges that are part of the path, and those not. So, my another question is:

I know I can change delta_edp to parameter and then write manually, if edge is part of path (1 for yes, 0 otherwise), but is there a way to do it automatically, to iterate through Demand_pathLinks declaration and assign value?

In C# I think it would be like that:

foreach( d in Demands){

for(int p = 1; p < demand_maxPath + 1; p ++){

foreach( e in Demand_pathLinks[d,p]){

     delta_edp [ e, d, p] = 1;