Re: [Help-glpk] Condensing a sparse matrix by creating a subset of parameter data

[Meketon, Marc]

Simply add:

 

var flow{arcs} >= 0;

s.t. FlowConservation{node in nodes_that_are_used}:

  sum{(node,head_node) in arcs} flow[node,head_node]

  =

  sum{(tail_node,node) in arcs} flow[tail_node,node]

  ;

 

After the set nodes_that_are_used is defined.

 

From: Abhishek Shivakumar [mailto:address@hidden
Sent: Thursday, March 31, 2016 10:53 AM
To: Meketon, Marc; address@hidden
Subject: RE: [Help-glpk] Condensing a sparse matrix by creating a subset of parameter data

 

Thanks for your message. That is indeed (almost) what I’m looking for. I would like to then apply a constraint to the subset of nodes that are being used. Specifically, I want to set a constraint on the ‘flow’ between the nodes.

 

I agree that reducing the matrix size won’t have a significant effect on the optimization time. However, we’re generating an lp file from our model and the time to generate the lp file is likely to be reduced significantly. I expect that there will be an optimal point between reducing the size of the matrix (and time to generate it) and the optimization time.

 

From: Meketon, Marc [mailto:address@hidden]
Sent: 31 March, 2016 4:11 PM
To: Abhishek Shivakumar <address@hidden>; address@hidden
Subject: RE: [Help-glpk] Condensing a sparse matrix by creating a subset of parameter data

 

Are you looking for something like the below that finds the subset of nodes being used?

 

set nodes := {"A", "B", "C", "D", "E"};

set arcs within nodes cross nodes := {("A","B"), ("B","E")};

 

display nodes;

display arcs;

 

set nodes_that_are_used :=

  setof{tail_node in nodes, head_node in nodes : (tail_node, head_node) in arcs } tail_node

  union

  setof{tail_node in nodes, head_node in nodes : (tail_node, head_node) in arcs } head_node;

     

display nodes_that_are_used;

 

end;

 

From: help-glpk-bounces+address@hidden [mailto:help-glpk-bounces+address@hidden] On Behalf Of Abhishek Shivakumar
Sent: Thursday, March 31, 2016 9:18 AM
To: address@hidden
Subject: [Help-glpk] Condensing a sparse matrix by creating a subset of parameter data

 

Hi,

 

I have an lp model that produces an extremely sparse constraint matrix. I would like to reduce the number of non-zero entries in this matrix (make the matrix more dense). The main cause of this sparse-ness is the relation between two parameters. They can be seen as ‘arcs’ and ‘nodes: not all nodes have arcs between them. Is there a way to create a subset of parameter data from the sets ‘arcs’ and ‘nodes’ based on whether they are connected? I would then be able to apply constraints only for this subset. In other languages (such as python) such an operation is possible through nested conditional statements. Is there a similar/equivalent approach in glpk/GNU mathprog?

 

Thanks!

Abhishek

 

 

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