Dear All,
Now the model is working fine for me. But it takes alot of time
when I increase number of processes very slightly. How can I see the room for
speeding up the solution ? Should I use other solver ? but what is the way to
optimize the model ?
Here is the updated model and the data that takes alot of time.
/* The set of processes that will
execute on different cores */
set Processes;
/* Total number of cores */
param p;
/* Number of cores per node */
param k;
/* The communication cost between
processes with ranks i and j */
param comm{i in Processes, j in
Processes};
/* Weight communicating across the
nodes between two processes */
param b_across_nodes;
/* Weight communicating within a node
between two processes */
param b_within_node;
/* Load on the process with rank i */
param load{i in Processes};
param tl := sum{i in
Processes}load[i];
param tc := b_across_nodes * sum{i in
Processes, j in Processes}comm[i,j];
/* x is a binary variable that shows
where process pi resides on core ki of node ni */
/* If there are p cores and k cores
per node then the number of nodes will be ceil(p/k) */
var x{pi in Processes, ni in
1..ceil(p/k), ki in 1..k}, binary;
var comcost{pi in Processes, pj in
Processes : pi > pj}, >= b_within_node;
var z;
s.t.
load_on_each_core{ni in 1..ceil(p/k), ki in 1..k}:
z >= sum{pi
in Processes} x[pi, ni, ki] * load[pi];
s.t.
comm_cost{pi in Processes, pj in Processes, ni in 1..ceil(p/k),
nj in
1..ceil(p/k) : (pi > pj) and (ni != nj)}:
comcost[pi,pj]
>= (comm[pj,pi]+comm[pi,pj])*
(b_within_node
+ (b_across_nodes-b_within_node)*
(sum{ki in
1..k} x[pi,ni,ki] + sum{kj in 1..k} x[pj,nj,kj] – 1));
minimize
timespan: z/tl + (sum{pi in Processes, pj in Processes: pi >
pj}comcost[pi,pj])/tc;
s.t. mapped{pi
in Processes}: sum{ni in 1..ceil(p/k), ki in 1..k} x[pi, ni, ki] = 1;
data;
set Processes := 1 2 3 4 5 6 7 8 9 10 11 12;
param p := 6;
param k := 2;
param b_across_nodes := 10;
param b_within_node := 3;
param load [1] 47 [2] 1 [3] 49 [4] 21 [5] 34 [6] 6 [7] 31 [8] 29 [9] 23 [10] 41
[11] 11 [12] 6;
param comm: 1 2 3 4 5 6 7 8 9 10 11 12 :=
1 0 0 0 0 2 6 0 0 0 0 0 0
2 0 0 0 7 0 0 6 0 0 0 0 6
3 0 0 0 0 1 7 0 2 0 4 10 0
4 0 6 1 0 1 0 0 0 0 0 9 10
5 8 4 8 0 0 0 0 8 1 2 0 0
6 5 0 0 5 4 0 3 6 0 8 0 0
7 8 0 4 0 0 0 0 0 7 0 0 1
8 0 0 0 9 8 1 3 0 0 8 0 0
9 10 0 0 5 0 4 9 6 0 0 0 0
10 10 0 3 0 0 0 0 0 0 0 0 8
11 0 9 0 0 0 0 0 0 0 0 0 0
12 0 0 2 0 5 2 5 0 0 0 0 0;
end;
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________________________________
From: "[email protected]" <[email protected]>
To: [email protected]
Cc: [email protected]
Sent: Saturday, October 22, 2011 8:53 PM
Subject: AW: Re: I need help to convert quadratic problem into linear
Hello Mudassar
in the objective function introduce the weights needed.
Best regards
Xypron_______________________________________________
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