Results of truss problems
We solve problems from truss topology design:
- trto are problems from single-load truss topology design.
Normally formulated as LPs, here reformulated as SDPs for testing
purposes
(see, eg, Kocvara-Zowe).
- vibra are single load truss topology problems with a
vibration constraint. The constraint guarantees that the minimal
self-vibration frequency of the optimal structure is bigger than a
given value; see Kocvara.
- buck are single load truss topology problems with
linearized global buckling constraint. Originally a nonlinear matrix
inequality, the constraint should guarantee that the optimal
structure is mechanically stable (does not buckle); see Kocvara.
All problems from this set are characterized by sparsity of the linear
matrix operato A. From all the tested SDP solvers, only SDPT3
and PENNON, followed by SDPA, could solve them efficiently. All the
other codes needed at least five times more CPU time to solve the large
problems.
Problem dimensions
problem |
n |
m |
Optimal value |
trto3 |
544 |
321+544 |
1.28 (e) |
trto4 |
1200 |
673+1200 |
1.276582 |
trto5 |
3280 |
1761+3280 |
1.28 (e) |
buck3 |
544 |
641+544 |
607.6055 |
buck4 |
1200 |
1345+1200 |
486.1421 |
buck5 |
3280 |
3521+3280 |
436.2292 |
vibra3 |
544 |
641+544 |
172.6130 |
vibra4 |
1200 |
1345+1200 |
165.6133 |
vibra5 |
3280 |
3521+3280 |
165.9029 |
(e) denotes known exact optimal value;
n is the number of variables, m the size of the
matrix constraint;
25+36 means: matrix constraint of size 25 and 36 linear constraints
Results
problem |
SDPA |
|
SDPT3 |
|
PENNON |
|
|
CPU |
s |
CPU |
s |
CPU |
s |
trto3 |
18 |
6 |
19 |
7 |
18 |
7 |
trto4 |
186 |
6 |
124 |
6 |
113 |
7 |
trto5 |
2808 |
5 |
1422 |
5 |
1575 |
7 |
buck3 |
36 |
6 |
43 |
4 |
40 |
7 |
buck4 |
369 |
6 |
241 |
7 |
229 |
7 |
buck5 |
7305 |
5 |
2766 |
7 |
3131 |
5 |
vibra3 |
49 |
5 |
45 |
5 |
34 |
7 |
vibra4 |
399 |
7 |
294 |
6 |
199 |
7 |
vibra5 |
7313 |
7 |
3601 |
5 |
2810 |
7 |
Test performed on Pentium IV PC (2.5 GHz) with 2GB RDRAM running
Linux-2.4.19.
"s" is the number of digits of accuracy, CPU in seconds.
Michal
Kocvara
June 27, 2003