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[Bug-glpk] [Fwd: Numerical instability may cause re-ordering of variable
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From: |
Andrew Makhorin |
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Subject: |
[Bug-glpk] [Fwd: Numerical instability may cause re-ordering of variables] |
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Date: |
Sat, 16 Apr 2011 03:47:25 +0400 |
-------- Forwarded Message --------
From: Robbie Morrison <address@hidden>
Reply-To: Robbie Morrison <address@hidden>
To: GLPK bug list <address@hidden>
Subject: Numerical instability may cause re-ordering of variables
Date: Sat, 16 Apr 2011 10:36:10 +1200 (NZST)
Hello list, hello Andrew
My application creates lots of flow network problems,
some are max-flow, some are min-cost. This one is
min-cost.
I have been recovering spurious results whenever I hit
the following problem:
Warning: numerical instability (dual simplex, phase II)
Please note too this recent thread on [glpk-help] on
the same topic:
http://lists.gnu.org/archive/html/help-glpk/2011-04/msg00040.html
There should be sufficient information is this email to
reproduce the issue and to compare your results with
mine. The GLPK problem instance was exported from my
application using 'glp_write_prob'. GLPSOL seems to
mirror the same behavior in relation to scaling and
pre-solving. That said, the terminal output from
application is not contained in this email.
It seems that the response by GLPK to this instability
re-orders the GLPK problem structure, leading to the
false reporting of individual variables?
My system runs 64-bit 10.04 LTS Ubuntu Linux on Intel
Core i5-520M hardware. GLPK and my application are
compiled with g++ 4.4.3. Its a bit dated, I know.
One can provoke the numerical instability thru GLPSOL
by selecting '--nointopt' to omit the MIP preprocessor.
However adding '--noscale' in addition removes the
problem.
I note that the next release of GLPK will probably
circumvent this problem entirely by using a different
strategy to deal with the matter of numerical
instability.
---------------------------------
GLPSOL without instability
---------------------------------
$ glpsol --intopt --glp 0088-pro-193639.dc-a.glpk
GLPSOL: GLPK LP/MIP Solver, v4.45
Parameter(s) specified in the command line:
--intopt --glp 0088-pro-193639.dc-a.glpk
Reading problem data from `0088-pro-193639.dc-a.glpk'...
Problem: pro-193639.dc-a
Objective: obj.tsolve-nodal
234 rows, 160 columns, 439 non-zeros
One variable is binary
1127 lines were read
GLPK Integer Optimizer, v4.45
234 rows, 160 columns, 439 non-zeros
1 integer variable, which is binary
Preprocessing...
95 rows, 138 columns, 278 non-zeros
1 integer variable, which is binary
Scaling...
A: min|aij| = 4.649e-08 max|aij| = 2.967e+08 ratio = 6.383e+15
GM: min|aij| = 2.894e-01 max|aij| = 3.456e+00 ratio = 1.194e+01
EQ: min|aij| = 8.468e-02 max|aij| = 1.000e+00 ratio = 1.181e+01
2N: min|aij| = 4.875e-02 max|aij| = 1.566e+00 ratio = 3.213e+01
Constructing initial basis...
Size of triangular part = 89
Solving LP relaxation...
GLPK Simplex Optimizer, v4.45
95 rows, 138 columns, 278 non-zeros
0: obj = -1.591498189e-13 infeas = 9.143e+09 (6)
* 32: obj = -3.275523922e-09 infeas = 1.490e-08 (0)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
+ 32: mip = not found yet >= -inf (1; 0)
+ 52: >>>>> -3.952013571e-09 >= -3.952013571e-09 0.0% (1; 0)
+ 52: mip = -3.952013571e-09 >= tree is empty 0.0% (0; 1)
INTEGER OPTIMAL SOLUTION FOUND
Time used: 0.0 secs
Memory used: 0.2 Mb (260716 bytes)
---------------------------------
GLPSOL with instability
---------------------------------
$ glpsol --nointopt --glp 0088-pro-193639.dc-a.glpk
GLPSOL: GLPK LP/MIP Solver, v4.45
Parameter(s) specified in the command line:
--nointopt --glp 0088-pro-193639.dc-a.glpk
Reading problem data from `0088-pro-193639.dc-a.glpk'...
Problem: pro-193639.dc-a
Objective: obj.tsolve-nodal
234 rows, 160 columns, 439 non-zeros
One variable is binary
1127 lines were read
Scaling...
A: min|aij| = 4.649e-08 max|aij| = 2.967e+08 ratio = 6.383e+15
GM: min|aij| = 2.861e-01 max|aij| = 3.495e+00 ratio = 1.221e+01
EQ: min|aij| = 8.265e-02 max|aij| = 1.000e+00 ratio = 1.210e+01
Constructing initial basis...
Size of triangular part = 234
GLPK Simplex Optimizer, v4.45
234 rows, 160 columns, 439 non-zeros
Preprocessing...
95 rows, 138 columns, 278 non-zeros
Scaling...
A: min|aij| = 4.649e-08 max|aij| = 2.967e+08 ratio = 6.383e+15
GM: min|aij| = 2.894e-01 max|aij| = 3.456e+00 ratio = 1.194e+01
EQ: min|aij| = 8.468e-02 max|aij| = 1.000e+00 ratio = 1.181e+01
Constructing initial basis...
Size of triangular part = 89
0: obj = -1.591498189e-13 infeas = 5.200e+08 (6)
* 11: obj = -3.135441073e-09 infeas = 1.104e-08 (3)
* 12: obj = -3.275523922e-09 infeas = 0.000e+00 (3)
OPTIMAL SOLUTION FOUND
GLPK Integer Optimizer, v4.45
234 rows, 160 columns, 439 non-zeros
1 integer variable, which is binary
Integer optimization begins...
+ 12: mip = not found yet >= -inf (1; 0)
Warning: numerical instability (dual simplex, phase II)
+ 32: >>>>> -3.952013571e-09 >= -3.952013571e-09 0.0% (1; 0)
+ 32: mip = -3.952013571e-09 >= tree is empty 0.0% (0; 1)
INTEGER OPTIMAL SOLUTION FOUND
Time used: 0.0 secs
Memory used: 0.2 Mb (247265 bytes)
---------------------------------
Representative solution side-by-side
---------------------------------
The following indicates that the solution ordering
becomes distorted when a numerical instability is
struck. The full output is given at the end of this
email.
--nointopt --write --intopt --write
------------------------------------------------
234 160 234 160
...
0 6916961.15113418
0 6916961.15113418
...
0 100000000
0 100000000
...
0 100000000
0 100000000
...
36274964.5916194 100000000
36274964.5916194 100000000
...
0 100000000
0 100000000
...
100000000 45535604.1516149
100000000 45535604.1516149
...
0 50413223.1404959
0 50413223.1404959
...
0 100000000
0 100000000
......
---------------------------------
Problem in GLPK format
---------------------------------
The problem involves a Californian-style electricity
auction. The binary variable controls whether or not a
thermal plant should shut down under low duty.
p mip min 234 160 439
n p pro-193639.dc-a
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i 212 u 539664567.551672
n i 212 con212.asop-lmp-bid-hydro1-a04.lmp-hydro-1.bid-01.hi-band
n i 213 con213.asop-lmp-bid-hydro1-a04.couple.osp-coupling
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n i 224 con224.buy-side.couple.osp-coupling
n i 225 con225.iface-bal
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n i 226 con226.gate-stated-tariff-elec-a02.tech-capacity.lo-bal
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n i 229 con229.buy-side.couple.osp-coupling
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n i 231 con231.gate-stated-tariff-oxid-s01.capset-capacity.lo-bal
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n i 233 con233.buy-side.couple.osp-coupling
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a 0 140 3.03051781687898e-09
a 0 141 -9.68064591719777e-11
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a 163 38 1
a 164 117 -1
a 164 19 1
a 165 120 -1
a 165 119 1
a 165 118 1
a 166 119 -1
a 166 56 1
a 167 120 -1
a 167 37 1
a 168 123 -1
a 168 122 1
a 168 121 1
a 169 121 -1
a 169 2 1
a 170 122 -1
a 170 74 1
a 171 123 -1
a 171 55 1
a 172 126 -1
a 172 125 1
a 172 124 1
a 173 125 -1
a 173 92 1
a 174 126 -1
a 174 73 1
a 175 128 -1
a 175 127 -1
a 176 127 -1
a 176 91 1
a 177 132 -1
a 177 129 1
a 178 133 1
a 178 130 -1
a 179 131 -2.75844812282828
a 179 133 -4.64889637111859e-08
a 179 132 1
a 180 133 1
a 180 131 -118699776
a 181 133 1
a 181 131 -296749440
a 182 130 -1
a 182 112 1
a 183 136 -1
a 183 134 1
a 184 137 -1
a 184 135 1
a 185 137 -1
a 185 136 2.466
a 186 135 1
a 187 134 -1
a 187 129 1
a 188 141 1
a 188 140 1
a 188 139 1
a 188 138 -1
a 189 139 1
a 190 139 1
a 191 140 1
a 192 140 1
a 193 141 1
a 194 141 1
a 195 138 -1
a 195 135 1
a 196 143 1
a 196 142 -1
a 197 143 1
a 198 143 1
a 199 142 -1
a 199 118 1
a 200 146 1
a 200 145 1
a 200 144 -1
a 201 145 1
a 202 145 1
a 203 146 1
a 204 146 1
a 205 144 -1
a 205 142 1
a 206 148 1
a 206 147 -1
a 207 148 1
a 208 148 1
a 209 147 -1
a 209 124 1
a 210 150 1
a 210 149 -1
a 211 150 1
a 212 150 1
a 213 149 -1
a 213 147 1
a 214 153 -1
a 214 151 1
a 215 154 1
a 215 152 -1
a 216 154 -1
a 216 153 4e-06
a 217 154 1
a 218 154 1
a 219 151 -1
a 219 110 1
a 220 152 -1
a 220 135 1
a 221 155 1
a 222 155 1
a 223 156 1
a 224 156 -1
a 224 155 1
a 225 155 -1
a 225 116 1
a 226 157 1
a 227 157 1
a 228 158 1
a 229 158 -1
a 229 157 1
a 230 157 -1
a 230 128 1
a 231 159 1
a 232 159 1
a 233 160 -1
a 233 159 1
a 234 159 -1
a 234 129 1
e o f
---------------------------------
Complete solution side-by-side
---------------------------------
--nointopt --write --intopt --write
------------------------------------------------
234 160 234 160
5 -3.95201357112375e-09 5 -3.95201357112375e-09
0 -1.49011611938477e-08
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0 6916961.15113418
0 6916961.15113418
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36274964.5916194 100000000
36274964.5916194 100000000
0 0
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0 100000000
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0 -1.32348898008484e-23
100000000 100000000
100000000 100000000
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0 1.49011611938477e-08
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0 0
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0 0
0 0
3.992874104833e-24 0
3.992874104833e-24 0
0 0
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100000000 45535604.1516149
100000000 45535604.1516149
0 0
100000000 100000000
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0 50413223.1404959
0 7.45058059692383e-09
0 100000000
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50413223.1404958 100000000
50413223.1404958 100000000
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30230175.534458 0
30230175.534458 0
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100000000 0
100000000 0
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0 -1.49011611938477e-08
100000000 53850629.4672027
100000000 53850629.4672027
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64477394.4860528 0
64477394.4860528 0
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6385224.27440633 6385224.27440634
6385224.27440633 6385224.27440634
0 0
0 0
0 0
0 1.49011611938477e-08
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0 0
0.000666666666666667 0.000666666666665705
178049664 178049664
-1.11377406234852e-06 0
0 0
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0 0
40.8238624253673 40.8238624253672
0 0
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40.8238624253673 40.8238624253672
40.8238624253673 40.8238624253672
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
55895694.2946253 160235853.741609
55895694.2946253 160235853.741609
0 0
0 0
55895694.2946253 160235853.741609
55895694.2946253 160235853.741609
0 0
0 0
0 0
0 -7.105427357601e-15
40.8238624253673 40.8238624253672
40.8238624253673 40.8238624253672
0 0
0 0
200000000 200000000
200000000 200000000
200000000 200000000
0 0
0 0
5000000 5000000
5000000 5000000
5000000 5000000
0 0
0 0
16.5546887369697 16.5546887369697
16.5546887369697 16.5546887369697
0 0
0 0
-113456525.606342 -58992129.7579567
-136274964.591619 -130487490.124211
0 6916961.15113418
0 6702592.52041721
0 0
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0 100000000
0 84504132.231405
0 100000000
0 78305785.1239669
36274964.5916194 100000000
35150740.482375 96900826.446281
0 100000000
0 90702479.338843
0 0
0 1.32348898008484e-23
100000000 100000000
78305785.1239669 78305785.1239669
-350413223.140496 -297636773.444437
-400000000 -345535604.151615
0 0
0 0
0 0
0 0
3.992874104833e-24 0
0 0
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0 0
100000000 45535604.1516149
96900826.446281 44124376.7502219
100000000 100000000
90702479.338843 90702479.338843
100000000 100000000
84504132.231405 84504132.231405
100000000 100000000
78305785.1239669 78305785.1239669
-130230175.534458 0
-150413223.140496 -97636773.4444368
0 50413223.1404959
0 48850829.8613483
0 100000000
0 90702479.338843
0 100000000
0 84504132.231405
0 100000000
0 78305785.1239669
0 100000000
0 96900826.446281
50413223.1404958 100000000
45726043.303053 90702479.338843
100000000 100000000
84504132.231405 84504132.231405
0 100000000
0 78305785.1239669
-103851532.631391 0
-130230175.534458 0
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30230175.534458 0
25545747.5074243 0
100000000 0
78305785.1239669 0
49510470.020219 153850629.467203
32423431.9602282 130487490.124211
100000000 53850629.4672027
96900826.446281 52181705.000244
0 0
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0 100000000
0 78305785.1239669
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64477394.4860528 0
50489529.979781 0
-5000000 -5000000
-6385224.27440633 -6385224.27440634
0 0
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6385224.27440633 6385224.27440634
5000000 5000000
-103250560 -48786164.1516149
10205965.6063418 10205965.6063418
-113456525.606342 -58992129.7579567
296749440 296749440
-400000000 -345535604.151615
-103250560 -48786164.1516149
-150413223.140496 -97636773.4444368
200000000 200000000
-350413223.140496 -297636773.444437
0 0
-130230175.534458 0
-130230175.534458 0
-136274964.591619 -130487490.124211
32423431.9602282 130487490.124211
-103851532.631391 0
55895694.2946254 160235853.741609
-6385224.27440633 -6385224.27440634
49510470.020219 153850629.467203
-5000000 -5000000
5000000 5000000
16.5546887369697 16.5546887369697
296749440 296749440
1 1
16.5546887369697 16.5546887369697
296749440 296749440
16.5546887369697 16.5546887369697
40.8238624253673 40.8238624253672
16.5546887369697 16.5546887369697
40.8238624253673 40.8238624253672
40.8238624253673 40.8238624253672
0 0
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40.8238624253673 40.8238624253672
0 0
0 0
0 0
0 0
0 0
55895694.2946253 160235853.741609
55895694.2946253 160235853.741609
55895694.2946253 160235853.741609
55895694.2946253 160235853.741609
10205965.6063418 10205965.6063418
40.8238624253673 40.8238624253672
10205965.6063418 10205965.6063418
40.8238624253673 40.8238624253672
200000000 200000000
200000000 200000000
5000000 5000000
5000000 5000000
16.5546887369697 16.5546887369697
16.5546887369697 16.5546887369697
------------------------------------------------
---
Robbie Morrison
PhD student -- policy-oriented energy system simulation
Institute for Energy Engineering (IET)
Technical University of Berlin (TU-Berlin), Germany
University email (redirected) : address@hidden
Webmail (preferred) : address@hidden
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