[Cbc] wrong optimal solution - preprocess SOS - preprocess aggregate works fine

Pieter Zieschang pieter.zieschang at modis.de
Tue Jan 28 13:16:50 EST 2020


Hi John,

thanks for looking into that.
I noticed that the time spent is always too little, but wasn't sure if 
that is a real bug. Glad you found that.


I still have a test run output on that problem with cplex, which was on 
another machine, i guess some cplex 12.x version back then.
I'd say your end solution is relatively near to optimal, as cplex reached 
optimal as 382710 (in 33 seconds).


Thanks for the tip with the eventhandler, i'll look into that.

Any options which could be a good idea to reduce solve time to anywhere 
around ~300 seconds?
I'd happily try some things if you can point me to something or a good 
direction.  :-)

Thank you.




CPLEX> read 23844-T1_0
Selected objective sense:  MINIMIZE
Selected objective  name:  OBJ
Selected RHS        name:  RHS1
Selected bound      name:  BND1
Problem '23844-T1_0.mps' read.
Read time = 0.23 sec. (46.52 ticks)
CPLEX> opt
Tried aggregator 3 times.
MIP Presolve eliminated 42470 rows and 27224 columns.
MIP Presolve modified 2970 coefficients.
Aggregator did 4530 substitutions.
Reduced MIP has 13575 rows, 13306 columns, and 117592 nonzeros.
Reduced MIP has 7871 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.28 sec. (291.99 ticks)
Found incumbent of value 6.1417173e+07 after 0.38 sec. (326.45 ticks)
Probing time = 0.03 sec. (7.70 ticks)
Tried aggregator 2 times.
MIP Presolve eliminated 2638 rows and 3354 columns.
MIP Presolve modified 34 coefficients.
Aggregator did 2 substitutions.
Reduced MIP has 10935 rows, 9946 columns, and 67620 nonzeros.
Reduced MIP has 8637 binaries, 1059 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.14 sec. (132.26 ticks)
Probing time = 0.02 sec. (6.15 ticks)
Clique table members: 15956.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 8 threads.
Root relaxation solution time = 1.03 sec. (699.23 ticks)

        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt Gap

*     0+    0                       4.20351e+07   369432.0000 99.12%
      0     0   376997.5000  1119   4.20351e+07   376997.5000       30 
99.10%
*     0+    0                       4.02933e+07   376997.5000 99.06%
      0     0   377106.5278   565   4.02933e+07     Cuts: 125     1277 
99.06%
*     0+    0                      1740037.6667   377106.5278 78.33%
      0     0   377209.3421   877  1740037.6667      Cuts: 66     2240 
78.32%
*     0+    0                       497583.0000   377209.3421 24.19%
      0     0   377210.0000   720   497583.0000      Cuts: 54     3172 
24.19%
*     0+    0                       423436.0000   377210.0000 10.92%
      0     0   377313.4091   773   423436.0000      Cuts: 50     3953 
10.89%
      0     0   377410.0000   456   423436.0000  ZeroHalf: 33     4510 
10.87%
      0     0   377697.5000   565   423436.0000  ZeroHalf: 40     5416 
10.80%
*     0+    0                       388340.0000   377697.5000 2.74%
      0     0   379711.5625   669   388340.0000  ZeroHalf: 28     7060 
2.22%
*     0+    0                       387815.0000   379711.5625 2.09%
      0     0   379917.6613   806   387815.0000      Cuts: 63     7559 
2.04%
      0     0   380124.1250   673   387815.0000      Cuts: 67     8145 
1.98%
      0     0   382454.6500   508   387815.0000      Cuts: 55     8479 
1.38%
*     0+    0                       382815.0000   382454.6500 0.09%

Repeating presolve.
Tried aggregator 5 times.
MIP Presolve eliminated 6846 rows and 6632 columns.
MIP Presolve added 14 rows and 0 columns.
MIP Presolve modified 337 coefficients.
Aggregator did 475 substitutions.
Reduced MIP has 3607 rows, 2827 columns, and 16429 nonzeros.
Reduced MIP has 2537 binaries, 90 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.08 sec. (78.55 ticks)
Probing fixed 120 vars, tightened 0 bounds.
Probing changed sense of 19 constraints.
Probing time = 0.02 sec. (2.82 ticks)
Cover probing fixed 25 vars, tightened 0 bounds.
Tried aggregator 2 times.
MIP Presolve eliminated 404 rows and 451 columns.
MIP Presolve modified 577 coefficients.
Aggregator did 68 substitutions.
Reduced MIP has 3123 rows, 2303 columns, and 12783 nonzeros.
Reduced MIP has 2217 binaries, 86 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.03 sec. (23.50 ticks)
Probing fixed 8 vars, tightened 0 bounds.
Probing changed sense of 7 constraints.
Probing time = 0.00 sec. (2.08 ticks)
Tried aggregator 2 times.
MIP Presolve eliminated 45 rows and 19 columns.
MIP Presolve modified 8 coefficients.
Aggregator did 15 substitutions.
Reduced MIP has 3063 rows, 2269 columns, and 12536 nonzeros.
Reduced MIP has 2183 binaries, 86 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.01 sec. (20.33 ticks)
Represolve time = 0.24 sec. (200.68 ticks)
Probing fixed 1 vars, tightened 0 bounds.
Probing changed sense of 1 constraints.
Probing time = 0.00 sec. (1.97 ticks)
Clique table members: 6970.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 8 threads.
Root relaxation solution time = 0.23 sec. (195.57 ticks)

        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt Gap

*     0+    0                       382815.0000   382455.2000 0.09%
      0     0   382459.3333   393   382815.0000   382459.3333     8526 
0.09%
      0     0   382460.0000   389   382815.0000      Cuts: 90     8634 
0.09%
      0     0   382460.0000   423   382815.0000      Cuts: 34     8684 
0.09%
      0     0   382460.0000   271   382815.0000       Cuts: 5     8766 
0.09%
      0     0   382460.0000   395   382815.0000      Cuts: 26     9141 
0.09%
*     0+    0                       382710.0000   382460.0000 0.07%
      0     2   382460.0000   139   382710.0000   382520.8500     9141 
0.05%
Elapsed time = 14.55 sec. (8080.38 ticks, tree = 0.01 MB, solutions = 15)
     31    21   382630.3125   303   382710.0000   382520.8500    12397 
0.05%
    164    86   382627.9558   282   382710.0000   382520.8500    30324 
0.05%
    292   140   382627.9558   286   382710.0000   382520.8500    50041 
0.05%
    372   180   382547.5636   275   382710.0000   382520.8500    64456 
0.05%
    481   233   382611.6667   267   382710.0000   382520.8500    75253 
0.05%
    600   289   382633.5317   286   382710.0000   382547.8667    89473 
0.04%
    748   347        cutoff         382710.0000   382560.2667   107733 
0.04%
    877   424   382676.3393   226   382710.0000   382576.4348   124048 
0.03%
   1039   485   382652.2885   237   382710.0000   382577.5000   146785 
0.03%
   1758   876        cutoff         382710.0000   382611.6667   239269 
0.03%
Elapsed time = 20.01 sec. (11210.54 ticks, tree = 3.57 MB, solutions = 15)
   2585  1068   382627.9558   282   382710.0000   382620.5556   318110 
0.02%
   3393  1424   382693.9000   181   382710.0000   382627.9558   415392 
0.02%
   4310  1842   382627.9558   349   382710.0000   382627.9558   516917 
0.02%
   5006  2244   382585.0000   100   382710.0000   382627.9558   620717 
0.02%
   5043    46   382646.8500   328   382710.0000   382627.9558   624613 
0.02%

Clique cuts applied:  12
Cover cuts applied:  5
Mixed integer rounding cuts applied:  8
Zero-half cuts applied:  170
Lift and project cuts applied:  7
Gomory fractional cuts applied:  33

Root node processing (before b&c):
  Real time             =   14.53 sec. (8079.98 ticks)
Parallel b&c, 8 threads:
  Real time             =   19.20 sec. (11312.85 ticks)
  Sync time (average)   =    2.06 sec.
  Wait time (average)   =    0.02 sec.
                          ------------
Total (root+branch&cut) =   33.73 sec. (19392.83 ticks)

Solution pool: 19 solutions saved.

MIP - Integer optimal, tolerance (0.0001/1e-06):  Objective = 
3.8271000000e+05
Current MIP best bound =  3.8267319672e+05 (gap = 36.8033, 0.01%)
Solution time =   33.77 sec.  Iterations = 659328  Nodes = 5309 (16)
Deterministic time = 19392.96 ticks  (574.33 ticks/sec)






Mit freundlichen Grüßen / Kind regards
________________________________________

Pieter Zieschang

Modis IT Outsourcing GmbH
Atriumstraße 1, 04315 Leipzig

Amtsgericht Düsseldorf: HRB 78227
Geschäftsführer: Martin Wimmer, Jörg Brinkmann

ito.modis.de






From:   "John Forrest" <jjhforrest at gmail.com>
To:     "Pieter Zieschang" <pieter.zieschang at modis.de>
Cc:     cbc at list.coin-or.org
Date:   28.01.2020 18:55
Subject:        Re: [Cbc] wrong optimal solution - preprocess SOS - 
preprocess aggregate works fine



Pieter,

There seems to be a minor bug in that the time spent before entering 
Branch and Bound counts twice against the maximum time limit!  So time 
in solving it was less than 600 seconds - just 460 Cpu seconds which is 
not a lot.  Problem still has 23000 rows after preprocessing so is not 
going to solve very quickly.

I have tried a local fix for time problem (needs a bit more thinking to 
make some printout better) just solved normally giving ratiogap of 0.001 
and 1500 seconds elapsed with 4 cores.

I had 710059 as solution at root node and 382785 at end.

Probably you should look at some of the examples using the event handler 
to decide when to stop - as that would give you greater control.

John Forrest

On 27/01/2020 09:37, Pieter Zieschang wrote:
> Hi John,
> 
> Presolve=SOS is working now for most problems i have.
> 
> Except this one 
> https://mega.nz/#!pvwDCC4A!GQBkhIZxkTdYaasgv_zGJwtIa1xQnWA98zisqsb2G-Q
> 
> 
> Seems like it didn't find any solution at all?
> Maybe my parameters are too bad.
> 
> 
> /opt/msp/cbc-trunk-2020-01-24/bin/cbc 23844-T1_0.mps timemode=elapsed 
> -seconds=600 -keepNames=on -threads=8 -dualt=1e-06 -perturb=on 
> -pertvalue=61 -constraint=on -cuts=on -clique=forceon -zero=forceon 
> -probing=forceonstrong -combine=on -combine2=on -ratiogap=0.001 
> -multiple=8 -preprocess=sos -solve
> 
> ...
> 
> Cbc0012I Integer solution of 1.0045498e+09 found by Multiple root 
> solvers after 0 iterations and 0 nodes (334.98 seconds)
> Cbc0030I Thread 0 used 0 times,  waiting to start 0.54918051, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 1 used 0 times,  waiting to start 0.48254895, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 2 used 0 times,  waiting to start 0.41087604, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 3 used 0 times,  waiting to start 0.34028697, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 4 used 0 times,  waiting to start 0.27142525, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 5 used 0 times,  waiting to start 0.20406055, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 6 used 0 times,  waiting to start 0.13375831, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Thread 7 used 0 times,  waiting to start 0.064822912, 0 cpu 
> time, 0 locks, 0 locked, 0 waiting for locks
> Cbc0030I Main thread 0 waiting for threads,  1 locks, 1.1205673e-05 
> locked, 2.1457672e-06 waiting for locks
> Cbc0020I Exiting on maximum time
> Cbc0005I Partial search - best objective 1.0045498e+09 (best possible 
> 376997.5), took 0 iterations and 0 nodes (335.73 seconds)
> Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
> Cuts at root node changed objective from 376997 to 376997
> Probing was tried 0 times and created 0 cuts of which 0 were active 
> after adding rounds of cuts (0.000 seconds)
> Gomory was tried 0 times and created 0 cuts of which 0 were active after 

> adding rounds of cuts (0.000 seconds)
> Knapsack was tried 0 times and created 0 cuts of which 0 were active 
> after adding rounds of cuts (0.000 seconds)
> Clique was tried 0 times and created 0 cuts of which 0 were active after 

> adding rounds of cuts (0.000 seconds)
> MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 
> were active after adding rounds of cuts (0.000 seconds)
> FlowCover was tried 0 times and created 0 cuts of which 0 were active 
> after adding rounds of cuts (0.000 seconds)
> TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active 
> after adding rounds of cuts (0.000 seconds)
> ZeroHalf was tried 0 times and created 0 cuts of which 0 were active 
> after adding rounds of cuts (0.000 seconds)
> 
> Result - Stopped on time limit
> 
> Objective value:                1004549786.00000000
> Lower bound:                  376997.500
> Gap:  2663.61
> Enumerated nodes:               0
> Total iterations:               0
> Time (CPU seconds):             459.71
> Time (Wallclock seconds):       341.82
> 
> Total time (CPU seconds):       460.09   (Wallclock seconds):     342.24
> 
> 
> Thank you
> 
> 
> Mit freundlichen Grüßen / Kind regards
> ________________________________________
> 
> *Pieter Zieschang*
> 
> *Modis IT Outsourcing GmbH*
> Atriumstraße 1, 04315 Leipzig
> 
> Amtsgericht Düsseldorf: HRB 78227
> Geschäftsführer: Martin Wimmer, Jörg Brinkmann
> 
> ito.modis.de <https://ito.modis.de/>
> 
> 
> 
> 
> 
> 
> From: "John Forrest" <jjhforrest at gmail.com>
> To: cbc at list.coin-or.org
> Date: 24.01.2020 18:57
> Subject: Re: [Cbc] wrong optimal solution - preprocess SOS - preprocess 
> aggregate works fine
> Sent by: "Cbc" <cbc-bounces at coin-or.org>
> ------------------------------------------------------------------------
> 
> 
> 
> Pieter,
> 
> I think I have fixed the problem in trunk.
> 
> With some options, pre-processing tries to move costs from continuous
> variables to integer variables - and when it does that the offset to the
> objective will change.  It does this before presolving the problem.
> Your model has some fixed variables at non-zero values (which would have
> vanished in presolving).  There was a section of the code in
> CglPreProcess.cpp which got confused and adjusted the objective 
incorrectly.
> 
> When I ran the problem the solution values produced by the bad code were
> good, but the objective value did not match the correct value.
> 
> I have tested the changes on other models - but if anyone finds they
> have problems, add -DSKIP_MOVE_COSTS_TO_INTEGERS to your configure AND
> inform me.
> 
> John Forrest
> 
> 
> 
> On 24/01/2020 09:18, Pieter Zieschang wrote:
>> Hi Ted,
>> 
>> the version is current trunk, as of January 22th.
>> 
>> 
>> The problem is available for testing here: 
>> https://mega.nz/#!c3Y0CA7R!jFnYcFVzcnYSWucZrCIdgb_AQzE5etB1JlySKom1QuE
>> 
>> Command is in the post below.
>> 
>> 
>> I'm not sure if i make it to opening an issue on github today.
>> 
>> 
>> Thank you
>> 
>> 
>> Mit freundlichen Grüßen / Kind regards
>> ________________________________________
>> 
>> *Pieter Zieschang*
>> 
>> *Modis IT Outsourcing GmbH*
>> Atriumstraße 1, 04315 Leipzig
>> 
>> Amtsgericht Düsseldorf: HRB 78227
>> Geschäftsführer: Martin Wimmer, Jörg Brinkmann
>> 
>> ito.modis.de <https://ito.modis.de/>
>> 
>> 
>> 
>> 
>> 
>> 
>> From: "Ted Ralphs" <ted at lehigh.edu>
>> To: "Pieter Zieschang" <pieter.zieschang at modis.de>
>> Cc: "cbc" <cbc at list.coin-or.org>
>> Date: 24.01.2020 04:36
>> Subject: Re: [Cbc] wrong optimal solution - preprocess SOS - preprocess
>> aggregate works fine
>> 
------------------------------------------------------------------------
>> 
>> 
>> 
>> Hi Pieter,
>> 
>> Forgive me if I missed something, but what Cbc version? Could you  open
>> an issue on Github?
>> 
>> Ted
>> 
>> On Thu, Jan 23, 2020 at 5:23 AM Pieter Zieschang 
>> <_pieter.zieschang at modis.de_ <mailto:pieter.zieschang at modis.de>> wrote:
>> Hello,
>> 
>> there seems to be something going wrong when preprocess=sos (the 
>> default) is used, cbc selecting the wrong branch?
>> 
>> When preprocess=aggregate the correct optimal solution is found, also
>> solution time is longer, probably the
>> 
>> 
>> Correct Optimal Solution:
>> 
>> $ cbc Problem_25581_0.mps timemode=elapsed -seconds=400 -keepNames=on
>> -threads=8 -dualt=1e-06 -perturb=on -pertvalue=61 -constraint=on 
>> -cuts=on -clique=forceon -zero=forceon -probing=forceonstrong 
>> -combine=on -combine2=on -ratiogap=0.001 -multiple=8 
>> -preprocess=aggregate -solve
>> 
>> Cbc0011I Exiting as integer gap of 3.0000005e-05 less than 1e-10 or 
0.1%
>> Cbc0001I Search completed - best objective 180.9999999999945, took 1048
>> iterations and 0 nodes (117.76 seconds)
>> Cbc0035I Maximum depth 0, 289 variables fixed on reduced cost
>> Cuts at root node changed objective from 177 to 181
>> Probing was tried 108 times and created 793 cuts of which 0 were active
>> after adding rounds of cuts (1152.645 seconds)
>> Gomory was tried 108 times and created 441 cuts of which 0 were active
>> after adding rounds of cuts (25.991 seconds)
>> Knapsack was tried 108 times and created 18 cuts of which 0 were active
>> after adding rounds of cuts (9.414 seconds)
>> Clique was tried 108 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.226 seconds)
>> MixedIntegerRounding2 was tried 108 times and created 27 cuts of which 
0
>> were active after adding rounds of cuts (15.430 seconds)
>> FlowCover was tried 108 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (6.004 seconds)
>> TwoMirCuts was tried 108 times and created 1530 cuts of which 0 were
>> active after adding rounds of cuts (33.287 seconds)
>> ZeroHalf was tried 108 times and created 27 cuts of which 0 were active
>> after adding rounds of cuts (67.834 seconds)
>> 
>> Result - Optimal solution found (within gap tolerance)
>> 
>> Objective value:                181.00000000
>> Lower bound:  181.000
>> Gap:        0.00
>> Enumerated nodes:              0
>> Total iterations:              1048
>> Time (CPU seconds):             656.08
>> Time (Wallclock seconds):       121.02
>> 
>> Total time (CPU seconds):       656.23   (Wallclock  seconds):       
121.18
>> 
>> 
>> 
>> 
>> 
>> Wrong Optimal Solution:
>> 
>> $ cbc Problem_25581_0.mps timemode=elapsed -seconds=400 -keepNames=on
>> -threads=8 -dualt=1e-06 -perturb=on -pertvalue=61 -constraint=on 
>> -cuts=on -clique=forceon -zero=forceon -probing=forceonstrong 
>> -combine=on -combine2=on -ratiogap=0.001 -multiple=8 -solve
>> Cbc0011I Exiting as integer gap of 49802 less than 1e-10 or 0.1%
>> Cbc0001I Search completed - best objective 1200049979, took 0 
iterations
>> and 0 nodes (67.05 seconds)
>> Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
>> Cuts at root node changed objective from 1.2e+09 to 1.2e+09
>> Probing was tried 0 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.000 seconds)
>> Gomory was tried 0 times and created 0 cuts of which 0 were active 
after
>> adding rounds of cuts (0.000 seconds)
>> Knapsack was tried 0 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.000 seconds)
>> Clique was tried 0 times and created 0 cuts of which 0 were active 
after
>> adding rounds of cuts (0.000 seconds)
>> MixedIntegerRounding2 was tried 0 times and created 0 cuts of which  0
>> were active after adding rounds of cuts (0.000 seconds)
>> FlowCover was tried 0 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.000 seconds)
>> TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.000 seconds)
>> ZeroHalf was tried 0 times and created 0 cuts of which 0 were active
>> after adding rounds of cuts (0.000 seconds)
>> Cgl0014I Postprocessing changed objective from 1.20005e+09 to 49979  -
>> possible tolerance issue - try without preprocessing
>> 
>> Result - Optimal solution found (within gap tolerance)
>> 
>> Objective value:                1200049979.00000000
>> Lower bound:  1200000177.000
>> Gap:        0.00
>> Enumerated nodes:              0
>> Total iterations:              0
>> Time (CPU seconds):             241.92
>> Time (Wallclock seconds):       72.52
>> 
>> Total time (CPU seconds):       242.06   (Wallclock  seconds):       
72.68
>> 
>> 
>> 
>> Thanks
>> 
>> 
>> 
>> 
>> 
>> Mit freundlichen Grüßen / Kind regards
>> ________________________________________
>> *
>> Pieter Zieschang*
>> *
>> Modis IT Outsourcing GmbH*
>> Atriumstraße 1, 04315 Leipzig
>> 
>> Amtsgericht Düsseldorf: HRB 78227
>> Geschäftsführer: Martin Wimmer, Jörg Brinkmann
>> _
>> __ito.modis.de_ <https://ito.modis.de/>
>> 
>> 
>> Diese E-Mail und alle Anhänge sind vertraulich und für den Adressaten
>> bestimmt und können auch privilegiert oder von der Offenlegung nach
>> geltendem Recht ausgenommen sein. Wenn Sie nicht der Adressat sind oder
>> diese E-Mail irrtümlicherweise erhalten haben, benachrichtigen Sie  den
>> Absender unverzüglich, löschen Sie die E-Mail aus Ihrem System und
>> kopieren Sie keine Teile dieser E-Mail oder deren Anhänge und geben Sie
>> sie nicht weiter.
>> 
>> This email and any attachments are confidential and intended for the
>> addressee and may also be privileged or exempt from disclosure under
>> applicable law. If you are not the addressee, or have received this
>> email in error, please notify the sender immediately, delete it from
>> your system and do not copy, or disclose or otherwise act upon any part
>> of this email or its attachments.
>> _______________________________________________
>> Cbc mailing list_
>> __Cbc at list.coin-or.org_ <mailto:Cbc at list.coin-or.org>_
>> __https://list.coin-or.org/mailman/listinfo/cbc_
>> 
>> 
>> -- 
>> Dr. Ted Ralphs
>> Professor, Industrial and Systems Engineering
>> Lehigh University
>> (610) 628-1280
>> ted 'at' lehigh 'dot' edu_
>> __coral.ie.lehigh.edu/~ted_ <http://coral.ie.lehigh.edu/~ted>
>> 
>> Diese E-Mail und alle Anhänge sind vertraulich und für den Adressaten
>> bestimmt und können auch privilegiert oder von der Offenlegung nach
>> geltendem Recht ausgenommen sein. Wenn Sie nicht der Adressat sind oder
>> diese E-Mail irrtümlicherweise erhalten haben, benachrichtigen Sie  den
>> Absender unverzüglich, löschen Sie die E-Mail aus Ihrem System und
>> kopieren Sie keine Teile dieser E-Mail oder deren Anhänge und geben Sie
>> sie nicht weiter.
>> 
>> This email and any attachments are confidential and intended for the
>> addressee and may also be privileged or exempt from disclosure under
>> applicable law. If you are not the addressee, or have received this
>> email in error, please notify the sender immediately, delete it from
>> your system and do not copy, or disclose or otherwise act upon any part
>> of this email or its attachments.
>> 
>> _______________________________________________
>> Cbc mailing list
>> Cbc at list.coin-or.org
>> https://list.coin-or.org/mailman/listinfo/cbc
>> 
> 
> _______________________________________________
> Cbc mailing list
> Cbc at list.coin-or.org
> https://list.coin-or.org/mailman/listinfo/cbc
> 
> 
> Diese E-Mail und alle Anhänge sind vertraulich und für den Adressaten 
> bestimmt und können auch privilegiert oder von der Offenlegung nach 
> geltendem Recht ausgenommen sein. Wenn Sie nicht der Adressat sind oder 
> diese E-Mail irrtümlicherweise erhalten haben, benachrichtigen Sie den 
> Absender unverzüglich, löschen Sie die E-Mail aus Ihrem System und 
> kopieren Sie keine Teile dieser E-Mail oder deren Anhänge und geben Sie 
> sie nicht weiter.
> 
> This email and any attachments are confidential and intended for the 
> addressee and may also be privileged or exempt from disclosure under 
> applicable law. If you are not the addressee, or have received this 
> email in error, please notify the sender immediately, delete it from 
> your system and do not copy, or disclose or otherwise act upon any part 
> of this email or its attachments.




Diese E-Mail und alle Anhänge sind vertraulich und für den Adressaten bestimmt und können auch privilegiert oder von der Offenlegung nach geltendem Recht ausgenommen sein. Wenn Sie nicht der Adressat sind oder diese E-Mail irrtümlicherweise erhalten haben, benachrichtigen Sie den Absender unverzüglich, löschen Sie die E-Mail aus Ihrem System und kopieren Sie keine Teile dieser E-Mail oder deren Anhänge und geben Sie sie nicht weiter. 

This email and any attachments are confidential and intended for the addressee and may also be privileged or exempt from disclosure under applicable law. If you are not the addressee, or have received this email in error, please notify the sender immediately, delete it from your system and do not copy, or disclose or otherwise act upon any part of this email or its attachments.  
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.coin-or.org/pipermail/cbc/attachments/20200128/6a574d27/attachment-0001.html>


More information about the Cbc mailing list