Topic
20 replies Latest Post - ‏2013-03-21T15:39:00Z by SystemAdmin
SystemAdmin
SystemAdmin
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Pinned topic Uncertainty of the Branch and Bound paths

‏2012-12-25T16:22:22Z |
Hi folks, I am solving an MIP model using an initial solution as a start.
However, I found even for the single thread, it still has uncertainties during the branch and bound course. (I've set up the time limit as 300 for the purpose of test)

For some of the runs, it is done as follows:

1 of 1 MIP starts provided solutions. MIP start 
'm1' defined initial solution with objective 29415.0000. Tried aggregator 2 times. MIP Presolve eliminated 856 rows and 654 columns. MIP Presolve modified 3 coefficients. Aggregator did 1 substitutions. Reduced MIP has 3664 rows, 3435 columns, and 115916 nonzeros. Reduced MIP has 3388 binaries, 0 generals, 0 SOSs, and 0 indicators. Probing time =    0.00 sec. Tried aggregator 2 times. MIP Presolve eliminated 143 rows and 170 columns. MIP Presolve modified 1 coefficients. Aggregator did 2 substitutions. Reduced MIP has 3519 rows, 3263 columns, and 111048 nonzeros. Reduced MIP has 3216 binaries, 47 generals, 0 SOSs, and 0 indicators. Presolve time =    0.42 sec. Probing time =    0.00 sec. Clique table members: 3473. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: none, using 1 thread. Root relaxation solution time = 1.34 sec.   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap   *     0+    0                        29415.0000                   4248     --- 0     0    30234.1437  1502    29415.0000    30234.1437     4248    2.78% 0     0    30225.4410  1316    29415.0000      Cuts: 61     6351    2.76% 0     0    30221.6799  1144    29415.0000     Cuts: 150     7388    2.74% 0     0    30220.2116  1198    29415.0000      Cuts: 97     8374    2.74% 0     0    30219.6513  1212    29415.0000      Cuts: 77    10750    2.74% 0     0    30218.7611  1004    29415.0000     Cuts: 100    12270    2.73% 0     0    30217.5722  1061    29415.0000     Cuts: 120    13820    2.73% 0     2    30217.5722  1061    29415.0000    30217.5722    13820    2.73% Elapsed real time =  15.32 sec. (tree size =  0.00 MB, solutions = 1) 1     3    30217.1252   899    29415.0000    30217.5722    14923    2.73% 2     4    30211.4494  1026    29415.0000    30217.5722    17168    2.73% 3     5    30215.1361   851    29415.0000    30217.5722    18847    2.73% 5     7    30212.3342   968    29415.0000    30217.5722    19976    2.73% 6     8    30212.0567   978    29415.0000    30217.5722    24513    2.73% 8    10    30207.2422  1013    29415.0000    30217.5722    26160    2.73% 10    10    30203.1989  1013    29415.0000    30217.5722    27398    2.73% 11    11    30203.9168   898    29415.0000    30217.5722    28720    2.73% 14    14    30200.6541  1036    29415.0000    30217.5722    30078    2.73% 20    18    30182.0826   750    29415.0000    30217.5722    33408    2.73% Elapsed real time =  23.10 sec. (tree size =  0.32 MB, solutions = 1) 39    31    30211.4697  1073    29415.0000    30215.1173    41288    2.72% 41    33    30209.5456  1042    29415.0000    30215.1173    46339    2.72% 49    41    30198.4125   875    29415.0000    30215.1173    49800    2.72% 54    46    30180.7791   688    29415.0000    30215.1173    54692    2.72% 63    55    30169.3663   737    29415.0000    30215.1173    59572    2.72% 70    54    30197.9121   953    29415.0000    30212.3126    64979    2.71% 79    61    30189.9977   962    29415.0000    30212.3126    69733    2.71% 86    68    30164.9366   751    29415.0000    30212.3126    73707    2.71% 93    71    30195.7981   834    29415.0000    30212.0567    81189    2.71% 98    76    30184.1520   872    29415.0000    30212.0567    86682    2.71% Elapsed real time =  41.92 sec. (tree size =  1.16 MB, solutions = 1) 105    83    30176.8135   848    29415.0000    30212.0567    91672    2.71% 116    90    30201.7181   917    29415.0000    30212.0567   100136    2.71% 123    97    30184.3818   826    29415.0000    30212.0567   105387    2.71% 130   104    30178.4349   799    29415.0000    30212.0567   110801    2.71% 132   106    30175.2996   968    29415.0000    30212.0567   114632    2.71% 150   118    30202.8225   920    29415.0000    30211.4494   121855    2.71% 155   123    30196.0854   788    29415.0000    30211.4494   127803    2.71% 163   131    30178.2001   764    29415.0000    30211.4494   135286    2.71% 184   144    30204.3624  1070    29415.0000    30211.3994   142960    2.71% 188   148    30196.2152   939    29415.0000    30211.3994   148229    2.71% Elapsed real time =  59.08 sec. (tree size =  1.56 MB, solutions = 1) 191   151    30191.5246   996    29415.0000    30211.3994   153061    2.71% 197   157    30176.0740   731    29415.0000    30211.3994   158120    2.71% 207   167    30132.1471   666    29415.0000    30211.3994   164143    2.71% 216   172    30204.0600   896    29415.0000    30211.2448   170837    2.71% 225   181    30194.6595   929    29415.0000    30211.2448   175528    2.71% 228   184    30185.9217   928    29415.0000    30211.2448   181458    2.71% 232   188    30168.4025   817    29415.0000 30211.2448   187848    2.71% 237   189    infeasible          29415.0000    30211.2448   191902    2.71% 238   190    30202.0607   967    29415.0000    30211.2019   197086    2.71% 250   202    30175.1503   715    29415.0000    30211.2019   202320    2.71% Elapsed real time =  74.07 sec. (tree size =  1.72 MB, solutions = 1) 272   216    30209.2333   971    29415.0000    30209.6682   208016    2.70% 277   221    30198.4478  1045    29415.0000    30209.6682   214374    2.70% 280   224    30191.1722   952    29415.0000    30209.6682   218664    2.70% 283   227    30177.6451   967    29415.0000    30209.6682   224928    2.70% 291   235    30172.3435   788    29415.0000    30209.6682   230066    2.70% 297   237    30200.9816   917    29415.0000    30209.6682   237590    2.70% 301   241    30191.8126   776    29415.0000    30209.6682   241388    2.70% 307   247    30150.3967   682    29415.0000    30209.6682   246348    2.70% 328   262    30204.7360   912    29415.0000    30209.5455   252584    2.70% 334   268    30202.5697   906    29415.0000    30209.5455   256996    2.70% Elapsed real time =  90.25 sec. (tree size =  1.90 MB, solutions = 1) 336   270    30195.6205   998    29415.0000    30209.5455   263366    2.70% 340   274    30183.7959   824    29415.0000    30209.5455   267687    2.70% 344   278    30172.0109   868    29415.0000    30209.5455   273910    2.70% 346   280    30164.5600   904    29415.0000    30209.5455   279257    2.70% 351   281    30203.0051  1093    29415.0000    30209.5398   285122    2.70% 359   289    30180.2294   760    29415.0000    30209.5398   288899    2.70% 374   300    30205.5605  1007    29415.0000    30209.2333   291855    2.70% 387   313    30193.9437  1000    29415.0000    30209.2333   295682    2.70% 391   317    30181.5406   955    29415.0000    30209.2333   298950    2.70% 394   320    30172.3471   969    29415.0000    30209.2333   302259    2.70% Elapsed real time = 107.08 sec. (tree size =  3.57 MB, solutions = 1) 401   323    30208.3630   999    29415.0000    30208.9185   305311    2.70% 408   330    30196.4174   841    29415.0000    30208.9185   308937    2.70% 422   344    30010.5858   651    29415.0000    30208.9185   312926    2.70% 430   348    30197.9237  1042    29415.0000    30208.7231   316018    2.70% 435   353    30195.0571   769    29415.0000    30208.7231   319860    2.70% 445   363    30167.2207   571    29415.0000    30208.7231   323156    2.70% 469   381    30182.4483   822    29415.0000    30208.3569   326582    2.70% 481   393    30155.5731   722    29415.0000    30208.3569   330830    2.70% 504   410    30203.5082  1120    29415.0000    30207.2260   336305    2.69% 507   413    30179.2579  1169    29415.0000    30179.2579   371911    2.60% Elapsed real time = 170.84 sec. (tree size =  5.76 MB, solutions = 1) 510   415    30178.7249  1025    29415.0000    30179.2579   374065    2.60% 511   416    30172.5340  1093    29415.0000    30179.2579   376157    2.60% 514   418    30159.7378   872    29415.0000    30179.2579   379805    2.60% 516   419    30161.2098   872    29415.0000    30179.2579   383672    2.60% 518   420    30160.1693   921    29415.0000    30179.2579   388392    2.60% 521   422    30171.9605  1028    29415.0000    30179.2579   390675    2.60% 526   425    30156.9154   801    29415.0000    30179.2579   396972    2.60% 534   431    30170.8669   955    29415.0000    30179.2579   399522    2.60% 536   432    30170.8513   954    29415.0000    30179.2579   402148    2.60% 537   433    30170.8312   948    29415.0000    30179.2579   402201    2.60% Elapsed real time = 196.61 sec. (tree size =  5.84 MB, solutions = 1) 541   436    30149.2137   754    29415.0000    30179.2579   406430    2.60% 544   438    30156.9344   888    29415.0000    30179.2579   409595    2.60% 551   431    30156.5606   792    29415.0000    30179.2579   416371    2.60% 556   434    30150.3117   652 29415.0000    30179.2579   418850    2.60% 557   435    30144.3117   718    29415.0000    30179.2579   419736    2.60% 567   433    30148.0560   639    29415.0000    30179.2579   423904    2.60% 573   437    30140.4418   575    29415.0000    30179.2579   427455    2.60% 583   429    infeasible          29415.0000    30179.2579   430602    2.60% 594   416    30099.2464   316    29415.0000    30179.2579   434563    2.60% 613   406    30116.4572   395    29415.0000    30179.2579   437228    2.60% Elapsed real time = 217.97 sec. (tree size =  6.33 MB, solutions = 1) 622   396    30179.2579  1168    29415.0000    30179.2578   439035    2.60% 626   396    30177.0094  1073    29415.0000    30179.2578   441540    2.60% 639   405    30176.3306  1060    29415.0000    30179.2578   443267    2.60% 641   406    30175.6200  1038    29415.0000    30179.2578   445590    2.60% 643   406    30174.8835  1099    29415.0000    30179.2578   448274    2.60% 655   408    30151.3951   671    29415.0000    30179.2578   451117    2.60% 660   413    30151.1708   577    29415.0000    30179.2578   453831    2.60% 670   404    30143.0757   465    29415.0000    30179.2578   457112    2.60% 678   409    30150.8227   590    29415.0000    30179.2578   460027    2.60% 721   412    30174.0967  1169    29415.0000    30178.8803   473014    2.60% Elapsed real time = 243.88 sec. (tree size =  9.25 MB, solutions = 1) 747   423    30168.3738  1006    29415.0000    30178.8803   480964    2.60% 772   434    30130.2455   688    29415.0000    30178.8803   490391    2.60% 814   445    30172.6498   890    29415.0000    30178.7243   501478    2.60% 866   466    infeasible          29415.0000    30178.7243   513361    2.60% *   907+  420                        30020.0000    30178.7243   522139    0.53% 910   418    30177.2626   902    30020.0000    30178.6869   524274    0.53% 942   433    30124.9890   735    30020.0000    30178.6869   536289    0.53%   Clique cuts applied:  481 Implied bound cuts applied:  2 Zero-half cuts applied:  66 Gomory fractional cuts applied:  1   Solution pool: 2 solutions saved.   MIP - Time limit exceeded, integer feasible:  Objective = 3.0020000000e+004 Current MIP best bound = 3.0178686851e+004 (gap = 158.687, 0.53%) Solution time =  300.01 sec.  Iterations = 546724  Nodes = 1023 (428)


and for some other runs it is done as follows:

1 of 1 MIP starts provided solutions. MIP start 
'm1' defined initial solution with objective 29415.0000. Tried aggregator 2 times. MIP Presolve eliminated 856 rows and 654 columns. MIP Presolve modified 3 coefficients. Aggregator did 1 substitutions. Reduced MIP has 3664 rows, 3435 columns, and 115916 nonzeros. Reduced MIP has 3388 binaries, 0 generals, 0 SOSs, and 0 indicators. Probing time =    0.00 sec. Tried aggregator 2 times. MIP Presolve eliminated 143 rows and 170 columns. MIP Presolve modified 1 coefficients. Aggregator did 2 substitutions. Reduced MIP has 3519 rows, 3263 columns, and 111048 nonzeros. Reduced MIP has 3216 binaries, 47 generals, 0 SOSs, and 0 indicators. Presolve time =    0.41 sec. Probing time =    0.00 sec. Clique table members: 3473. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: none, using 1 thread. Root relaxation solution time =    1.08 sec.   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap   *     0+    0                        29415.0000                   4248     --- 0     0    30234.1437  1502    29415.0000    30234.1437     4248    2.78% 0     0    30225.4410  1316    29415.0000      Cuts: 61     6351    2.76% 0     0    30221.6799  1144    29415.0000     Cuts: 150     7388    2.74% 0     0    30220.2116  1198    29415.0000      Cuts: 97     8374    2.74% 0     0    30219.6513  1212    29415.0000      Cuts: 77    10750    2.74% 0     0    30218.7611  1004    29415.0000     Cuts: 100    12270    2.73% 0     0    30217.5722  1061    29415.0000     Cuts: 120    13820    2.73% 0     2    30217.5722  1061    29415.0000    30217.5722    13820    2.73% Elapsed real time =  13.04 sec. (tree size =  0.00 MB, solutions = 1) 1     3    30217.1252   899    29415.0000    30217.5722    14923    2.73% 2     4    30211.4494  1026    29415.0000    30217.5722    17168    2.73% 3     5    30215.1361   851    29415.0000    30217.5722    18847    2.73% 5     7    30212.3342   968    29415.0000    30217.5722    19976    2.73% 6     8    30212.0567   978    29415.0000    30217.5722    24513    2.73% 8    10    30207.2422  1013    29415.0000    30217.5722    26160    2.73% 10    10    30203.1989  1013    29415.0000    30217.5722    27398    2.73% 11    11    30203.9168   898    29415.0000    30217.5722    28720    2.73% 14    14    30200.6541  1036    29415.0000    30217.5722    30078    2.73% 20    18    30182.0826   750    29415.0000    30217.5722    33408    2.73% Elapsed real time =  19.70 sec. (tree size =  0.32 MB, solutions = 1) 39    31    30211.4697  1073    29415.0000    30215.1173    41288    2.72% 41    33    30209.5456  1042    29415.0000    30215.1173    46339    2.72% 49    41    30198.4125   875    29415.0000    30215.1173    49800    2.72% 54    46    30180.7791   688    29415.0000    30215.1173    54692    2.72% 63    55    30169.3663   737    29415.0000    30215.1173    59572    2.72% 70    54    30197.9121   953    29415.0000    30212.3126    64979    2.71% 79    61    30189.9977   962    29415.0000    30212.3126    69733    2.71% 86    68    30164.9366   751    29415.0000    30212.3126    73707    2.71% 93    71    30195.7981   834    29415.0000    30212.0567    81189    2.71% 98    76    30184.1520   872    29415.0000    30212.0567    86682    2.71% Elapsed real time =  37.05 sec. (tree size =  1.16 MB, solutions = 1) 105    83    30176.8135   848    29415.0000    30212.0567    91672    2.71% 116    90    30201.7181   917    29415.0000    30212.0567   100136    2.71% 123    97    30184.3818   826    29415.0000    30212.0567   105387    2.71% 130   104    30178.4349   799    29415.0000    30212.0567   110801    2.71% 132   106    30175.2996   968    29415.0000    30212.0567   114632    2.71% 150   118    30202.8225   920    29415.0000    30211.4494   121855    2.71% 155   123    30196.0854   788    29415.0000    30211.4494   127803    2.71% 163   131    30178.2001   764    29415.0000    30211.4494   135286    2.71% 184   144    30204.3624  1070    29415.0000    30211.3994   142960    2.71% 188   148    30196.2152   939    29415.0000    30211.3994   148229    2.71% Elapsed real time =  52.14 sec. (tree size =  1.56 MB, solutions = 1) 191   151    30191.5246   996    29415.0000    30211.3994   153061    2.71% 197   157    30176.0740   731    29415.0000    30211.3994   158120    2.71% 207   167    30132.1471   666    29415.0000    30211.3994   164143    2.71% 216   172    30204.0600   896    29415.0000    30211.2448   170837    2.71% 225   181    30194.6595   929    29415.0000    30211.2448   175528    2.71% 228   184    30185.9217   928    29415.0000    30211.2448   181458    2.71% 232   188    30168.4025   817    29415.0000    30211.2448   187848    2.71% 237   189    infeasible          29415.0000    30211.2448   191902    2.71% 238   190    30202.0607   967    29415.0000    30211.2019   197086    2.71% 250   202    30175.1503   715    29415.0000    30211.2019   202320    2.71% Elapsed real time =  64.97 sec. (tree size =  1.72 MB, solutions = 1) 272   216    30209.2333   971    29415.0000    30209.6682   208016    2.70% 277   221    30198.4478  1045    29415.0000    30209.6682   214374    2.70% 280   224    30191.1722   952    29415.0000    30209.6682   218664    2.70% 283 227    30177.6451   967    29415.0000    30209.6682   224928    2.70% 291   235    30172.3435   788    29415.0000    30209.6682   230066    2.70% 297   237    30200.9816   917    29415.0000    30209.6682   237590    2.70% 301   241    30191.8126   776    29415.0000    30209.6682   241388    2.70% 307   247    30150.3967   682    29415.0000    30209.6682   246348    2.70% 328   262    30204.7360   912    29415.0000    30209.5455   252584    2.70% 334   268    30202.5697   906    29415.0000    30209.5455   256996    2.70% Elapsed real time =  78.98 sec. (tree size =  1.90 MB, solutions = 1) 336   270    30195.6205   998    29415.0000    30209.5455   263366    2.70% 340   274    30183.7959   824    29415.0000    30209.5455   267687    2.70% 344   278    30172.0109   868    29415.0000    30209.5455   273910    2.70% 346   280    30164.5600   904    29415.0000    30209.5455   279257    2.70% 351   281    30203.0051  1093    29415.0000    30209.5398   285122    2.70% 359   289    30180.2294   760    29415.0000    30209.5398   288899    2.70% 374   300    30205.5605  1007    29415.0000    30209.2333   291855    2.70% 387   313    30193.9437  1000    29415.0000    30209.2333   295682    2.70% 391   317    30181.5406   955    29415.0000    30209.2333   298950    2.70% 394   320    30172.3471   969    29415.0000    30209.2333   302259    2.70% Elapsed real time =  93.60 sec. (tree size =  3.57 MB, solutions = 1) 401   323    30208.3630   999    29415.0000    30208.9185   305311    2.70% 408   330    30196.4174   841    29415.0000    30208.9185   308937    2.70% 422   344    30010.5858   651    29415.0000    30208.9185   312926    2.70% 430   348    30197.9237  1042    29415.0000    30208.7231   316018    2.70% 435   353    30195.0571   769    29415.0000    30208.7231   319860    2.70% 445   363    30167.2207   571    29415.0000    30208.7231   323156    2.70% 469   381    30182.4483   822    29415.0000    30208.3569   326582    2.70% 481   393    30155.5731   722    29415.0000    30208.3569   330830    2.70% 504   410    30203.5082  1120    29415.0000    30207.2260   336305    2.69% 507   413    30179.2579  1169    29415.0000    30179.2579   371911    2.60% Elapsed real time = 141.91 sec. (tree size =  5.76 MB, solutions = 1) 510   415    30178.7249  1025    29415.0000    30179.2579   374065    2.60% 511   416    30172.5340  1093    29415.0000    30179.2579   376157    2.60% 514   418    30159.7378   872    29415.0000    30179.2579   379805    2.60% 516   419    30161.2098   872    29415.0000    30179.2579   383672    2.60% 518   420    30160.1693   921    29415.0000    30179.2579   388392    2.60% 521   422    30171.9605  1028    29415.0000    30179.2579   390675    2.60% 526   425    30156.9154   801    29415.0000    30179.2579   396972    2.60% 534   431    30170.8669   955    29415.0000    30179.2579   399522    2.60% 536   432    30170.8513   954    29415.0000    30179.2579   402148    2.60% 537   433    30170.8312   948    29415.0000    30179.2579   402201    2.60% Elapsed real time = 158.67 sec. (tree size =  5.84 MB, solutions = 1) 541   436    30149.2137   754    29415.0000    30179.2579   406430    2.60% 544   438    30156.9344   888    29415.0000    30179.2579   409595    2.60% 551   431    30156.5606   792    29415.0000    30179.2579   416371    2.60% 556   434    30150.3117   652    29415.0000    30179.2579   418850    2.60% 557   435    30144.3117   718    29415.0000    30179.2579   419736    2.60% 567   433    30148.0560   639    29415.0000    30179.2579   423904    2.60% 573   437    30140.4418   575    29415.0000    30179.2579   427455    2.60% 583   429    infeasible          29415.0000    30179.2579   430602    2.60% 594   416    30099.2464   316    29415.0000    30179.2579   434563    2.60% 613   406    30116.4572   395    29415.0000    30179.2579   437228    2.60% Elapsed real time = 173.82 sec. (tree size =  6.33 MB, solutions = 1) 622   396    30179.2579  1168    29415.0000    30179.2578   439035    2.60% 626   396    30177.0094  1073    29415.0000    30179.2578   441540    2.60% 639   405    30176.3306  1060    29415.0000    30179.2578   443267    2.60% 641   406    30175.6200  1038    29415.0000    30179.2578   445590    2.60% 643   406    30174.8835  1099    29415.0000    30179.2578   448274    2.60% 655   408    30151.3951   671    29415.0000    30179.2578   451117    2.60% 660   413    30151.1708   577    29415.0000    30179.2578   453831    2.60% 670   404    30143.0757   465    29415.0000    30179.2578   457112    2.60% 678   409    30150.8227   590    29415.0000    30179.2578   460027    2.60% 721   412    30174.0967  1169    29415.0000    30178.8803   473014    2.60% Elapsed real time = 191.44 sec. (tree size =  9.25 MB, solutions = 1) 747   423    30168.3738  1006    29415.0000    30178.8803   480964    2.60% 772   434    30130.2455   688    29415.0000    30178.8803   490391    2.60% 814   445    30172.6498   890    29415.0000    30178.7243   501478    2.60% 866   466    infeasible          29415.0000    30178.7243   513361    2.60% 910   467    30177.2626   902    29415.0000    30178.6869   524314    2.60% 941   487    30124.9890   719    29415.0000    30178.6869   537650    2.60% 987   494    30084.8462   462    29415.0000    30178.6869   554250    2.60% 997   493    30170.7872   853    29415.0000    30178.5154   562226    2.60% 1009   500    30157.5281   813    29415.0000    30178.5154   573373    2.60% 1047   516    30143.3915   666    29415.0000    30178.5154   586663    2.60% Elapsed real time = 246.01 sec. (tree size = 13.49 MB, solutions = 1) 1104   540    30137.1321   603    29415.0000    30178.5154   600973    2.60% 1153   534    30170.1924  1191    29415.0000    30177.9282   613434    2.59% 1166   540    30162.9119  1057    29415.0000    30177.9282   621589    2.59% 1213   574    30142.3107   849    29415.0000    30177.9282 630764    2.59% 1283   624    30168.9770   964    29415.0000    30177.2615   647837    2.59% *  1307+  604                        30060.0000    30177.2615   654491    0.39% 1321   618    30139.1638   579    30060.0000    30177.2615   658438    0.39% 1354   643    30149.6112   691    30060.0000    30177.2306   668519    0.39% 1383   666    30164.0131  1040    30060.0000    30177.0067   680799    0.39% 1417   699    30105.1025   570    30060.0000    30177.0067   690986    0.39% 1449   722    30153.6713   844    30060.0000    30176.4137   698734    0.39% Elapsed real time = 299.16 sec. (tree size = 22.32 MB, solutions = 2)   Clique cuts applied:  553 Implied bound cuts applied:  2 Zero-half cuts applied:  69 Gomory fractional cuts applied:  1   Solution pool: 2 solutions saved.   MIP - Time limit exceeded, integer feasible:  Objective = 3.0060000000e+004 Current MIP best bound = 3.0176413712e+004 (gap = 116.414, 0.39%) Solution time =  300.01 sec.  Iterations = 700560  Nodes = 1450 (722)


And s
Updated on 2013-03-21T15:39:00Z at 2013-03-21T15:39:00Z by SystemAdmin
  • SystemAdmin
    SystemAdmin
    7944 Posts
    ACCEPTED ANSWER

    Re: Uncertainty of the Branch and Bound paths

    ‏2012-12-25T16:24:36Z  in response to SystemAdmin
    And some other runs like:
    
    1 of 1 MIP starts provided solutions. MIP start 
    'm1' defined initial solution with objective 29415.0000. Tried aggregator 2 times. MIP Presolve eliminated 856 rows and 654 columns. MIP Presolve modified 3 coefficients. Aggregator did 1 substitutions. Reduced MIP has 3664 rows, 3435 columns, and 115916 nonzeros. Reduced MIP has 3388 binaries, 0 generals, 0 SOSs, and 0 indicators. Probing time =    0.01 sec. Tried aggregator 2 times. MIP Presolve eliminated 143 rows and 170 columns. MIP Presolve modified 1 coefficients. Aggregator did 2 substitutions. Reduced MIP has 3519 rows, 3263 columns, and 111048 nonzeros. Reduced MIP has 3216 binaries, 47 generals, 0 SOSs, and 0 indicators. Presolve time =    0.50 sec. Probing time =    0.02 sec. Clique table members: 3473. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: none, using 1 thread. Root relaxation solution time =    1.50 sec.   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap   *     0+    0                        29415.0000                   4248     --- 0     0    30234.1437  1502    29415.0000    30234.1437     4248    2.78% 0     0    30225.4410  1316    29415.0000      Cuts: 61     6351    2.76% 0     0    30221.6799  1144    29415.0000     Cuts: 150     7388    2.74% 0     0    30220.2116  1198    29415.0000      Cuts: 97     8374    2.74% 0     0    30219.6513  1212    29415.0000      Cuts: 77    10750    2.74% 0     0    30218.7611  1004    29415.0000     Cuts: 100 12270    2.73% 0     0    30217.5722  1061    29415.0000     Cuts: 120    13820    2.73% 0     2    30217.5722  1061    29415.0000    30217.5722    13820    2.73% Elapsed real time =  17.94 sec. (tree size =  0.00 MB, solutions = 1) 1     3    30217.1252   899    29415.0000    30217.5722    14923    2.73% 2     4    30211.4494  1026    29415.0000    30217.5722    17168    2.73% 3     5    30215.1361   851    29415.0000    30217.5722    18847    2.73% 5     7    30212.3342   968    29415.0000    30217.5722    19976    2.73% 6     8    30212.0567   978    29415.0000    30217.5722    24513    2.73% 8    10    30207.2422  1013    29415.0000    30217.5722    26160    2.73% 10    10    30203.1989  1013    29415.0000    30217.5722    27398    2.73% 11    11    30203.9168   898    29415.0000    30217.5722    28720    2.73% 14    14    30200.6541  1036    29415.0000    30217.5722    30078    2.73% 20    18    30182.0826   750    29415.0000    30217.5722    33408    2.73% Elapsed real time =  27.66 sec. (tree size =  0.32 MB, solutions = 1) 39    31    30211.4697  1073    29415.0000    30215.1173    41288    2.72% 41    33    30209.5456  1042    29415.0000    30215.1173    46339    2.72% 49    41    30198.4125   875    29415.0000    30215.1173    49800    2.72% 54    46    30180.7791   688    29415.0000    30215.1173    54692    2.72% 63    55    30169.3663   737    29415.0000    30215.1173    59572    2.72% 70    54    30197.9121   953    29415.0000    30212.3126    64979    2.71% 79    61    30189.9977   962    29415.0000    30212.3126    69733    2.71% 86    68    30164.9366   751    29415.0000    30212.3126    73707    2.71% 93    71    30195.7981   834    29415.0000    30212.0567    81189    2.71% 98    76    30184.1520   872    29415.0000    30212.0567    86682    2.71% Elapsed real time =  51.23 sec. (tree size =  1.16 MB, solutions = 1) 105    83    30176.8135   848    29415.0000    30212.0567    91672    2.71% 116    90    30201.7181   917    29415.0000    30212.0567   100136    2.71% 123    97    30184.3818   826    29415.0000    30212.0567   105387    2.71% 130   104    30178.4349   799    29415.0000    30212.0567   110801    2.71% 132   106    30175.2996   968    29415.0000    30212.0567   114632    2.71% 150   118    30202.8225   920    29415.0000    30211.4494   121855    2.71% 155   123    30196.0854   788    29415.0000    30211.4494   127803    2.71% 163   131    30178.2001   764    29415.0000    30211.4494   135286    2.71% 184   144    30204.3624  1070    29415.0000    30211.3994   142960    2.71% 188   148    30196.2152   939    29415.0000    30211.3994   148229    2.71% Elapsed real time =  72.56 sec. (tree size =  1.56 MB, solutions = 1) 191   151    30191.5246   996    29415.0000    30211.3994   153061    2.71% 197   157    30176.0740   731    29415.0000    30211.3994   158120    2.71% 207   167    30132.1471   666    29415.0000    30211.3994   164143    2.71% 216   172    30204.0600   896    29415.0000    30211.2448   170837    2.71% 225   181    30194.6595   929    29415.0000    30211.2448   175528    2.71% 228   184    30185.9217   928    29415.0000    30211.2448   181458    2.71% 232   188    30168.4025   817    29415.0000    30211.2448   187848    2.71% 237   189    infeasible          29415.0000    30211.2448   191902    2.71% 238   190    30202.0607   967    29415.0000    30211.2019   197086    2.71% 250   202    30175.1503   715    29415.0000    30211.2019   202320    2.71% Elapsed real time =  91.24 sec. (tree size =  1.72 MB, solutions = 1) 272   216    30209.2333   971    29415.0000    30209.6682   208016    2.70% 277   221    30198.4478  1045    29415.0000    30209.6682   214374    2.70% 280   224    30191.1722   952    29415.0000    30209.6682   218664    2.70% 283   227    30177.6451   967    29415.0000    30209.6682   224928    2.70% 291   235    30172.3435   788    29415.0000 30209.6682   230066    2.70% 297   237    30200.9816   917    29415.0000    30209.6682   237590    2.70% 301   241    30191.8126   776    29415.0000    30209.6682   241388    2.70% 307   247    30150.3967   682    29415.0000    30209.6682   246348    2.70% 328   262    30204.7360   912    29415.0000    30209.5455   252584    2.70% 334   268    30202.5697   906    29415.0000    30209.5455   256996    2.70% Elapsed real time = 111.49 sec. (tree size =  1.90 MB, solutions = 1) 336   270    30195.6205   998    29415.0000    30209.5455   263366    2.70% 340   274    30183.7959   824    29415.0000    30209.5455   267687    2.70% 344   278    30172.0109   868    29415.0000    30209.5455   273910    2.70% 346   280    30164.5600   904    29415.0000    30209.5455   279257    2.70% 351   281    30203.0051  1093    29415.0000    30209.5398   285122    2.70% 359   289    30180.2294   760    29415.0000    30209.5398   288899    2.70% 374   300    30205.5605  1007    29415.0000    30209.2333   291855    2.70% 387   313    30193.9437  1000    29415.0000    30209.2333   295682    2.70% 391   317    30181.5406   955    29415.0000    30209.2333   298950    2.70% 394   320    30172.3471   969    29415.0000    30209.2333   302259    2.70% Elapsed real time = 132.96 sec. (tree size =  3.57 MB, solutions = 1) 401   323    30208.3630   999    29415.0000    30208.9185   305311    2.70% 408   330    30196.4174   841    29415.0000    30208.9185   308937    2.70% 422   344    30010.5858   651    29415.0000    30208.9185   312926    2.70% 430   348    30197.9237  1042    29415.0000    30208.7231   316018    2.70% 435   353    30195.0571   769    29415.0000    30208.7231   319860    2.70% 445   363    30167.2207   571    29415.0000    30208.7231   323156    2.70% 469   381    30182.4483   822    29415.0000    30208.3569   326582    2.70% 481   393    30155.5731   722    29415.0000    30208.3569   330830    2.70% 504   410    30203.5082  1120 29415.0000    30207.2260   336305    2.69% 507   413    30179.2579  1169    29415.0000    30179.2579   371911    2.60% Elapsed real time = 201.40 sec. (tree size =  5.76 MB, solutions = 1) 510   415    30178.7249  1025    29415.0000    30179.2579   374065    2.60% 511   416    30172.5340  1093    29415.0000    30179.2579   376157    2.60% 514   418    30159.7378   872    29415.0000    30179.2579   379805    2.60% 516   419    30161.2098   872    29415.0000    30179.2579   383672    2.60% 518   420    30160.1693   921    29415.0000    30179.2579   388392    2.60% 521   422    30171.9605  1028    29415.0000    30179.2579   390675    2.60% 526   425    30156.9154   801    29415.0000    30179.2579   396972    2.60% 534   431    30170.8669   955    29415.0000    30179.2579   399522    2.60% 536   432    30170.8513   954    29415.0000    30179.2579   402148    2.60% 537   433    30170.8312   948    29415.0000    30179.2579   402201    2.60% Elapsed real time = 227.47 sec. (tree size =  5.84 MB, solutions = 1) 541   436    30149.2137   754    29415.0000    30179.2579   406430    2.60% 544   438    30156.9344   888    29415.0000    30179.2579   409595    2.60% 551   431    30156.5606   792    29415.0000    30179.2579   416371    2.60% 556   434    30150.3117   652    29415.0000    30179.2579   418850    2.60% 557   435    30144.3117   718    29415.0000    30179.2579   419736    2.60% 567   433    30148.0560   639    29415.0000    30179.2579   423904    2.60% 573   437    30140.4418   575    29415.0000    30179.2579   427455    2.60% 583   429    infeasible          29415.0000    30179.2579   430602    2.60% 594   416    30099.2464   316    29415.0000    30179.2579   434563    2.60% 613   406    30116.4572   395    29415.0000    30179.2579   437228    2.60% Elapsed real time = 248.26 sec. (tree size =  6.33 MB, solutions = 1) 622   396    30179.2579  1168    29415.0000    30179.2578   439035    2.60% 626   396    30177.0094  1073 29415.0000    30179.2578   441540    2.60% 639   405    30176.3306  1060    29415.0000    30179.2578   443267    2.60% 641   406    30175.6200  1038    29415.0000    30179.2578   445590    2.60% 643   406    30174.8835  1099    29415.0000    30179.2578   448274    2.60% 655   408    30151.3951   671    29415.0000    30179.2578   451117    2.60% 660   413    30151.1708   577    29415.0000    30179.2578   453831    2.60% 670   404    30143.0757   465    29415.0000    30179.2578   457112    2.60% 678   409    30150.8227   590    29415.0000    30179.2578   460027    2.60% 721   412    30174.0967  1169    29415.0000    30178.8803   473014    2.60% Elapsed real time = 274.51 sec. (tree size =  9.25 MB, solutions = 1) 747   423    30168.3738  1006    29415.0000    30178.8803   480964    2.60% 772   434    30130.2455   688    29415.0000    30178.8803   490391    2.60% *   807+  379                        30020.0000    30178.8803   498106    0.53% 814   380    30172.6498   890    30020.0000    30178.7243   501325    0.53%   Clique cuts applied:  481 Implied bound cuts applied:  2 Zero-half cuts applied:  66 Gomory fractional cuts applied:  1   Solution pool: 2 solutions saved.   MIP - Time limit exceeded, integer feasible:  Objective = 3.0020000000e+004 Current MIP best bound = 3.0178724329e+004 (gap = 158.724, 0.53%) Solution time =  300.01 sec.  Iterations = 501374  Nodes = 815 (380)
    


    It seems that CPLEX found different solutions at different nodes by heuristics. Should a single thread have a deterministic solution course? I am so confused. I really appreciate for any help. Thanks in advance. The model and the initial solution files are attached.
  • SystemAdmin
    SystemAdmin
    7944 Posts
    ACCEPTED ANSWER

    Re: Uncertainty of the Branch and Bound paths

    ‏2012-12-25T16:25:52Z  in response to SystemAdmin
    the model file
    • SystemAdmin
      SystemAdmin
      7944 Posts
      ACCEPTED ANSWER

      Re: Uncertainty of the Branch and Bound paths

      ‏2012-12-25T16:26:29Z  in response to SystemAdmin
      the solution file
      • SystemAdmin
        SystemAdmin
        7944 Posts
        ACCEPTED ANSWER

        Re: Uncertainty of the Branch and Bound paths

        ‏2012-12-25T21:04:34Z  in response to SystemAdmin
        Hi There,

        Following is the output at iteration 406430 from the three runs you pasted:

        {clip}
        Nodes Cuts/
        Node Left Objective IInf Best Integer Best Node ItCnt Gap

        541 436 30149.2137 754 29415.0000 30179.2579 406430 2.60%

        541 436 30149.2137 754 29415.0000 30179.2579 406430 2.60%

        541 436 30149.2137 754 29415.0000 30179.2579 406430 2.60%
        {clip}

        All three match. Could be that the machine load is acting up on the final results. Maybe an iteration limit instead of time limit, would tell for sure.

        Regards,
        Vivek
        • SystemAdmin
          SystemAdmin
          7944 Posts
          ACCEPTED ANSWER

          Re: Uncertainty of the Branch and Bound paths

          ‏2012-12-25T23:46:17Z  in response to SystemAdmin
          Sorry, I was looking at the wrong column. I now see the problem!
  • Eumpfenbach
    Eumpfenbach
    198 Posts
    ACCEPTED ANSWER

    Re: Uncertainty of the Branch and Bound paths

    ‏2012-12-25T18:35:17Z  in response to SystemAdmin
    Does this help you any? Specifically, the last bullet.

    http://www-01.ibm.com/support/docview.wss?uid=swg21400040

    You are using Dynamic Search, which is a proprietary search algorithm in Cplex that the IBM guys can't really say TOO much about. You could try switching to traditional branch-and-cut, to see if the solution results are more stable. This will print the branching variables (set the mip display parameter accordingly). It is obvious from your incumbent solutions that the search path it took was different. Why? I dunno (assuming you absolutely changed no parameters).

    See if that gives you the desired repeatability, though.
    • SystemAdmin
      SystemAdmin
      7944 Posts
      ACCEPTED ANSWER

      Re: Uncertainty of the Branch and Bound paths

      ‏2012-12-26T01:47:23Z  in response to Eumpfenbach
      I don't think dynamic search is an opportunistic search even IBM did not release anything about it. In my mind, that would not be the trigger. The hardware would affect the solution time (or time/iteration) over different runs, but it should still result in the same path. My log shows that CPLEX is finding different solutions at different nodes by heuristics over runs, this might not be explained by the factor of hardware. Thank you all the same
      • SystemAdmin
        SystemAdmin
        7944 Posts
        ACCEPTED ANSWER

        Re: Uncertainty of the Branch and Bound paths

        ‏2012-12-26T18:47:32Z  in response to SystemAdmin
        There could be some random element in the heuristics. Even randomly breaking ties could cause the kind of minor changes like the one we see here.
  • Laci Ladanyi
    Laci Ladanyi
    50 Posts
    ACCEPTED ANSWER

    Re: Uncertainty of the Branch and Bound paths

    ‏2012-12-27T16:06:22Z  in response to SystemAdmin
    Whenever you post a log it is very useful if you also post the non-default parameter settings, since they can't always be deduced from the log itself. In this case this line
    MIP - Time limit exceeded, integer feasible: Objective = 3.0020000000e+004
    revealed that you have set a time limit. That is the cause of your differences. As CPLEX gets close to the time limit it switches the priorities of various components of the algorithm (like places more emphasis on heuristics). Obviously, if the machine is more loaded in one run than in another then the priorities will change at a different time, so from then on the trees will diverge.

    You need to use some other limit (deterministic time, node, iteration) to make sure the trees will be the same.

    --Laci
    • SystemAdmin
      SystemAdmin
      7944 Posts
      ACCEPTED ANSWER

      Re: Uncertainty of the Branch and Bound paths

      ‏2012-12-29T03:03:41Z  in response to Laci Ladanyi
      Thanks for your comments. I actually did mention the non-default setting regarding the time limit at the very beginning, but perhaps I should mark it as code to be more evident. I see the reason through your explanation. It helps me a lot. Happy New Year!
    • SystemAdmin
      SystemAdmin
      7944 Posts
      ACCEPTED ANSWER

      Re: Uncertainty of the Branch and Bound paths

      ‏2013-01-04T08:53:45Z  in response to Laci Ladanyi
      Hi Laci,

      How would you use the limit of iterations to make sure the trees will be the same? I did not see the parameter settings on ItCnt for MIP problem. Thanks.
      • SystemAdmin
        SystemAdmin
        7944 Posts
        ACCEPTED ANSWER

        Re: Uncertainty of the Branch and Bound paths

        ‏2013-01-04T09:50:38Z  in response to SystemAdmin
        A limit on the simplex iterations or barrier iterations would applied to MIP too, based on what sub algorithm you use to solve the MIP.

        ItLim or BarItLim.

        Would like to know how to set the deterministic time limit.

        Vivek.
        • SystemAdmin
          SystemAdmin
          7944 Posts
          ACCEPTED ANSWER

          Re: Uncertainty of the Branch and Bound paths

          ‏2013-01-04T09:56:34Z  in response to SystemAdmin
          The deterministic time limit is set via parameter CPX_PARAM_DETTILIM which is available since CPLEX 12.5.
        • SystemAdmin
          SystemAdmin
          7944 Posts
          ACCEPTED ANSWER

          Re: Uncertainty of the Branch and Bound paths

          ‏2013-01-05T02:08:39Z  in response to SystemAdmin
          If I did not get it wrong, the iteration limit for simplex/barrier when applied to MIP would only matter sub problems of each node, it does not impact the Iteration count displayed in the B&C tree log file which I think is the total iterations on simplex/barrier. If so, this is not what I want. I would like a limit on the total iterations for simplex/barrier for the nodes processed so far.
          • SystemAdmin
            SystemAdmin
            7944 Posts
            ACCEPTED ANSWER

            Re: Uncertainty of the Branch and Bound paths

            ‏2013-01-05T06:58:37Z  in response to SystemAdmin
            You are right. There seems to be no param that limits the total number of simplex/barrier iterations in MIP.

            Vivek.
    • SystemAdmin
      SystemAdmin
      7944 Posts
      ACCEPTED ANSWER

      Re: Uncertainty of the Branch and Bound paths

      ‏2013-01-05T03:25:07Z  in response to Laci Ladanyi
      Also another question for setting up a time limit for CPLEX when solving MIP.
      If I use MIPInfoCallback to check if the solution time is exceeding a time limit (set as an input for the instance of MIPInfoCallback) and use this criteria to terminate the solver, is this equivalent to use IloCplex.set(TimLim, AnNumberYouSetUpHere) which will change the priorities of heuristics when reaching the end?
      • SystemAdmin
        SystemAdmin
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        Re: Uncertainty of the Branch and Bound paths

        ‏2013-01-06T17:57:31Z  in response to SystemAdmin
        No, this will not affect heuristic decisions. If you don't that a time limit parameter but check for time limits in your info callback then CPLEX behaves as if no time limit was set. So using an info callback to terminate a solve is way to get rid of the non-deterministic behavior that CPLEX applies if a time limit is set. Notice however:
        1. Using any kind of wallclock or CPU time limit is inherently non-deterministic since the exact expiration of that limit will heavily depend on the OS scheduler and background load on the machine.
        2. CPLEX makes no guarantee for the frequency with which it invokes the info callback. The info callback is invoked with a "reasonable" frequency but you cannot implement high-resolution time limits with that.
        • SystemAdmin
          SystemAdmin
          7944 Posts
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          Re: Uncertainty of the Branch and Bound paths

          ‏2013-01-07T03:34:14Z  in response to SystemAdmin
          I see...Thanks
        • SystemAdmin
          SystemAdmin
          7944 Posts
          ACCEPTED ANSWER

          Re: Uncertainty of the Branch and Bound paths

          ‏2013-03-21T15:39:00Z  in response to SystemAdmin
          I just have met uncertainties of B & C paths again and I cannot explain it myself.

          Here are my CPLEX settings

          
          _cplex.setParam(IloCplex::EpGap, 0.02); _cplex.setParam(IloCplex::TreLim, 1024); _cplex.setParam(IloCplex::NodeFileInd, 2); _cplex.setParam(IloCplex::Threads, 1); _cplex.setParam(IloCplex::ClockType, 1);
          


          A set of lazy constraints are also added to CPLEX.

          Callback is also used for a more complex termination criteria and it is ILOMIPINFOCALLBACK.
          Here is the core of the stopping criteria
          
          #define TIME_LIMIT_FOR_NO_IMPROVEMENT        120 #define REL_GAP_FOR_NO_IMPROVEMENT  25   
          
          if ( !aborted  &&  hasIncumbent() ) 
          { IloNum gap = 100.0 * getMIPRelativeGap(); 
          
          long 
          
          long obj = (
          
          long 
          
          long)getIncumbentObjValue(); 
          
          if(obj < curObj) 
          { timeLastImproved = (
          
          int)cplex.getCplexTime(); curObj = obj; 
          } 
          
          else 
          { 
          
          int timeNotImproved = (
          
          int)cplex.getCplexTime() - timeLastImproved; 
          
          if(timeNotImproved > TIME_LIMIT_FOR_NO_IMPROVEMENT && gap < REL_GAP_FOR_NO_IMPROVEMENT) 
          { aborted = IloTrue; abort(); 
          } 
          } 
          }
          


          However I got different paths for a same problem
          First possibility:
          
          Tried aggregator 2 times. MIP Presolve eliminated 1377 rows and 1 columns. Aggregator did 109 substitutions. Reduced MIP has 17815 rows, 11187 columns, and 123335 nonzeros. Reduced MIP has 18 binaries, 10000 generals, 0 SOSs, and 0 indicators. Probing fixed 0 vars, tightened 4681 bounds. Probing time =    0.06 sec. Tried aggregator 1 time. MIP Presolve eliminated 12329 rows and 4681 columns. Reduced MIP has 5486 rows, 6506 columns, and 55933 nonzeros. Reduced MIP has 18 binaries, 5319 generals, 0 SOSs, and 0 indicators. Presolve time =    0.22 sec. Probing time =    0.03 sec. Clique table members: 2. Problem contains 221 lazy constraints. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: none, using 1 thread. Root relaxation solution time =    0.05 sec.   Nodes                                         Cuts/  Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap   0     0   238870.0000    17                 238870.0000      230 0     0   238870.0000    18                  MIRcuts: 2      238 0     0   238870.0000    23                 MIRcuts: 14      252 *     0+    0                      1.00819e+009   238870.0000      252   99.98% *     0+    0                      1.72934e+007   238870.0000      252   98.62% *     0+    0                       238870.0000   238870.0000      252    0.00% 0     0        cutoff         238870.0000   238870.0000      252    0.00% Elapsed time =   2.79 sec. (tree size =  0.00 MB, solutions = 3)   Lazy constraints applied:  56
          


          Second possibility
          
          Tried aggregator 2 times. MIP Presolve eliminated 1377 rows and 1 columns. Aggregator did 109 substitutions. Reduced MIP has 17815 rows, 11187 columns, and 123335 nonzeros. Reduced MIP has 18 binaries, 10000 generals, 0 SOSs, and 0 indicators. Probing fixed 0 vars, tightened 4681 bounds. Probing time =    0.06 sec. Tried aggregator 1 time. MIP Presolve eliminated 12329 rows and 4681 columns. Reduced MIP has 5486 rows, 6506 columns, and 55933 nonzeros. Reduced MIP has 18 binaries, 5319 generals, 0 SOSs, and 0 indicators. Presolve time =    0.22 sec. Probing time =    0.02 sec. Clique table members: 2. Problem contains 221 lazy constraints. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: none, using 1 thread. Root relaxation solution time =    0.06 sec.   Nodes Cuts/  Node  Left     Objective  IInf  Best Integer     Best Node    ItCnt     Gap   0     0   238870.0000    17                 238870.0000      230 0     0   238870.0000    13                    Cuts: 15      236 0     0   238870.0000    14                    Cuts: 17      266 0     0   238870.0000    15                 MIRcuts: 16      277 *     0+    0                      2.25514e+009   238870.0000      277   99.99% *     0+    0                      4.60213e+008   238870.0000      277   99.95% *     0+    0                      1.72607e+007   238870.0000      277   98.62% *     0+    0                      3271620.0000   238870.0000      277   92.70% *     0+    0                       272700.0000   238870.0000      277   12.41% *     0+    0                       270540.0000   238870.0000      277   11.71% *     0+    0                       269460.0000   238870.0000      277   11.35% 0     2   238870.0000    15   269460.0000   238870.0000      277   11.35% Elapsed time =   1.84 sec. (tree size =  0.00 MB, solutions = 7) *    10     0      integral     0   238870.0000   238870.0000      412    0.00%   Mixed integer rounding cuts applied:  4 Lazy constraints applied:  109
          


          And although both of them reach the same optimality, they generate different solution vectors.

          From the discussions we had several months ago, I don't think the reasons we listed in the thread could explain this behavior. Any thoughts of this phenomena? Many thanks in advance...

          Best,
          Jim