Hi. I would like to know what means that CPLEX restart the root node solution after found an infeaseable objective. When it happens usually the second root solution takes much longer (especially in the relaxation), so it would be great if there is some way to prevent that.
My problem is a MIQP. Part of the solution output is shown below.
Presolve eliminates 0 constraints and 166208 variables.
Adjusted problem:
135861 variables:
1392 binary variables
1131 integer variables
48960 nonlinear variables
84378 linear variables
216417 constraints, all linear; 904423 nonzeros
101370 equality constraints
115047 inequality constraints
1 nonlinear objective; 74847 nonzeros.
CPLEX 20.1.0.0: mipgap=3e2
mipdisplay=2
rinsheur=100
nodes=1000
return_mipgap=7
Retaining values of one MIP start for possible repair.
MIQP Presolve eliminated 78530 rows and 3422 columns.
MIQP Presolve modified 31 coefficients.
Reduced MIQP has 135736 rows, 130288 columns, and 814482 nonzeros.
Reduced MIQP has 984 binaries, 1131 generals, 0 SOSs, and 0 indicators.
Reduced MIQP objective Q matrix has 47052 nonzeros.
Probing fixed 0 vars, tightened 254813 bounds.
Probing time = 5.91 sec. (3673.54 ticks)
Reduced MIQP has 135736 rows, 130288 columns, and 814482 nonzeros.
Reduced MIQP has 984 binaries, 1131 generals, 0 SOSs, and 0 indicators.
Reduced MIQP objective Q matrix has 47052 nonzeros.
Classifier predicts products in MIQP should be linearized.
Probing fixed 0 vars, tightened 120180 bounds.
Probing time = 4.81 sec. (1342.51 ticks)
Clique table members: 2208.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 12 threads.
Root relaxation solution time = 756.09 sec. (1183507.55 ticks)
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
0 0 infeasible 25951
Root node processing (before b&c):
Real time = 804.08 sec. (1230112.84 ticks)
Parallel b&c, 12 threads:
Real time = 0.00 sec. (0.00 ticks)
Sync time (average) = 0.00 sec.
Wait time (average) = 0.00 sec.

Total (root+branch&cut) = 804.08 sec. (1230112.84 ticks)
Clique table members: 1522.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 12 threads.
Root relaxation solution time = 2007.50 sec. (2199398.66 ticks)
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
0 0 17022.6839 1023 17022.6839 124610

0+ 0 18140.4799 17022.6839 6.16% 0 0 17139.0531 1079 18140.4799 Cuts: 567 128178 5.52% 0 0 17139.7121 1086 18140.4799 MIRcuts: 46 128339 5.52% 0 0 17139.8192 1086 18140.4799 MIRcuts: 5 128389 5.52%
Heuristic still looking.
0 2 17139.8192 1086 18140.4799 17139.8192 128389 5.52%
Elapsed time = 4468.66 sec. (3533283.43 ticks, tree = 0.02 MB)
1 3 17142.1491 1088 18140.4799 17139.8192 130043 5.52%
2 4 17142.6028 1082 18140.4799 17139.8192 132083 5.52%
3 5 17169.6273 1081 18140.4799 17139.8192 132267 5.52%
4 3 17288.7713 1102 18140.4799 17139.8192 133662 5.52%
5 4 17270.7188 1083 18140.4799 17139.8192 132678 5.52%
6 6 17174.0142 1062 18140.4799 17139.8192 134415 5.52%
7 7 17294.8080 1094 18140.4799 17142.1790 139536 5.50%
8 9 17193.8068 1072 18140.4799 17142.6028 143547 5.50%
9 10 17294.9808 1089 18140.4799 17142.6028 144982 5.50%
10 7 17306.2008 1089 18140.4799 17142.6028 139465 5.50%
Elapsed time = 4707.67 sec. (3622505.19 ticks, tree = 0.02 MB)
11 11 17195.1018 1070 18140.4799 17142.6028 146341 5.50%
12 12 17298.2337 1096 18140.4799 17142.6028 146931 5.50%
Thanks in advance