The Mixed Integer Linear Programming Solver

Node Log

The following information about the status of the branch-and-bound algorithm is printed in the node log:

Node
indicates the sequence number of the current node in the search tree.
Active
indicates the current number of active nodes in the branch-and-bound tree.
Sols
indicates the number of feasible solutions found so far.
BestInteger
indicates the best upper bound (assuming minimization) found so far.
BestBound
indicates the best lower bound (assuming minimization) found so far.
Gap
indicates the relative gap between BestInteger and BestBound, displayed as a percentage. If the relative gap is larger than 1000, then the absolute gap is displayed. If there are no active nodes remaining, the value of Gap is 0.
Time
indicates the elapsed real time.

The PRINTFREQ= option can be used to control the amount of information printed in the node log. By default a new entry is included in the log at the first node, at the last node, and at 100-node intervals. A new entry is also included each time a better integer solution is found. The PRINTFREQ= option enables you to change the interval between entries in the node log. Output 9.3 shows a sample node log.

NOTE: The problem has 10 variables (0 free, 0 fixed).                            
NOTE: The problem has 0 binary and 10 integer variables.                         
NOTE: The problem has 2 linear constraints (2 LE, 0 EQ, 0 GE, 0 range).          
NOTE: The problem has 20 linear constraint coefficients.                         
NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).       
NOTE: The OPTMILP presolver value AUTOMATIC is applied.                          
NOTE: The OPTMILP presolver removed 0 variables and 0 constraints.               
NOTE: The OPTMILP presolver removed 0 constraint coefficients.                   
NOTE: The OPTMILP presolver modified 0 constraint coefficients.                  
NOTE: The presolved problem has 10 variables, 2 constraints, and 20 constraint   
      coefficients.                                                              
NOTE: The MIXED INTEGER LINEAR solver is called.                                 
          Node  Active    Sols    BestInteger      BestBound      Gap    Time    
             0       1       1              0     88.0955497  100.00%       0    
             0       1       2     83.0000000     88.0626822    5.75%       0    
             0       1       2     83.0000000     87.9665871    5.65%       0    
             0       1       2     83.0000000     87.9660825    5.65%       0    
             0       1       3     85.0000000     87.9331742    3.34%       0    
             0       1       3     85.0000000     87.9140538    3.31%       0    
NOTE: OPTMILP added 3 cuts with 30 cut coefficients at the root.                 
             5       2       4     86.0000000     87.6821242    1.92%       0    
             8       0       5     87.0000000              .    0.00%       0    
NOTE: Optimal.                                                                   
NOTE: Objective = 87.                                                            
                                                                                 
                                                                                 


Figure 9.3: Sample Node Log

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