The Mixed Integer Linear Programming Solver: Node Log :: SAS/OR(R) 9.2 User's Guide: Mathematical Programming

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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