The Mixed Integer Linear Programming Solver
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 1,000, then the absolute gap is displayed. If no active nodes remain, the value of Gap is 0.
- Time
-
indicates the elapsed real time.
The LOGFREQ= 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 LOGFREQ= option enables you to change the interval between entries in the node log. Figure 7.3 shows a sample node log.
Figure 7.3: Sample Node Log
| NOTE: Problem generation will use 4 threads. |
| 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 OPTMODEL presolver is disabled for linear problems. |
| NOTE: The MILP presolver value AUTOMATIC is applied. |
| NOTE: The MILP presolver removed 0 variables and 0 constraints. |
| NOTE: The MILP presolver removed 0 constraint coefficients. |
| NOTE: The MILP presolver modified 0 constraint coefficients. |
| NOTE: The presolved problem has 10 variables, 2 constraints, and 20 constraint |
| coefficients. |
| NOTE: The MILP solver is called. |
| Node Active Sols BestInteger BestBound Gap Time |
| 0 1 3 85.0000000 178.0000000 52.25% 0 |
| 0 1 3 85.0000000 88.0955497 3.51% 0 |
| 0 1 3 85.0000000 88.0626822 3.48% 0 |
| 0 1 3 85.0000000 87.9666563 3.37% 0 |
| 0 1 3 85.0000000 87.9661593 3.37% 0 |
| 0 1 3 85.0000000 87.8181818 3.21% 0 |
| NOTE: The MILP solver added 2 cuts with 13 cut coefficients at the root. |
| 3 2 5 87.0000000 87.4545455 0.52% 0 |
| NOTE: Optimal. |
| NOTE: Objective = 87. |