I am having trouble interpreting the cplex.log file for an MIP problem. In my understanding the "Best Integer", as the name suggests refers to the best integer solution found so far, while the best "Objective" refers to the objective value at a given node. Is this correct? What exactly is the "Best Bound"? Is it the best lower bound found so far?

I have included below the cplex.log file for one of my problem instances. The problem considered is a minimization problem. As you can see, the "Best Bound" remains constant and is equal to the optimal solution, while the "Best Integer" gradually converges to the optimal value. I am not sure how to interpret this result. I am currently using the default cplex settings. Note that I have also supplied the MIP with a list of initial solutions.

This structure remains the same as the problem instances get bigger, with the "Best Integer" taking a considerable amount of time to converge. In your opinion, what is the best way to tune cplex for problems with this structure?

Kind regards,

A.

Nodes Cuts/

Node Left Objective IInf Best Integer Best Bound ItCnt Gap

- 0+ 0 387.7251 1037 ---

0 2 343.4073 292 387.7251 343.4073 1037 11.43%

Elapsed real time = 0.40 sec. (tree size = 0.01 MB, solutions = 1)

107 105 372.0909 302 387.7251 343.4073 7893 11.43%

621 607 359.5931 216 387.7251 343.4073 15206 11.43%

1094 1070 344.2520 127 387.7251 343.4073 31249 11.43%

- 1566+ 1508 387.7249 343.4073 42369 11.43%
- 1566+ 1508 387.4713 343.4073 42369 11.37%
- 1566+ 1508 386.4955 343.4073 42369 11.15%
- 1566+ 1508 383.9290 343.4073 42369 10.55%
- 1566+ 1508 383.1734 343.4073 42369 10.38%
- 1566+ 1508 382.2235 343.4073 42369 10.16%
- 1566+ 1508 379.4078 343.4073 42369 9.49%
- 1566+ 1508 378.2825 343.4073 42369 9.22%

- 1568+ 1510 371.4925 343.4073 42373 7.56%
- 1572+ 1502 367.0792 343.4073 42393 6.45%

- 1575+ 435 366.9893 343.4073 43347 6.43%

1577 438 343.4073 324 366.9893 343.4073 43406 6.43%

1581 441 343.4073 356 366.9893 343.4073 43511 6.43%

1587 445 359.9756 292 366.9893 343.4073 43741 6.43%

1941 578 361.9970 277 366.9893 343.4073 49665 6.43%

Elapsed real time = 6.06 sec. (tree size = 0.67 MB, solutions = 39)

2364 639 357.2918 212 366.9893 343.4073 59320 6.43%

- 3957 1851 integral 0 366.9035 343.4073 76520 6.40%
- 4815 2201 integral 0 365.2044 343.4073 87871 5.97%
- 6734 2780 integral 0 364.4900 343.4073 124609 5.78%
- 7103 2281 integral 0 362.3471 343.4073 131777 5.23%

- 9944 3462 integral 0 362.2291 343.4073 183613 5.20%
- 10326 3733 integral 0 361.2585 343.4073 189000 4.94%
- 11542 2747 integral 0 361.1162 343.4073 214161 4.90%
- 11926 2863 integral 0 360.2285 343.4073 220807 4.67%

- 13915 3315 integral 0 357.4021 343.4073 254310 3.92%
- 15854 2782 integral 0 357.1389 343.4073 281111 3.84%
- 16040 2918 integral 0 357.1389 343.4073 283118 3.84%
- 16452 3088 integral 0 356.6919 343.4073 290983 3.72%
- 17092+ 2334 352.1388 343.4073 299892 2.48%
- 17522+ 816 349.5491 343.4073 306612 1.76%
- 17522+ 797 347.9436 343.4073 306612 1.30%
- 17522+ 787 346.5327 343.4073 306612 0.90%