ILOG CPLEX 11.0 User's Manual

NodesCuts/Node Left Objective IInf Best Integer Best Node ItCnt Gap0 0 452.1107 27 452.1107 51* 0+ 0 549.0000 452.1107 51 17.65%0 0 468.2224 23 549.0000 Cuts: 17 64 14.71%* 0+ 0 512.0000 468.2224 64 8.55%0 0 470.5942 23 512.0000 Cuts: 2 68 8.09%0 0 470.6800 20 512.0000 Cuts: 3 70 8.07%0 2 470.6800 20 512.0000 470.6800 70 8.07%* 10 6 integral 0 499.0000 479.9271 129 3.82%Cover cuts applied: 2Zero-half cuts applied: 2Gomory fractional cuts applied: 1Populate: phase IIMIP emphasis: balance optimality and feasibility.100 26 infeasible 499.0000 500.0000 234 -0.20%Cover cuts applied: 2Zero-half cuts applied: 2Gomory fractional cuts applied: 1Solution pool: 20 solutions saved.Populate - Populate solution limit exceeded, integer optimal: Objective =4.9900000000e+02Solution time = 0.54 sec. Iterations = 261 Nodes = 193 (34)In that log, you see that the procedure executed its first and second phases. It reportsparameter settings, such as MIP emphasis, like other optimization logs. It also reports howmany solutions it found. It stops when it reaches the populate limit (20 solutions in thisexample).Interestingly, the gap printed in that log becomes negative in the second phase of populate.At the end of the first phase of populate, the model was solved to optimality; the best nodevalue and the best integer value coincided and were equal to the optimal objective value; thegap was zero. Early in the second phase, the best integer value remained equal to the optimalobjective value, but as populate progressed, nodes were explored and fathomed. At somepoint, all nodes with a relaxation value equal to the optimal objective value were fathomed.This fathoming explains why the best node value increased above the optimal objectivevalue (for a minimization problem, such as this example) as the search space was explored inthe second phase. Recall that the gap value is computed as:(best integer - best node ) * objsen / (abs (best integer) + 1e-10)Consequently, the gap can become negative. A negative gap value ( -g%) indicates that thesearch space explored by populate does not contain any more solutions that are less than g%worse than the optimal objective value.You can invoke the populate procedure multiple times. In successive invocations, it willre-use information it has accumulated in previous invocations. For example, if you then308 ILOG CPLEX 11.0 — USER’ S MANUAL