ILOG CPLEX 11.0 User's Manual

Here is an example of a log file for a barrier optimization (without crossover):Tried aggregator 1 time.LP Presolve eliminated 9 rows and 11 columns.Aggregator did 6 substitutions.Reduced LP has 12 rows, 15 columns, and 38 nonzeros.Presolve time = 0.00 sec.Number of nonzeros in lower triangle of A*A' = 26Using Approximate Minimum Degree orderingTotal time for automatic ordering = 0.00 sec.Summary statistics for Cholesky factor:Rows in Factor = 12Integer space required = 12Total non-zeros in factor = 78Total FP ops to factor = 650Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf0 -1.3177911e+01 -1.2600000e+03 6.55e+02 0.00e+00 3.92e+011 -4.8683118e+01 -5.4058675e+02 3.91e+01 0.00e+00 1.18e+012 -1.6008142e+02 -3.5969226e+02 1.35e-13 7.11e-15 5.81e+003 -3.5186681e+02 -6.1738305e+02 1.59e-10 1.78e-15 5.16e-014 -4.5808732e+02 -4.7450513e+02 5.08e-12 1.95e-14 4.62e-025 -4.6435693e+02 -4.6531819e+02 1.66e-12 1.27e-14 1.59e-036 -4.6473085e+02 -4.6476678e+02 5.53e-11 2.17e-14 2.43e-157 -4.6475237e+02 -4.6475361e+02 5.59e-13 2.99e-14 2.19e-158 -4.6475312e+02 -4.6475316e+02 1.73e-13 1.55e-14 1.17e-159 -4.6475314e+02 -4.6475314e+02 1.45e-13 2.81e-14 2.17e-15Barrier - Optimal: Objective = -4.6475314194e+02Solution time = 0.01 sec. Iterations = 9Preprocessing in the Log FileThe opening lines of that log file record information about preprocessing by theILOG CPLEX presolver and aggregator. After those preprocessing statistics, the next linerecords the number of nonzeros in the lower triangle of a particular matrix, AA T , denotedA*A' in the log file.Nonzeros in Lower Triangle of AA T in the Log FileThe number of nonzeros in the lower triangle of AA T gives an early indication of how longeach barrier iteration will take in terms of a relative measure of time. The larger this number,the more time each barrier iteration requires. If this number is close to 50% of the square ofthe number of rows of the reduced LP, then the problem may contain dense columns that arenot being detected. In that case, examine the histogram of column counts; then considersetting the barrier column-nonzeros parameter to a value that enables ILOG CPLEX to treatmore columns as being dense.In the Interactive Optimizer, you can examine the histogram of column counts with thecommand display problem histogram.ILOG CPLEX 11.0 — USER’ S MANUAL 203