Dense columns can significantly degrade the performance of the barrier optimizer. A dense column is one in which a given variable appears in many rows. So that you can detect dense columns, the Interactive Optimizer contains a display feature that shows a histogram of the number of nonzeros in the columns of your model, display problem histogram c.

In fact, when a few dense columns are present in a problem, it is often effective to reformulate the problem to remove those dense columns from the model.

Otherwise, you can control whether ILOG CPLEX perceives columns as dense by setting the column nonzeros parameter. At its default setting, ILOG CPLEX calculates an appropriate value for this parameter automatically. However, if your problem contains one (or a few) dense columns that remain undetected at the default setting (according to the log file), you can adjust this parameter yourself to help ILOG CPLEX detect it (or them). For example, in a large problem in which one column contains forty entries while the other columns contain less than five entries, you may benefit by setting the column nonzeros parameter to 30. This setting allows ILOG CPLEX to recognize that column as dense and thus invoke techniques to handle it.

To set the dense column threshold, set the parameter BarColNz to a positive integer. The default value of 0 (zero) means that ILOG CPLEX will set the threshold.