ILOG CPLEX offers several different algorithms in the ILOG CPLEX Barrier Optimizer for ordering the rows of a matrix:

Automatic ordering, the default option, will usually be the best choice. This option attempts to choose the most effective of the available ordering methods, and it usually results in the best order. It may require more time than the other settings. The ordering time is usually small relative to the total solution time, and a better order can lead to a smaller total solution time. In other words, a change in this parameter is unlikely to improve performance very much.

The AMD algorithm provides good quality order within moderate ordering time. AMF usually provides better order than AMD (usually 5-10% smaller factors) but it requires somewhat more time (10-20% more). ND often produces significantly better order than AMD or AMF. Ten-fold reductions in runtimes of the ILOG CPLEX Barrier Optimizer have been observed with it on some problems. However, ND sometimes produces worse order, and it requires much more time.

To select an ordering algorithm, set the parameter BarOrder to a value 0, 1, 2, or 3.