Figure 4.50: The Barrier Tab In CPLEX Options Dialog Box
You can change the Barrier options for CPLEX by choosing CPLEX parameters from the Options menu and then pressing the Barrier tab. This will display the dialog box shown below:
Figure 4.50: The Barrier Tab In CPLEX Options Dialog Box
| Option Name | MPL Name | Solver Param | ParamNr | Type | Default | Min | Max |
|---|---|---|---|---|---|---|---|
| Barrier Algorithm | BarrierAlgorithm | BarAlg | 3007 | list | 0 | 0 | 3 |
| Ordering Algorithm | BarrierOrderingAlg | BarOrder | 3014 | list | 0 | 0 | 3 |
| Starting Point Algorithm | BarrierStartPointAlg | BarStartAlg | 3017 | list | 1 | 1 | 4 |
| Column Nonzeros | BarrierColNonzeros | BarColNz | 3009 | int | 0 | 0 | MAXINT |
| Max Correction Limit | BarrierMaxCorrLimit | BarMaxCor | 3013 | int | -1 | -1 | 10 |
| Iteration Limit | BarrierIterationLimit | BarItLim | 3012 | int | 200 | 0 | MAXINT |
| Growth Limit | BarrierGrowthLimit | BarGrowth | 3003 | real | 1e6 | 1 | MAXREAL |
| Objective Range | BarrierObjectiveRange | BarObjRng | 3004 | real | 1e20 | 0 | MAXREAL |
| Variable Upper | BarrierVariableUpper | BarVarUp | real | 1e20 | 0.001 | 1e20 | |
| Barrier Convergence Tolerance | BarrierConvergeTol | BarEpComp | 3002 | real | 1e-8 | 1e-10 | MAXREAL |
The default barrier algorithm is almost always fastest. However, on problems that are primal or dual infeasible, the default algorithm may not work as well as alternatives. The two alternative algorithms may eliminate numerical difficulties related to infeasibility, but will generally be slower.
| Primal Dual Log (0) | Use standard algorithm. This is the default |
| Infeasibility-Estimate (1) | Use infeasibility-estimate start |
| Infeasibility-Constant (2) | Use infeasibility-constant start |
| Standard Barrier (3) | Use Standard Barrier for problems other than MIP, it is fastest. |
The Ordering option sets the algorithm to be used to permute the rows of the constraint matrix in order to reduce fill in the Cholesky factor.
| Automatic (0) | The default automatic option will usually be the best choice. This option attempts to choose the most effective of the available ordering methods. It usually requires more ordering runtime than any of the alternatives, but it typically chooses the best ordering. The ordering runtime is usually small relative to the total solution time, and a better ordering can lead to smaller total solution time. |
| AMD (1) | The AMD algorithm provides good quality orderings in moderate ordering runtime. |
| AMF (2) | The AMF algorithm usually gives better orderings than AMD (usually 5-10% smaller factors), but requires somewhat more runtime (10-20%). |
| ND (3) | The ND algorithm produces significantly better orderings than AMD or AMF. Ten-fold reductions in barrier solvers runtimes have been observed for some problems. This option sometimes produces worse orderings, though, and it requires much more ordering runtime. |
This option="" sets the algorithm to be used to compute the initial starting point for the barrier solver. The default starting point is satisfactory for most problems. Other starting points may provide better performance for certain problems, or provide better convergence properties for the barrier algorithm. Since the default starting point is tuned for primal problems, using the other starting points may be worthwhile in conjunction with the Presolve Pass Dual Problem option.
| Dual is zero (1) | Default primal, dual pi is 0. |
| Estimate Dual (2) | Default primal, estimate dual. |
| Avg. primal, Dual is zero (3) | Primal average, dual pi is 0. |
| Avg. primal, Estimate dual (4) | Primal average, estimate dual. |
The Column Nonzeros value is used in the recognition of dense columns. If columns (in the presolved and aggregated problem) exist with more entries than the value of this option, these columns will be considered "dense" and CPLEX Barrier will treat the dense columns specially in order to reduce their effect. At the default setting of 0 this option is determined automatically, considering factors such as the size of the problem. If a number greater than 0 is entered, this number will be used as the "cutoff" number of entries for considering columns to be dense.
Note: If the problem (after Presolve and Aggregator) contains less than 400 rows, dense column handling will not be initiated, regardless of the column nonzero setting.
This option sets the maximum number of centering correction done on each iteration. By default the barrier solver automatically computes an estimate value for this parameter (the computed value can be observed by setting the barrier progress info log option to diagnostics information in the log file option dialog box). When the using the default barrier algorithm, if the computed value is zero setting the value to an explicit value greater than zero may improve the numerical performance of the algorithm at the expense of computation time.
| (-1) | Automatically determined |
| (0) | None. |
| (>0) | Maximum number of corrections. |
The Iterations Limit sets the number of barrier iterations before termination. When set to 0, no barrier iterations will occur, but problem "setup" will occur and information about the setup will be displayed (Cholesky factorization information).
The Growth Limit is used to detect unbounded optimal faces. At higher values, the barrier algorithm will be less likely to conclude that the problem has an unbounded optimal face, but more likely to have numerical difficulties if the problem has an unbounded face. The default value is 1e-6.
The Objective Range value sets the maximum absolute value of the objective function. The barrier algorithm looks at this limit to detect unbound problems. The default value is le+l5.
The Variable Upper value sets the upper bound for all variables that have infinite upper bounds. This limit is used to prevent difficulties associated with unbound optimal faces. The default value is le+20.
The Convergence Tolerance sets the tolerance on complementarity for convergence. The barrier algorithm will terminate with an optimal solution if the relative complementarity is smaller than this value. The default value is le-8.