The OPTMODEL Procedure

ODS Table and Variable Names

PROC OPTMODEL assigns a name to each table it creates. You can use these names to reference the table when you use the Output Delivery System (ODS) to select tables and create output data sets. The names of tables common to all solvers are listed in Table 5.12. Some solvers can generate additional tables; see the individual solver chapters for more information. For more information about ODS, see SAS Output Delivery System: User’s Guide.

Table 5.12: ODS Tables Produced in PROC OPTMODEL

ODS Table Name	Description	Statement/Option
DerivMethods	List of derivatives used by the solver, including the method of computation	SOLVE
OptStatistics	Solver-dependent description of the resources required for solution, including function evaluations and solver time	SOLVE
PrintTable	Specified parameter or variable values	PRINT
ProblemSummary	Description of objective, variables, and constraints	SOLVE
SolutionSummary	Overview of solution, including solver-dependent solution quality values	SOLVE
SolverOptions	List of solver options and their values	SOLVE
PerformanceInfo	List of performance options and their values	SOLVE
Timing	Detailed solution timing	PERFORMANCE / DETAILS

To guarantee that ODS output data sets contain information from all executed statements, use the PERSIST= option in the ODS OUTPUT statement. For details, see SAS Output Delivery System: User's Guide. Note: The SUBMIT statement resets ODS SELECT and EXCLUDE lists.

Table 5.13 lists the variable names of the preceding tables used in the ODS template of the OPTMODEL procedure.

Table 5.13: Variable Names for the ODS Tables Produced in PROC OPTMODEL

ODS Table Name	Variables
DerivMethods	Label $1$ , cValue $1$ , and nValue $1$
OptStatistics	Label $1$ , cValue $1$ , and nValue $1$
PrintTable (matrix form)	ROW, COL $1$ – COL $n$
PrintTable (table form)	COL $1$ – COL $n$ , identifier-expression(_suffix)
ProblemSummary	Label $1$ , cValue $1$ , and nValue $1$
SolutionSummary	Label $1$ , cValue $1$ , and nValue $1$
SolverOptions	Label $1$ , cValue $1$ , nValue $1$ , cValue $2$ , and nValue $2$
PerformanceInfo	Label $1$ , cValue $1$ , and nValue $1$
Timing	Label $1$ , cValue $1$ , nValue $1$ , cValue $2$ , and nValue $2$

The PRINT statement produces an ODS table named PrintTable. The variable names that are used depend on the display format used. See the section Formatted Output for details about choosing the display format.

For the PRINT statement with table format, the columns that display array indices are named COL $1$ –COL $n$ , where $n$ is the number of index elements. Columns that display values from identifier expressions are named using the expression’s name and suffix. The identifier name becomes the output variable name if no suffix is used. Otherwise the variable name is formed by appending an underscore (_) and the suffix to the identifier name. Columns that display the value of expressions are named COL $n$ , where $n$ is the column number in the table.

For the PRINT statement with matrix format, the first column has the variable name ROW. The remaining columns are named COL $1$ –COL $n$ , where $n$ is the number of distinct column indices. When an ODS table displays values from identifier expressions, a label is generated based on the expression’s name and suffix, as described for column names in the case of table format.

The PRINTLEVEL= option controls the ODS tables produced by the SOLVE statement. When PRINTLEVEL=0, the SOLVE statement produces no ODS tables. When PRINTLEVEL=1, the SOLVE statement produces the ODS tables ProblemSummary, SolutionSummary, and PerformanceInfo. When PRINTLEVEL=2, the SOLVE statement produces the ODS tables ProblemSummary, SolverOptions, DerivMethods, SolutionSummary, OptStatistics, and PerformanceInfo.

The PERFORMANCE statement controls additional ODS tables that can be produced by the SOLVE statement. The PerformanceInfo table displays options that are controlled by the PERFORMANCE statement. If you specify the DETAILS option in the PERFORMANCE statement, then the SOLVE statement also produces the ODS table Timing.

The following statements generate several ODS tables and write each table to a SAS data set:

proc optmodel printlevel=2;
   ods output PrintTable=expt ProblemSummary=exps DerivMethods=exdm
              SolverOptions=exso SolutionSummary=exss OptStatistics=exos
              Timing=exti;
   performance details;
   var x{1..2} >= 0;
   min z = 2*x[1] + 3 * x[2] + x[1]**2 + 10*x[2]**2
           + 2.5*x[1]*x[2] + x[1]**3;
   con c1: x[1] - x[2] <= 1;
   con c2: x[1] + 2*x[2] >= 100;
   solve;
   print x;

The data set expt contains the PrintTable table and is shown in Figure 5.46. The variable names are COL $1$ and x.

Figure 5.46: PrintTable ODS Table

PrintTable

Obs	COL1	x
1	1	10.448
2	2	44.776

The data set exps contains the ProblemSummary table and is shown in Figure 5.47. The variable names are Label $1$ , cValue $1$ , and nValue $1$ . The rows describe the instance, and the description depends on the form of the problem. In most solvers, the rows describe the objective function, variables, and constraints. In the network solver, the rows describe the number of nodes, the number of edges, the directedness of the graph, and the type of problem solved over the graph.

Figure 5.47: ProblemSummary ODS Table

ProblemSummary

Obs	Label1	cValue1	nValue1
1	Objective Sense	Minimization	.
2	Objective Function	z	.
3	Objective Type	Nonlinear	.
4			.
5	Number of Variables	2	2.000000
6	Bounded Above	0	0
7	Bounded Below	2	2.000000
8	Bounded Below and Above	0	0
9	Free	0	0
10	Fixed	0	0
11			.
12	Number of Constraints	2	2.000000
13	Linear LE (<=)	1	1.000000
14	Linear EQ (=)	0	0
15	Linear GE (>=)	1	1.000000
16	Linear Range	0	0

The data set exso contains the SolverOptions table and is shown in Figure 5.48. The variable names are Label $1$ , cValue $1$ , nValue $1$ , cValue $2$ , and nValue $2$ . The rows, which depend on the solver called by PROC OPTMODEL, list the values taken by each of the solver options. The presence of an asterisk (*) next to an option indicates that a value has been specified for that option.

Figure 5.48: SolverOptions ODS Table

SolverOptions

Obs	Label1	cValue1	nValue1	nValue2
1	ALGORITHM	INTERIORPOINT	.	.
2	FEASTOL	1E-6	0.000001000	.
3	HESSTYPE	FULL	.	.
4	LOGFREQ	1	1.000000	.
5	MAXITER	5000	5000.000000	.
6	MAXTIME	I	I	.
7	NOMULTISTART		.	.
8	OBJLIMIT	1E20	1E20	.
9	OPTTOL	1E-6	0.000001000	.
10	SOLTYPE	1	1.000000	.
11	TIMETYPE	REAL	.	.

The data set exdm contains the DerivMethods table, which displays the methods of derivative computation, and is shown in Figure 5.49. The variable names are Label $1$ , cValue $1$ , and nValue $1$ . The rows, which depend on the derivatives used by the solver, specify the method used to calculate each derivative.

Figure 5.49: DerivMethods ODS Table

DerivMethods

Obs	Label1	cValue1	nValue1
1	Objective Gradient	Analytic Formulas	.
2	Objective Hessian	Analytic Formulas	.

The data set exss contains the SolutionSummary table and is shown in Figure 5.50. The variable names are Label $1$ , cValue $1$ , and nValue $1$ . The rows give an overview of the solution, including the solver chosen, the objective value, and the solution status. Depending on the values returned by the solver, the SolutionSummary table might also include some solution quality values such as optimality error and infeasibility. The values in the SolutionSummary table appear in the _OROPTMODEL_ macro variable; each solver chapter has a section that describes the solver’s contribution to this macro variable.

Figure 5.50: SolutionSummary ODS Table

SolutionSummary

Obs	Label1	cValue1	nValue1
1	Solver	NLP	.
2	Algorithm	Interior Point	.
3	Objective Function	z	.
4	Solution Status	Optimal	.
5	Objective Value	22623.347101	22623
6			.
7	Optimality Error	5E-7	0.000000500
8	Infeasibility	0	0
9			.
10	Iterations	5	5.000000
11	Presolve Time	0.00	0
12	Solution Time	0.02	0.017000

The data set exos contains the OptStatistics table, which displays the optimization statistics, and is shown in Figure 5.51. The variable names are Label $1$ , cValue $1$ , and nValue $1$ . The rows, which depend on the solver called by PROC OPTMODEL, describe the amount of time and the function evaluations that are used by the solver and associated processing. Times are displayed in seconds of clock or CPU time according to the value of the TIMETYPE= option that is used by the solver.

Figure 5.51: OptStatistics ODS Table

OptStatistics

Obs	Label1	cValue1	nValue1
1	Function Evaluations	28	28.000000
2	Gradient Evaluations	28	28.000000
3	Hessian Evaluations	6	6.000000
4	Problem Generation Time	0.00	0.001000
5	Code Generation Time	0.01	0.014000
6	Presolve Time	0.00	0
7	Solution Time	0.02	0.017000
8	Total Time	0.15	0.153000

Problem generation is the process of combining the model with the data into a format that solvers can use. This includes computing equation coefficients, but it does not include reading data or evaluating other programming statements. Code generation is compiles code for nonlinear equations in the model and performs other analysis that is needed prior to solver evaluations. The time required for problem generation will be negligible if the model contains only linear equations. The presolve time in this table includes the time used by the PROC OPTMODEL presolver and any presolver that is part of the solver. Solution time is the sum of the times used by the presolvers and the solver. The presolve and solution times also appear in the SolutionSummary table. The OptStatistics table includes a total time, which is the sum of times for problem generation, code generation, solution, and overhead in the SOLVE statement. Overhead includes solver setup, postprocessing, and ODS table output.

The Timing table provides an alternate breakdown of SOLVE statement timing. Times in this table are shown in seconds of clock time. The data set exti, which is shown in Figure 5.52, contains the Timing table data and statistics. The variable names are Label $1$ , cValue $1$ , nValue $1$ , cValue $2$ , and nValue $2$ . The values present depend on the solver and on the context of the SOLVE statement.

Figure 5.52: Timing ODS Table

Timing

Obs	Label1	cValue1	nValue1	cValue2	nValue2
1	Problem Generation	0.001	0.00	0.0065359477	0.65%
2	OPTMODEL Presolver	0	0.00	0	0.00%
3	Solver Initialization	0.121	0.12	0.7908496732	79.08%
4	Code Generation	0.014	0.01	0.091503268	9.15%
5	Solver	0.017	0.02	0.1111111111	11.11%
6	Solver Postprocessing	0	0.00	0	0.00%

Some of the Timing table values have already been described for the OptStatistics table. Solver initialization time is overhead in the SOLVE statement before the solver starts. Solver time includes execution of the solver and its associated preprocessor, if any. A “Wait after Solver” time appears when a SOLVE statement is executed within a COFOR loop. It represents the time between solver completion and the resumption of the SOLVE statement in the invoking loop iteration for processing of the results. Solver postprocessing time is overhead in the SOLVE statement after the solver has completed.