The Linear Programming Solver

LP Solver Options

Solver Options
Presolve Options
Control Options
Simplex Algorithm Options
Interior Point Algorithm Options
Decomposition Algorithm Options

This section describes the options recognized by the LP solver. These options can be specified after a forward slash (/) in the SOLVE statement, provided that the LP solver is explicitly specified using a WITH clause.

If the LP solver terminates before reaching an optimal solution, an intermediate solution is available. You can access this solution by using the .sol variable suffix in the OPTMODEL procedure. See the section Suffixes for details.

Solver Options

IIS=number $\mid$ string

specifies whether the LP solver attempts to identify a set of constraints and variables that form an irreducible infeasible set (IIS). Table 6.2 describes the valid values of the IIS= option.

Table 6.2: Values for IIS= Option

number	string	Description
0	OFF	Disables IIS detection.
1	ON	Enables IIS detection.

If an IIS is found, information about the infeasibilities can be found in the .status values of the constraints and variables. The default value of this option is OFF. See the section Irreducible Infeasible Set for details about the IIS= option. See Suffixes for details about the .status suffix.

ALGORITHM=option SOLVER=option SOL=option

specifies one of the following LP solvers:

Option	Description
PRIMAL (PS)	Uses primal simplex solver.
DUAL (DS)	Uses dual simplex solver.
NETWORK (NS)	Uses network simplex solver.
INTERIORPOINT (IP)	Uses interior point solver.
CONCURRENT (CON) (experimental)	Uses several different algorithms in parallel.

The valid abbreviated value for each option is indicated in parentheses. By default, the dual simplex solver is used.

ALGORITHM2=option SOLVER2=option

specifies one of the following LP solvers if ALGORITHM=NS:

Option	Description
PRIMAL (PS)	Uses primal simplex solver (after network simplex).
DUAL (DS)	Uses dual simplex solver (after network simplex).

The valid abbreviated value for each option is indicated in parentheses. By default, the LP solver decides which algorithm is best to use after calling the network simplex solver on the extracted network.

Presolve Options

PRESOLVER=number | string

specifies one of the following presolve options:

number	string	Description
0	NONE	Disables presolver.
–1	AUTOMATIC	Applies presolver by using default setting.
1	BASIC	Performs basic presolve like removing empty rows, columns, and fixed variables.
2	MODERATE	Performs basic presolve and apply other inexpensive presolve techniques.
3	AGGRESSIVE	Performs moderate presolve and apply other aggressive (but expensive) presolve techniques.

The default option is AUTOMATIC. See the section Presolve for details.

Control Options

FEASTOL= $\epsilon$

specifies the feasibility tolerance, $\epsilon \in$ [1E–9, 1E–4], for determining the feasibility of a variable. The default value is 1E–6.

LOGFREQ=k PRINTFREQ=k

specifies that the printing of the solution progress to the iteration log is to occur after every k iterations. The print frequency, k, is an integer between zero and the largest four-byte signed integer, which is $2^{31} - 1$ .

The value k = 0 disables the printing of the progress of the solution. If the primal or dual simplex algorithms are used, the default value of this option is determined dynamically according to the problem size. If the network simplex algorithm is used, the default value of this option is 10,000. If the interior point algorithm is used, the default value of this option is 1.

LOGLEVEL=number | string PRINTLEVEL2=number | string

controls the amount of information displayed in the SAS log by the LP solver, from a short description of presolve information and summary to details at each iteration. Table 6.3 describes the valid values for this option.

Table 6.3: Values for LOGLEVEL= Option

number	string	Description
0	NONE	Turns off all solver-related messages to SAS log.
1	BASIC	Displays a solver summary after stopping.
2	MODERATE	Prints a solver summary and an iteration log by using the interval dictated by the LOGFREQ= option.
3	AGGRESSIVE	Prints a detailed solver summary and an iteration log by using the interval dictated by the LOGFREQ= option.

The default value is MODERATE.

MAXITER=k

specifies the maximum number of iterations. The value k can be any integer between one and the largest four-byte signed integer, which is $2^{31} - 1$ . If you do not specify this option, the procedure does not stop based on the number of iterations performed. For network simplex, this iteration limit corresponds to the solver called after network simplex (either primal or dual simplex).

MAXTIME=t

specifies an upper limit of t units of time for the optimization process, including problem generation time and solution time. The value of the TIMETYPE= option determines the type of units used. If you do not specify the MAXTIME= option, the solver does not stop based on the amount of time elapsed. The value of t can be any positive number; the default value is the positive number that has the largest absolute value that can be represented in your operating environment.

OPTTOL= $\epsilon$

specifies the optimality tolerance, $\epsilon \in$ [1E–9, 1E–4], for declaring optimality. The default value is 1E–6.

TIMETYPE=number $\mid$ string

specifies the units of time used by the MAXTIME= option and reported by the PRESOLVE_TIME and SOLUTION_TIME terms in the _OROPTMODEL_ macro variable. Table 6.4 describes the valid values of the TIMETYPE= option.

Table 6.4: Values for TIMETYPE= Option

number	string	Description
0	CPU	Specifies units of CPU time.
1	REAL	Specifies units of real time.

The “Optimization Statistics” table, an output of the OPTMODEL procedure if you specify the PRINTLEVEL=2 option in the PROC OPTMODEL statement, also includes the same time units for “Presolver Time” and “Solver Time.” The other times (such as “Problem Generation Time”) in the “Optimization Statistics” table are always CPU times.

The default value of the TIMETYPE= option depends on the values of the NTHREADS= and NODES= options in the PERFORMANCE statement of the OPTMODEL procedure. See the section PERFORMANCE Statement in Chapter 4: Shared Concepts and Topics. for more information about the NTHREADS= and NODES= options.

If you specify a value greater than 1 for either the NTHREADS= or NODES= option, the default value of the TIMETYPE= option is REAL. If you specify a value of 1 for both the NTHREADS= and NODES= options, the default value of the TIMETYPE= option is CPU.

Simplex Algorithm Options

BASIS=number | string

specifies the following options for generating an initial basis:

number	string	Description
0	CRASH	Generate an initial basis by using crash techniques (Maros, 2003). The procedure creates a triangular basic matrix consisting of both decision variables and slack variables.
1	SLACK	Generate an initial basis by using all slack variables.
2	WARMSTART	Start the primal and dual simplex solvers with available basis.

The default option for the primal simplex solver is CRASH (0). The default option for the dual simplex solver is SLACK(1). For network simplex, this option has no effect.

PRICETYPE=number | string

specifies one of the following pricing strategies for the primal and dual simplex solvers:

number	string	Description
0	HYBRID	Use hybrid Devex and steepest-edge pricing strategies. Available for primal simplex solver only.
1	PARTIAL	Use partial pricing strategy. Optionally, you can specify QUEUESIZE=. Available for primal simplex solver only.
2	FULL	Use the most negative reduced cost pricing strategy.
3	DEVEX	Use Devex pricing strategy.
4	STEEPESTEDGE	Use steepest-edge pricing strategy.

The default pricing strategy for the primal simplex solver is HYBRID and that for the dual simplex solver is STEEPESTEDGE. For the network simplex solver, this option applies only to the solver specified by the ALGORITHM2= option. See the section Pricing Strategies for the Primal and Dual Simplex Solvers for details.

QUEUESIZE= $k$

specifies the queue size, $k\in [1, n]$ , where n is the number of decision variables. This queue is used for finding an entering variable in the simplex iteration. The default value is chosen adaptively based on the number of decision variables. This option is used only when PRICETYPE=PARTIAL.

SCALE=number | string

specifies one of the following scaling options:

number	string	Description
0	NONE	Disable scaling.
–1	AUTOMATIC	Automatically apply scaling procedure if necessary.

The default option is AUTOMATIC.

Interior Point Algorithm Options

CROSSOVER=number | string

specifies whether to convert the interior point solution to a basic simplex solution. The values of this option are:

number	string	Description
0	OFF	Disable crossover.
1	ON	Apply the crossover algorithm to the interior point solution.

If the interior point algorithm terminates with a solution, the crossover algorithm uses the interior point solution to create an initial basic solution. After performing primal fixing and dual fixing, the crossover algorithm calls a simplex algorithm to locate an optimal basic solution. The default value of the CROSSOVER= option is OFF.

STOP_DG= $\delta$

specifies the desired relative duality gap, $\delta \in$ [1E–9, 1E–4]. This is the relative difference between the primal and dual objective function values and is the primary solution quality parameter. The default value is 1E–6. See the section The Interior Point Algorithm for details.

STOP_DI= $\beta$

specifies the maximum allowed relative dual constraints violation, $\beta \in$ [1E–9, 1E–4]. The default value is 1E–6. See the section The Interior Point Algorithm for details.

STOP_PI= $\alpha$

specifies the maximum allowed relative bound and primal constraints violation, $\alpha \in$ [1E–9, 1E–4]. The default value is 1E–6. See the section The Interior Point Algorithm for details.

Decomposition Algorithm Options

The following options are available for the decomposition algorithm in the LP solver. For information about the decomposition algorithm, see Chapter 13: The Decomposition Algorithm.

DECOMP=(options): enables the decomposition algorithm and specifies overall control options for the algorithm. For more information about this option, see Chapter 13: The Decomposition Algorithm.
DECOMP_MASTER=(options): specifies options for the master problem. For more information about this option, see Chapter 13: The Decomposition Algorithm.
DECOMP_SUBPROB=(options): specifies option for the subproblem. For more information about this option, see Chapter 13: The Decomposition Algorithm.