The Decomposition Algorithm

Decomposition Algorithm Options in the PROC OPTMILP Statement or the SOLVE WITH MILP Statement in PROC OPTMODEL

To solve a mixed integer linear program, you can specify the decomposition algorithm in a SOLVE WITH MILP statement in the OPTMODEL procedure or in a PROC OPTMILP statement in the OPTMILP procedure. To control the overall decomposition algorithm, you can specify one or more of the MILP solver options shown in Table 18.2. (As the table indicates, you can specify some options only in the PROC OPTMILP statement.)

The options in Table 18.2 control the overall process flow for solving a mixed integer linear program; they are equivalent to the options that are used in the OPTMILP and OPTMODEL procedures with standard methods. These options are called main solver options in this chapter. They are described in detail in the section Syntax: MILP Solver and the section Syntax: OPTMILP Procedure.

Table 18.2: MILP Options in the PROC OPTMILP Statement or SOLVE WITH MILP Statement

Description	option
Data Table Options (OPTMILP procedure only)
Specifies the input data table	DATA=
Specifies the constraint activities output data table	DUALOUT=
Specifies whether the model is a maximization or minimization problem	OBJSENSE=
Specifies the primal solution input data table (warm start)	PRIMALIN=
Specifies the primal solution output data table	PRIMALOUT=
Presolve Option
Specifies the type of presolve	PRESOLVER=
Control Options
Specifies the stopping criterion based on an absolute objective gap	ABSOBJGAP=
Specifies the cutoff value for node removal	CUTOFF=
Emphasizes feasibility or optimality	EMPHASIS=
Specifies the maximum violation of variables and constraints	FEASTOL=
Specifies the maximum difference allowed between an integer variable’s value and an integer	INTTOL=
Specifies how frequently to print the node log	LOGFREQ=
Specifies the level of detail of solution progress to print in the log	LOGLEVEL=
Specifies the maximum number of nodes to process	MAXNODES=
Specifies the maximum number of solutions to find	MAXSOLS=
Specifies the time limit for the optimization process	MAXTIME=
Specifies the overall capacity for the number of active threads (per machine)	NTHREADS=
Specifies the tolerance to use in determining the optimality of nodes in the branch-and-bound tree	OPTTOL=
Uses the input primal solution (warm start) (OPTMODEL procedure only)	PRIMALIN
Enables or disables printing summary (OPTMILP procedure only)	PRINTLEVEL=
Specifies the probing level	PROBE=
Specifies the stopping criterion based on a relative objective gap	RELOBJGAP=
Specifies the scale of the problem matrix	SCALE=
Specifies the initial seed for the random number generator	SEED=
Specifies the stopping criterion based on a target objective value	TARGET=
Specifies whether time units are CPU time or real time	TIMETYPE=
Control Options (OPTMODEL procedure only)
Specifies the maximum number of solutions to return from the pool	MAXPOOLSOLS=
Heuristics Option
Specifies the primal heuristics level	HEURISTICS=
Search Options
Specifies the restarting strategy	RESTARTS=
Specifies the number of iterations to perform on each variable for strong branching	STRONGITER=
Specifies the number of candidates for strong branching	STRONGLEN=
Specifies the level of symmetry detection	SYMMETRY=
Specifies the rule for selecting the branching variable	VARSEL=
Cut Options
Specifies the cut level for all cuts	ALLCUTS=
Specifies the clique cut level	CUTCLIQUE=
Specifies the flow cover cut level	CUTFLOWCOVER=
Specifies the flow path cut level	CUTFLOWPATH=
Specifies the Gomory cut level	CUTGOMORY=
Specifies the generalized upper bound (GUB) cover cut level	CUTGUB=
Specifies the implied bounds cut level	CUTIMPLIED=
Specifies the knapsack cover cut level	CUTKNAPSACK=
Specifies the lift-and-project cut level	CUTLAP=
Specifies the mixed lifted 0-1 cut level	CUTMILIFTED=
Specifies the mixed integer rounding (MIR) cut level	CUTMIR=
Specifies the multicommodity network flow cut level	CUTMULTICOMMODITY=
Specifies the row multiplier factor for cuts	CUTSFACTOR=
Specifies the overall cut aggressiveness	CUTSTRATEGY=
Specifies the zero-half cut level	CUTZEROHALF=

The HYBRID= option in the DECOMP statement indicates the processing mode for the root node of the branch-and-bound search tree. When HYBRID=TRUE, the root node is first processed using standard MILP techniques, as described in the section Details: MILP Solver. When HYBRID=FALSE, the root processing is done solely by the decomposition algorithm, and the following direct MILP options are ignored: CUTOFF=, EMPHASIS=, RESTARTS=, SEED=, TARGET=, and all the cut options.

The following search options, listed in Table 18.2, have a different interpretation or a different set of options from what is described in the MILP solver sections:

LOGFREQ=number PRINTFREQ=number

specifies how often to print information in the node log, where number can be any 32-bit integer greater than or equal to 0. If number is 0, then the node log is disabled. If number is positive, then an entry is made every number seconds. An entry is also made in the node log each time the solver finds a better integer solution or improved bound. By default, LOGFREQ=10.

STRONGITER=number | AUTOMATIC

specifies the number of pricing iterations that are performed for each variable in the candidate list when you use the strong branching variable selection strategy. The value of number can be any positive 32-bit integer. If you specify the keyword AUTOMATIC, the MILP solver uses the default value, which is calculated automatically.

VARSEL=AUTOMATIC | MAXINFEAS | PSEUDO | RYANFOSTER | STRONG

specifies the rule for selecting the branching variable. You can specify the following values:

AUTOMATIC: uses automatic branching variable selection.
MAXINFEAS: selects the variable in the original compact formulation with maximum infeasibility.
PSEUDO: selects the variable in the original compact formulation that maximizes the weighted up and down pseudocosts.
RYANFOSTER: when appropriate, uses a specialized branching rule known as Ryan-Foster branching.
STRONG: selects the variable in the original compact formulation that maximizes the estimated improvement in the objective value based on strong branching.

By default, VARSEL=AUTOMATIC. For more information about variable selection, see the sections Variable Selection and Special Case: Identical Blocks and Ryan-Foster Branching.

Last updated: June 14, 2018