The Decomposition Algorithm
DECOMPSUBPROB Statement
DECOMPSUBPROB <subprob-options>;
DECOMPOSITIONSUBPROB <subprob-options>;
SUBPROB <subprob-options>;
The DECOMPSUBPROB statement controls the subproblem.
Table 6 summarizes the options available for the decomposition algorithm in the DECOMPSUBPROB statement when the chosen subproblem algorithm is an LP algorithm. (As the table indicates, you can specify the PRINTLEVEL= option only in the OPTLP procedure.) For descriptions of these options, see the section LP Solver Options in Chapter 13, The Linear Programming Solver, and the section PROC OPTLP Statement in Chapter 5, The OPTLP Procedure. Some options have different defaults when you use the decomposition algorithm, as shown in Table 6.
Table 6: Options in the DECOMPSUBPROB Statement Used with an LP Algorithm
| Description | subprob-option | Different |
|---|---|---|
| Default | ||
| Algorithm Option | ||
| Specifies the subproblem algorithm | ALGORITHM= | † |
| Presolve Option | ||
| Controls the dualization of the problem | DUALIZE= | OFF |
| Controls the folding of the problem | FOLD= | AUTOMATIC |
| Specifies, for the first subproblem solve only, the type of presolve | INITPRESOLVER= | |
| Specifies the type of presolve | PRESOLVER= | NONE† |
| Control Options | ||
| Specifies the feasibility tolerance | FEASTOL= | 1E–7 |
| Specifies how frequently to print the solution progress | LOGFREQ= | |
| Specifies the level of detail of solution progress to print in the log | LOGLEVEL= | NONE |
| Specifies the time limit for the optimization process | MAXTIME= | |
| Specifies the number of threads to use in the subproblem solver | NTHREADS= | |
| Specifies the optimality tolerance | OPTTOL= | 1E–7 |
| Enables or disables printing summary (OPTLP procedure only) | PRINTLEVEL= | |
| Specifies the initial seed for the random number generator | SEED= | |
| Specifies whether time units are CPU time or real time | TIMETYPE= | |
| Simplex Algorithm Options | ||
| Specifies the type of initial basis | BASIS= | WARMSTART† |
| Specifies the type of pricing strategy | PRICETYPE= | |
| Specifies the queue size for determining entering variable | QUEUESIZE= | |
| Enables or disables scaling of the problem | SCALE= | |
| Interior Point Algorithm Options | ||
| Enables or disables interior crossover | CROSSOVER= | |
| Specifies the stopping criterion based on a duality gap | DUALITYGAP= |
† When you specify METHOD=USER, METHOD=AUTO or METHOD=COMMUNITY in the DECOMP statement, ALGORITHM=PS, PRESOLVER=NONE, and BASIS=WARMSTART by default. The reason for these defaults is that primal feasibility of the subproblem is preserved when the objective is changed, so a warm start from the previous optimal basis tends to be more efficient than solving the subproblem from scratch at each iteration. When METHOD=NETWORK, ALGORITHM=NETWORKPURE by default because each subproblem is a pure network, causing the specialized pure network solver to usually be the most efficient choice. When METHOD=CONCOMP, ALGORITHM=DS by default because dual simplex generally has the best performance on linear programs and, in this case, one outer iteration is sufficient (that is, warm starts are not required).
Table 7 summarizes the options available in the DECOMPSUBPROB statement when the chosen subproblem algorithm is a MILP algorithm. When the subproblem consists of multiple blocks (a block-diagonal structure), these settings apply to all subproblems. For descriptions of these options, see the section MILP Solver Options in Chapter 14, The Mixed Integer Linear Programming Solver, and the section PROC OPTMILP Statement in Chapter 6, The OPTMILP Procedure.
Table 7: Options in the DECOMPSUBPROB Statement Used with a MILP Algorithm
| Description | subprob-option | Different |
|---|---|---|
| Default | ||
| Algorithm Option | ||
| Specifies the subproblem algorithm | ALGORITHM= | |
| Presolve Option | ||
| Specifies, for the first subproblem solve only, the type of presolve | INITPRESOLVER= | |
| Specifies the type of presolve | PRESOLVER= | |
| Control Options | ||
| Specifies the stopping criterion based on an absolute objective gap | ABSOBJGAP= | |
| Emphasizes feasibility or optimality | EMPHASIS= | |
| Specifies the maximum violation on variables and constraints | FEASTOL= | 1E–7 |
| 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 number of threads to use in the subproblem solver | NTHREADS= | |
| Specifies the tolerance to use in determining the optimality of nodes in the branch-and-bound tree | OPTTOL= | 1E–7 |
| Specifies whether to use the previous best primal solution as a warm start | PRIMALIN= | |
| 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= | |
| Heuristics Option | ||
| Specifies the primal heuristics level | HEURISTICS= | |
| Search Options | ||
| Specifies the level of conflict search | CONFLICTSEARCH= | |
| Specifies the node selection strategy | NODESEL= | |
| Specifies the restarting strategy | RESTARTS= | |
| Specifies the number of iterations to perform 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 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 following options, listed in Table 6 and Table 7, are specific to the DECOMPSUBPROB statement and are not described in the LP or MILP solver sections:
-
ALGORITHM=string
SOLVER=string
SOL=string -
specifies the algorithm to use for the subproblem solves. You can specify the following values (the valid abbreviated value for each string follows the vertical bar):
- PRIMAL | PS
uses the primal simplex algorithm.
- DUAL | DS
uses the dual simplex algorithm.
- NETWORK | NS
uses the network simplex algorithm.
- NETWORKPURE | NSPURE
uses the network simplex algorithm for pure networks.
- INTERIORPOINT | IP
uses the interior point algorithm.
- MILP
uses the mixed integer linear solver.
By default, ALGORITHM=NETWORKPURE if METHOD=NETWORK, ALGORITHM=MILP for mixed integer linear programming subproblems, and ALGORITHM=PS for linear programming subproblems.
-
INITPRESOLVER=AUTOMATIC | NONE | BASIC | MODERATE | AGGRESSIVE
INITPRESOL=AUTOMATIC | NONE | BASIC | MODERATE | AGGRESSIVE -
specifies, for the first subproblem solve only, the presolve level. You can specify the following values:
- AUTOMATIC
applies the default level of presolve processing.
- NONE
disables the presolver.
- BASIC
performs minimal presolve processing.
- MODERATE
applies a higher level of presolve processing.
- AGGRESSIVE
applies the highest level of presolve processing.
By default, INITPRESOLVER=AUTOMATIC.
-
NTHREADS=number
NUMTHREADS=number specifies the number of threads to use in the subproblem solver (if the selected solver method supports multithreading). The value of the NTHREADS= option in the main solver statement serves as the overall capacity for the number of active threads that can run at one time. By default, the number of subproblem threads is
, where p is the value of the NTHREADS= option in the main solver statement; 
, which is the number of blocks being processed simultaneously; d is the number of block threads; and m is the number of compute nodes (which can be more than one, when you run the decomposition algorithm in distributed mode). -
PRIMALIN=FALSE | TRUE
PIN=FALSE | TRUE -
specifies (for MILP problems only) whether the MILP solver is to use the values of the previous best solution’s variables as a starting solution (warm start). If the MILP solver finds that the input solution is feasible, then the input solution provides an incumbent solution and a bound for the branch-and-bound algorithm. If the solution is not feasible, the MILP solver tries to repair it. When it is difficult to find a good integer feasible solution for a problem, a warm start can reduce solution time significantly. You can specify the following values:
- FALSE
ignores the previous solution.
- TRUE
starts from the previous solution.
By default, PRIMALIN=TRUE.