The Decomposition Algorithm

DECOMP_MASTER_IP Statement

DECOMP_MASTER_IP <decomp-master-ip-options>;

MASTER_IP <decomp-master-ip-options>;

For mixed integer linear programming problems, the DECOMP_MASTER_IP statement controls the (restricted) master problem, which is solved as a MILP with the current set of columns in an effort to obtain an integer-feasible solution.

Table 15.14 summarizes the options available in the DECOMP_MASTER_IP statement. These options control the MILP solver that is used to solve the integer version of the master problem. For descriptions of these options, see the section MILP Solver Options in Chapter 8: The Mixed Integer Linear Programming Solver, and the section PROC OPTMILP Statement in Chapter 13: The OPTMILP Procedure. Some options have different defaults when you use the decomposition algorithm, as shown in Table 15.14.

Table 15.14: Options in the DECOMP_MASTER_IP Statement

Description	decomp-master-ip-option	Different
		Default
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 on variables and constraints	FEASTOL=	1E–7
Specifies the maximum allowed difference 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 be processed	MAXNODES= ^†
Specifies the maximum number of solutions to be found	MAXSOLS=
Specifies the time limit for the optimization process	MAXTIME=
Specifies the number of threads to use in the master integer solver	NTHREADS=
Specifies the tolerance used when deciding on 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=	0.01
Specifies the scale of the problem matrix	SCALE=
Specifies the stopping criterion based on the 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 initial seed for the random number generator	SEED=
Specifies the number of simplex iterations performed on each variable in strong branching strategy	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=

† MAXNODES=100000 in the root node, and MAXNODES=10000 in nodes that are not the root.

The following options are listed in Table 15.14 but are not described in the MILP solver sections. These options are specific to the DECOMP_MASTER_IP statement.

NTHREADS=number

specifies the number of threads to use in the master integer solver (if the selected solver method supports multithreading). The value of the NTHREADS= option in the PERFORMANCE statement, which is described in the section PERFORMANCE Statement, serves as the overall capacity for the number of active threads that can run at one time. By default, the number of master integer threads is $t = \min (p,m)$ , where p is the value of the NTHREADS= option in the PERFORMANCE statement and m is the value of the NTHREADS= option in the DECOMP_MASTER_IP statement.

PRIMALIN=number | string PIN=number | string

specifies whether the MILP solver is to use the previous best solution’s variables values 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, warm start can reduce solution time significantly. Table 15.15 describes the valid values of the PRIMALIN= option.

Table 15.15: Values for PRIMALIN= Option

number	string	Description
0	OFF	Ignores the previous solution.
1	ON	Starts from the previous solution.

The default is ON.