The Network Solver

Functional Summary

Table 9.2 summarizes the options and suboptions available in the SOLVE WITH NETWORK statement.

Table 9.2: Functional Summary of SOLVE WITH NETWORK Options

Description		Option
			Suboption
General Options
Specifies directed or undirected graphs		GRAPH_DIRECTION=
Includes self links in the graph definition		INCLUDE_SELFLINK=
Specifies the iteration log frequency		LOGFREQ=
Controls the amount of information that is displayed in the SAS log		LOGLEVEL=
Specifies the maximum time spent calculating results		MAXTIME=
Specifies whether time units are in CPU time or real time		TIMETYPE=
Input and Output Options
Groups link-indexed data		LINKS=()
	Names a set of links to include in the graph definition even if no weights or bounds are available for them		INCLUDE=
	Specifies the flow lower bound for each link		LOWER=
	Specifies the flow upper bound for each link		UPPER=
	Specifies link weights		WEIGHT=
Groups node-indexed data		NODES=()
	Names a set of nodes to include in the graph definition even if no weights are available for them		INCLUDE=
	Specifies node weights		WEIGHT=
	Specifies node supply upper bounds in the minimum-cost network flow problem		WEIGHT2=
Specifies the input sets that enable you to solve a problem over a subgraph		SUBGRAPH=()
	Specifies the subset of links to use		LINKS=
	Specifies the subset of nodes to use		NODES=
Specifies the output sets or arrays for each algorithm (see Table 9.4 for which OUT= suboptions you can specify for each algorithm)		OUT=()
	Specifies the output set for articulation points		ARTPOINTS=
	Specifies the output set for linear assignment		ASSIGNMENTS=
	Specifies the array to contain the biconnected component of each link		BICONCOMP=
	Specifies the output set for cliques		CLIQUES=
	Specifies the output array for connected components		CONCOMP=
	Specifies the output set for the cut-sets for minimum cuts		CUTSETS=
	Specifies the output set for cycles		CYCLES=
	Specifies the output array for the flow on each link		FLOW=
	Specifies the output set for the minimum spanning tree (forest)		FOREST=
	Specifies the output set for the links that remain after the SUBGRAPH= option is applied		LINKS=
	Specifies the output set for the nodes that remain after the SUBGRAPH= option is applied		NODES=
	Specifies the output array for the node order in the traveling salesman problem		ORDER=
	Specifies the output set for the partitions for minimum cuts		PARTITIONS=
	Specifies the set to contain the link sequence for each path		SPPATHS=
	Specifies the numeric array to contain the path weight for each source and sink node pair		SPWEIGHTS=
	Specifies the output set for the tour in the traveling salesman problem		TOUR=
	Specifies the set to contain the pairs $(u,v)$ of nodes where v is reachable from u		TRANSCL=
Algorithm Options and Suboptions
Finds biconnected components and articulation points of an undirected input graph		BICONCOMP
Finds maximal cliques in the input graph		CLIQUE=
	Specifies the maximum number of cliques to return		MAXCLIQUES=
Finds the connected components of the input graph		CONCOMP=
	Specifies the algorithm to use for calculating connected components		ALGORITHM=
Finds the cycles (or the existence of a cycle) in the input graph		CYCLE=
	Specifies the maximum number of cycles to return		MAXCYCLES=
	Specifies the maximum link count for the cycles to return		MAXLENGTH=
	Specifies the maximum link weight for the cycles to return		MAXLINKWEIGHT=
	Specifies the maximum sum of node weights to allow in a cycle		MAXNODEWEIGHT=
	Specifies the minimum link count for the cycles to return		MINLENGTH=
	Specifies the minimum link weight for the cycles to return		MINLINKWEIGHT=
	Specifies the minimum node weight for the cycles to return		MINNODEWEIGHT=
	Specifies whether to stop after finding the first cycle		MODE=
Solves the minimal-cost linear assignment problem		LINEAR_ASSIGNMENT
Solves the minimum-cost network flow problem		MINCOSTFLOW
Finds the minimum link-weighted cut of an input graph		MINCUT=
	Specifies the maximum number of cuts to return from the algorithm		MAXNUMCUTS=
	Specifies the maximum weight of each cut to return from the algorithm		MAXWEIGHT=
Solves the minimum link-weighted spanning tree problem on an input graph		MINSPANTREE
Calculates shortest paths between sets of nodes on the input graph		SHORTPATH=
	Specifies the type of output for shortest paths results		PATHS=
	Specifies the set of sink nodes		SINK=
	Specifies the set of source nodes		SOURCE=
	Specifies whether to use weights in calculating shortest paths		USEWEIGHT=
Calculates the transitive closure of an input graph		TRANSITIVE_CLOSURE
Solves the traveling salesman problem		TSP=
	Requests that the stopping criterion be based on the absolute objective gap		ABSOBJGAP=
	Specifies the level of conflict search		CONFLICTSEARCH=
	Specifies the cutoff value for branch-and-bound node removal		CUTOFF=
	Specifies the level of cutting planes to be generated by the network solver		CUTSTRATEGY=
	Emphasizes feasibility or optimality		EMPHASIS=
	Specifies the initial and primal heuristics level		HEURISTICS=
	Specifies the maximum number of branch-and-bound nodes to be processed		MAXNODES=
	Specifies the maximum number of feasible tours to be identified		MAXSOLS=
	Specifies whether to use a mixed integer linear programming solver		MILP=
	Specifies the branch-and-bound node selection strategy		NODESEL=
	Specifies the probing level		PROBE=
	Requests that the stopping criterion be based on relative objective gap		RELOBJGAP=
	Specifies the number of simplex iterations to be performed on each variable in the strong branching strategy		STRONGITER=
	Specifies the number of candidates for the strong branching strategy		STRONGLEN=
	Requests that the stopping criterion be based on the target objective value		TARGET=
	Specifies the rule for selecting branching variable		VARSEL=

Table 9.3 lists the valid GRAPH_DIRECTION= values for each algorithm option in the SOLVE WITH NETWORK statement.

Table 9.3: Supported Graph Directions by Algorithm

	Direction
Algorithm	Undirected	Directed
BICONCOMP	x
CLIQUE	x
CONCOMP	x	x
CYCLE	x	x
LINEAR_ASSIGNMENT		x
MINCOSTFLOW		x
MINCUT	x
MINSPANTREE	x
SHORTPATH	x	x
TRANSITIVE_CLOSURE	x	x
TSP	x

Table 9.4 indicates, for each algorithm option in the SOLVE WITH NETWORK statement, which output options you can specify, and what their types can be. The types vary depending on whether nodes are of type STRING or NUMBER.

Table 9.4: Output Suboptions and Types by Algorithm

Algorithm Option
	OUT= Suboption	OPTMODEL Type
BICONCOMP
	ARTPOINTS=	SET<STRING> or SET<NUMBER>
	BICONCOMP=	NUMBER indexed over links (<NUMBER,NUMBER> or <STRING,STRING>)
CLIQUE
	CLIQUES=	SET<NUMBER,NUMBER> or SET<NUMBER,STRING>
CONCOMP
	CONCOMP=	NUMBER indexed over nodes (NUMBER or STRING)
CYCLE
	CYCLES=	SET<NUMBER,NUMBER,NUMBER> or SET<NUMBER,NUMBER,STRING>
LINEAR_ASSIGNMENT
	ASSIGNMENTS=	SET<NUMBER,NUMBER> or SET<STRING,STRING>
MINCOSTFLOW
	FLOW=	NUMBER indexed over links (<NUMBER,NUMBER> or <STRING,STRING>)
MINCUT
	CUTSETS=	SET<NUMBER,NUMBER,NUMBER> or SET<NUMBER,STRING,STRING>
	PARTITIONS=	SET<NUMBER,NUMBER> or SET<NUMBER,STRING>
MINSPANTREE
	FOREST=	SET<NUMBER,NUMBER> or SET<STRING,STRING>
SHORTPATH
	SPPATHS=	SET<NUMBER,NUMBER,NUMBER,NUMBER,NUMBER> or SET<STRING,STRING,NUMBER,STRING,STRING>
	SPWEIGHTS=	NUMBER indexed over sink and source node pairs (<NUMBER,NUMBER> or <STRING,STRING>)
TRANSITIVE_CLOSURE
	CLOSURE=	SET<NUMBER,NUMBER> or SET<STRING,STRING>
TSP
	ORDER=	NUMBER indexed over nodes (NUMBER or STRING)
	TOUR=	SET<NUMBER,NUMBER> or SET<STRING,STRING>