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cycle(+Edges, ++EdgeWeights, -CycleCost, ++Configuration)

A constraint that forces a Hamiltonian cycle in a directed graph
Edges
A list of ic variables
EdgeWeights
A square matrix of integers
CycleCost
The cost of the cycle
Configuration
A list of key:value configuration elements

Description

	Edges is a list of length VertexCount of ic variables, where VertexCount is the number of 
	vertices in the graph. Each variable needs to have a domain which is the subset of 
	[1..VertexCount]. The values in the i-th variable's domain correspond to edges in the 
	graph, so the domain value j of the i-th variable corresponds to an edge (i,j). 

	EdgeWeights is a square matrix (array of arrays) of size VertexCount*VertexCount of nonnegative 
	integers. The value indexed [i,j] corresponds to the cost of the edge (i,j). Values on the diagonal
	([i,i]) are unimportant since the correspond to edges (i,i) which are automatically removed by
	the constraint.

	CycleCost is an ic variable that corresponds to the cost of the cycle. 

	Configuration is a list of key:value pairs that configure the filtering level of the constraint. 
	rc_varfix:yes/no (default is yes), enables or disables the propagation of reduced cost variable 
	fixing constraints. These constraints are based on the solution of the LP relaxation for the cycle. 
	cut_planes:yes/no (default is yes), enables or disables the iterative strengthening of the LP 
	relaxation by generation of cutting planes for the LP model. 
	bound_upd:yes/no (default is yes), enables or disables the tightening of the upper bound on cost 
	by solving a LP relaxation. 
	opt_dir:min/max (default is min), the propagation is optimised for minimisation (min) 
	or maximisation (max) of the CycleCost. 

	The default configuration for the constraint is to use the maximal available propagation 
	and cost tightening. This setting is also used by the cycle/3. 

	The most basic propagation level for cycle is achieved by setting
	Configuration=[rc_varfix:no,cut_planes:no,bound_upd:no].

Modes and Determinism

Fail Conditions

It is impossible to find any Hamiltonian cycle in the graph

Exceptions

(1) general error
Wrong edge weigh matrix size.
(1) general error
Wrong edge list length.
(6) out of range
Wrong edge domain values.
(1) general error
Wrong weight value.
(8) bad argument list
Unknown options

See Also

cycle / 3