Hyperedges

A hyperedge typically couples variables belonging to different nodes via equality or inequality constraints (or both). Each hyperedge is defined using a dedicated code block. This code block must be started by either the #HYPEREDGE keyword or the :#LINK keyword (the two can be used interchangeably). A hyperedge must have a unique \(\texttt{<identifier>}\) and no two hyperedges or hyperedge and node may have the same identifier. In addition, a hyperedge may have its own parameters and constraints. Hence, valid hyperedge blocks have the following structure:

#HYPEREDGE <identifier 1>
#PARAMETERS
// parameter definitions
#CONSTRAINTS
// constraint definitions

#LINK <identifier 2>
#PARAMETERS
// parameter definitions
#CONSTRAINTS
// constraint definitions

Parameters and constraints are further described below.

Parameters

Parameters defined in a #HYPEREDGE block follow the exact same rules as the ones defined in #NODE blocks.

Constraints

While affine constraints involving all variables declared in a #NODE block can be defined in the same block, constraints defined in #HYPEREDGE blocks couple \(\texttt{external}\) variables associated with any subset of nodes. The syntax for defining constraints is otherwise the same as the one used in #NODE blocks:

#CONSTRAINTS
 <expression> == <expression> <expansion range>;
 <expression> <= <expression> <expansion range>;
 <expression> >= <expression> <expansion range>;

Similarly to the constraints defined in nodes, hyperedges can also be named by adding an identifier with colon defore the constraint, as follows,

\[\texttt{<constraint identifier>: <constraint>;}\]

Given these syntax rules, the following is an example including valid hyperedge blocks (and associated #NODE blocks):

#TIMEHORIZON
// time horizon definition

#NODE node1
#VARIABLES
external : x;
external : inflow[T];
// further node content

#NODE node2
#VARIABLES
external : y;
external : outflow[T];
// further node content

#HYPEREDGE hyperedge1
#CONSTRAINTS
node1.inflow[t] == node2.outflow[t];

#NODE node3
#VARIABLES
external : z;
// further node content

#LINK hyperedge2
#PARAMETERS
weight = {1/3,2/3};
#CONSTRAINTS
node1.x <= weight[0]*node2.y + weight[1]*node3.z;
node2.y <= node3.z;