addVariables#

addVariables(problem, indexset, name='x', lb=0, ub=1e+20, threshold=1, vartype=0)[source]#

Create and add multiple variables (corresponding to an index-set) to the xpress problem.

This function extends xpress’s problem.addVariables method by wrapping it and returning VarDict1D/VarDictND data structures - that can efficiently sum subsets of variables with a user-friendly syntax based on wildcard patterns.

Parameters:
problemxpress.problem

Xpress problem.

indexsetIndexSet1D or IndexSetND

Index-set for defining the variables. The name/names attribute of IndexSet1D/IndexSetND will be set as the key_name/key_names attribute of VarDict1D/VarDictND.

namestr, optional

Variable name, by default 'x'. It will also be used as the value_name attribute of VarDict1D/VarDictND.

lbint or float or dict or ParamDict, optional

Lower bound, in one of the following forms:

  • A number - if all variables share the same lower bound.

  • A dict/ParamDict - with keys following the same structute as the index-set elements and values representing the lower bound; will fallback to the default for index-set elements not found in dict/ParamDict keys.

Default is 0.0.

ubint or float or dict or ParamDict, optional

Upper bound, in one of the following forms:

  • A number - if all variables share the same upper bound.

  • A dict/ParamDict - with keys following the same structute as the index-set elements and values representing the upper bound; will fallback to the default for index-set elements not found in dict/ParamDict keys.

Default is 1.0 for binary variable type and infinity for other types.

thresholdint or float or dict or ParamDict, optional

Threshold, in one of the following forms:

  • A number - if all variables share the same threshold.

  • A dict/ParamDict - with keys following the same structute as the index-set elements and values representing the threshold; will fallback to the default for index-set elements not found in dict/ParamDict keys.

Only applies to semi-continuous, semi-integer, and partially integer variables; it must be between its lower and its upper bound. Default is 1.

vartypeint

Variable type, in one of the following forms:

  • xpress.continuous

  • xpress.binary

  • xpress.integer

  • xpress.semicontinuous

  • xpress.semiinteger

  • xpress.partiallyinteger

Default is xpress.continuous.

Returns:
VarDict1D or VarDictND
Raises:
ValueError

If the index-set is empty.

Examples

Create xpress problem:

>>> import xpress as xp
>>> import warnings
>>> warnings.filterwarnings('ignore', category=xp.LicenseWarning)

>>> prob = xp.problem()

Create index-sets:

>>> nodes = IndexSet1D(['A', 'B', 'C'], name='node')
>>> arcs = IndexSetND([('A', 'B'), ('B', 'C'), ('C', 'B')], names=['ori', 'des'])

Add variables:

>>> node_select = addVariables(prob, nodes, name='select', vartype=xp.binary)
>>> node_select
VarDict1D: node -> select
{'A': select(A), 'B': select(B), 'C': select(C)}

>>> arc_flow = addVariables(prob, arcs, name='flow', ub=10, vartype=xp.continuous)
>>> arc_flow
VarDictND: (ori, des) -> flow
{('A', 'B'): flow(('A', 'B')),
 ('B', 'C'): flow(('B', 'C')),
 ('C', 'B'): flow(('C', 'B'))}
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