UnitJuMP

This is an experimental and proof-of-concept package that allows JuMP to be combined with units using Unitful.

Currently, the package only supports a limited set of modelling with linear and quadratic constraints using the @variable and @constraint macros.

Variables

Variables are defined with units using the @variable macro by adding the unit as a separate argument:

@variable(m, speed, u"m/s")
@variable(m, length, u"cm")

Constraints

Constraints are automatically created with units using the @constraint macro if any of the involved parameters or variables have units. It is possible to specify the unit used for the constraint by adding it is an extra argument (e.g., for consistent scaling):

period = 1.4u"s"
max_length = 1200u"ft"
@constraint(m, period * speed + length  <= max_length, u"km")

If no unit is provided, the unit of the first term is used. Note that it may cause problems if using numerical parameters with units directly in the macro expression. Instead, create a separate parameter to hold the value.

Expressions and objective

Both the @expression and @objective macros will handle variables with units, but it is not possible to specify units as part of the macro arguments. If one wants to use a different unit for the objective, the best approach is to create the objective as a separate expression and then convert it to the required unit before setting the objective:

obj = Unitful.uconvert(u"km/hr", @expression(m, x + y))
@objective(m, Max, obj)

As an alternative the objective can also be built incrementally as a UnitExpression of a given unit:

obj = UnitExpression(AffExpr(), u"km/hr")
obj += x + y
@objective(m, Max, obj)

Usage

using UnitJuMP, HiGHS
m = Model(HiGHS.Optimizer)
@variable(m, x >= 0, u"m/s")
@variable(m, y >= 0, u"ft/s")
max_speed = 60u"km/hr"
@constraint(m, x + y <= max_speed, u"km/hr")
@constraint(m, x <= 0.5y)
obj = @objective(m, Max, x + y)
optimize!(m)
println("x = $(value(x))  y = $(value(y))")
println("objective value = $(value(obj))")

#output x = 5.555555555555556 m s^-1  y = 36.45377661125693 ft s^-1
#       objective value = 16.666666666666668 m s^-1