LinearFractional is an extension for JuMP to optimize linear programs with fractional objectives. LinearFractional implements the Charnes-Cooper transformation behind-the-scenes so that the user only needs to specify the problem as any ordinary JuMP problem, but specifying a numerator and denominator instead of a single objective function.
To install the latest tagged version, run the following command from pkg-mode:
] add LinearFractionalThen you can run the built-in unit tests with
] test LinearFractionalto verify that everything is functioning properly on your machine.
This toy example refers to the reference problem in http://www.ams.jhu.edu/~castello/625.414/Handouts/FractionalProg.pdf.
using LinearFractional
using JuMP
using Clp
lfp = LinearFractionalModel(with_optimizer(Clp.Optimizer))
x1 = @variable(lfp, base_name="x1", lower_bound=0)
x2 = @variable(lfp, base_name="x2", lower_bound=0, upper_bound=6)
@constraint(lfp, -x1 + x2 <= 4)
@constraint(lfp, 2x1 + x2 <= 14)
@constraint(lfp, x2 <= 6)
numer = @expression(lfp, -2x1 + x2 + 2)
denom = @expression(lfp, x1 + 3x2 + 4)
set_objective(lfp, JuMP.MOI.MIN_SENSE, numer, denom)
optimize!(lfp)
termination_status(lfp)
objective_value(lfp)
value(x1)
value(x2)