joehuchette
commented
3 years ago Yes, it's supposed to happen. By default, we will evaluate the user-provided function at the center of each cell in order to select the orientation of the triangulation in that cell (https://github.com/joehuchette/PiecewiseLinearOpt.jl/blob/3ee7d49aa92ce86b095b8147b22fad9b95e0e22c/src/types.jl#L71-L79). If this is a problem for you, you can explicitly pass in a different triangulation pattern, e.g.
BivariatePWLFunction(x_brkpts, y_brkpts, nl_func; pattern=:UnionJack)
Hello there, thanks for reading this message. I have a question about the PiecewiseLinearOpt.jl package. I thought when defining the breakpoints for the piecewise approximation, my non-linear function (nl_func) would be evaluated only in the prespecified points for the later linear interpolation. Coding some examples, a realized that it's not much like that. In the code below (Example code), i defined the following breakpoints for the x and y dimensions: -x breakpoints: 0.0, 3.0, 6.0 -y breakpoints: 0.0, 4.0, 8.0 Inside my NL function, i'm printing the inputs received so that i'm able to see whats going on in the backend. On the log messages produced by the model, its possible to see the the NL function is evaluated in points outside the breakpoints defined, like (x, y) = (1.5, 6.0) for example. Is this supposed to happen? Can someone explain that?
Example code:
Packages
using JuMP, Cbc, PiecewiseLinearOpt;
Creating optimization problem
Set optimizer
model=Model(Cbc.Optimizer)
Adding variables to the model
@variable(model, x>=0.0) @variable(model, y>=0.0)
Defining breakpoints for piecewise linear approximations
x_brkpts=[0.0, 3.0, 6.0]; y_brkpts=[0.0, 4.0, 8.0]; pos_x_axis=5.0; pos_y_axis=5.0;
Non-linear constraint
r(x, y; x_pos, y_pos) = (x-x_pos)^2+(y-y_pos)^2
Piecewise approx. for r
r_approx=piecewiselinear(model, x, y, x_brkpts, y_brkpts, (x, y) -> r(x, y, x_pos=pos_x_axis, y_pos=pos_y_axis))
Adding constraints to the model
@constraint(model, 2.0*x+y>=18.0) @constraint(model, r_approx <= 15.0) # NL constraint
Defining objective function
function nl_func(x, y) println("Inputs: X=$x / Y=$y") return y - x^2 end
Piecewiselinear approx. for objective function
nl_func_approx=piecewiselinear(model, x, y, x_brkpts, y_brkpts, (u, v) -> nl_func(u, v))
Adding objective function
@objective(model, Max, nl_func_approx)
Show model
println(model)
Optimizing
optimize!(model)
Results
println("Optimal value: $(objective_value(model))") println("Opt. X: $(value(x))") println("Opt. Y: $(value(y))")