Failure with SOS1 reformulation

[frapac]

The SOS1 reformulation fails on this LPCC example:

using JuMP
using ComplementOpt
using HiGHS

model = Model()
@variable(model, 0 <= z1, start=0.0)
@variable(model, 0 <= z2, start=1.0)
@variable(model, z3, start=0.0)
# z3 = 1.0
@objective(model, Min, z1 + z2 - z3)
@constraint(model, -4 * z1 + z3 <= 0)
@constraint(model, -4 * z2 + z3 <= 0)
@constraint(model, comp, [z1, z2] ∈ MOI.Complements(2))

JuMP.set_optimizer(model, () -> ComplementOpt.Optimizer(
        MOI.Bridges.full_bridge_optimizer(HiGHS.Optimizer(), Float64)
    )
)
JuMP.optimize!(model)

Returning an error in final_touch:

ERROR: LoadError: MathOptInterface.Bridges.BridgeRequiresFiniteDomainError{MathOptInterface.Bridges.Constraint.SOS1ToMILPBridge{Float64, MathOptInterface.VectorOfVariables}, MathOptInterface.VariableIndex}:                                 
                                                                                                                                                                                                                                               
There was an error reformulating your model into a form supported by the                                                                                                                                                                       
solver because one of the bridges requires that all variables have a                                                                                                                                                                           
finite domain.  

The error remains if I add bound on z1 and z2. I am wondering what would be the correct usage for the SOS1 bridge? Should we allow the user to pass the big-M constraint manually?

[blegat]

What would you expect the MILP formulation to be ?

[frapac]

Good question. I don't see any good solution if the users do not provide the big-M constant by themselves.

I think we can use HiGHS in our tests, so we can test the SOS1 bridge in our pipeline. I guess that most people interested into the SOS1 formulation will use a solver that supports SOS1 for that purpose.

I would be good to test MathOptComplements with Gurobi, just to see how easy is it to solve a MPCC with the SOS1 formulation. I can take care of this.

[blegat]

One solution would be to add a bridge attribute for SOS1ToMILPBridge that is the big-M constant but we might as well ask the user to add this as bounds to z1 and z2 ?

[frapac]

I am in favor of using the easiest solution. Specifying the bounds in z1 and z2 is fine by me, but what if the bridges add new variables with only a lower bound?

[blegat]

At the moment, the bridge just change the set, it's just the same variables. You can see that func is passed as-is:

MathOptComplements.jl/src/Bridges/to_sos1_bridge.jl

Lines 33 to 37 in fa2a4f6

	func::MOI.VectorOfVariables,
	set::ComplementsWithSetType{MOI.Nonnegatives},
	) where {T}
	@assert set.dimension == 2
	ci = MOI.add_constraint(model, func, MOI.SOS1(T[1.0, 2.0]))

[frapac]

MWE with big-M introduced manually:

using JuMP
using MathOptComplements
using HiGHS

big_M = 1e3

model = Model()
@variable(model, 0 <= z1 <= big_M, start=0.0)
@variable(model, 0 <= z2 <= big_M, start=1.0)
@variable(model, z3, start=0.0)
# z3 = 1.0
@objective(model, Min, z1 + z2 - z3)
@constraint(model, -4 * z1 + z3 <= 0)
@constraint(model, -4 * z2 + z3 <= 0)
@constraint(model, comp, [z1, z2] ∈ MOI.Complements(2))

JuMP.set_optimizer(model, () -> MathOptComplements.Optimizer(
        MOI.Bridges.full_bridge_optimizer(HiGHS.Optimizer(), Float64)
    )
)
JuMP.optimize!(model)