Check how to deal with equalities when computing Benders cuts right-hand side

[najaverzat]

In Benders _compute_cut_rhs_contrib we separate the contribution of classic linear inequalities from the contribution of the bounding constraints. The bounding contraints costs are given by dual_sol and their contribution depends on the sense of the bounding (UPPER, LOWER and LOWER_AND_UPPER).

In the case of LOWER_AND_UPPER (i.e. equality) we have to check how to compute the good contribution. For the moment, given bounded variable constr: value <= x <= value, the contribution equals value*cost(constr).

[guimarqu]

Equality is treated as two constraints: 'x <= value' & 'x >= value', and only one of them will be active. Consequently, the case LOWER_AND_UPPER should not happen. I think we should remove it from the ActiveBound.

Remove from the enum:

Coluna.jl/src/MathProg/solutions.jl

Line 129 in 3420cd4

@enum ActiveBound LOWER UPPER LOWER_AND_UPPER

Remove from the condition in Benders:

Coluna.jl/src/Algorithm/benders/default.jl

Line 290 in 3420cd4

if active_bound == MathProg.LOWER || active_bound == MathProg.LOWER_AND_UPPER

Remove these 3 lines because they are not correct (see counterexample below but it can break some unit tests):

Coluna.jl/src/MathProg/MOIinterface.jl

Lines 326 to 328 in 3420cd4

	push!(varids, var_id)
	push!(varvals, sense * cost)
	push!(activebounds, LOWER_AND_UPPER)

Remove from the test:

Coluna.jl/test/unit/Benders/benders_cuts.jl

Line 169 in 3420cd4

Coluna.MathProg.VarId[vids["y1"], vids["x1"], vids["y2"], vids["x2"]], Float64[10.0, 5.0, 2.0, 3.0], Coluna.MathProg.ActiveBound[MathProg.LOWER, MathProg.UPPER, MathProg.UPPER, MathProg.LOWER_AND_UPPER], ## x2 fixed to 1.0

counterexample:

MinSense + 1.0 y3 + 2.0 y1 + 1.0 y2 + 1.0 art1 + 1.0 art2 + 1.0 art3  
sp_c1 : + 1.0 y3 + 1.0 y1 + 2.0 y2 + 1.0 art1  >= 2.0 (BendSpPureConstrConstraintu1 | true)
sp_c2 : + 5.0 y1 - 1.0 y2 + 1.0 art2  >= 5.0 (BendSpTechnologicalConstrConstraintu2 | true)
sp_c3 : - 2.0 y3 + 1.0 art3  >= 3.0 (BendSpTechnologicalConstrConstraintu3 | true)
0.0 <= y3 <= 2.0 (Continuous | BendSpSepVar | true)
1.0 <= y1 <= 1.0 (Continuous | BendSpSepVar | true)
0.0 <= y2 <= 2.0 (Continuous | BendSpSepVar | true)
0.0 <= art1 <= Inf (Continuous | BendSpSecondStageArtVar | true)
0.0 <= art2 <= Inf (Continuous | BendSpSecondStageArtVar | true)
0.0 <= art3 <= Inf (Continuous | BendSpSecondStageArtVar | true)

Solutions:

primal = Primal solution
| y1 = 1.0
| y2 = 0.5
| art2 = 0.5
| art3 = 3.0
└ value = 6.00 

dual = Dual solution
| sp_c1 = 1.0
| sp_c2 = 1.0
| sp_c3 = 1.0
| y1 = -4.0 (UPPER)
| y3 = 2.0 (LOWER)
└ value = 6.00